ann-1.1.2+doc/0000755000175000017500000000000011644667625013733 5ustar sylvestresylvestreann-1.1.2+doc/lib/0000755000175000017500000000000011330212441014447 5ustar sylvestresylvestreann-1.1.2+doc/sample/0000755000175000017500000000000011330212441015162 5ustar sylvestresylvestreann-1.1.2+doc/sample/Makefile0000644000175000017500000000624011330212441016624 0ustar sylvestresylvestre#----------------------------------------------------------------------------- # Makefile for the sample program # # ANN: Approximate Nearest Neighbors # Version: 1.1.1 08/04/06 #----------------------------------------------------------------------------- # Copyright (c) 1997-2005 University of Maryland and Sunil Arya and # David Mount. All Rights Reserved. # # This software and related documentation is part of the Approximate # Nearest Neighbor Library (ANN). This software is provided under # the provisions of the Lesser GNU Public License (LGPL). See the # file ../ReadMe.txt for further information. # # The University of Maryland (U.M.) and the authors make no # representations about the suitability or fitness of this software for # any purpose. It is provided "as is" without express or implied # warranty. #----------------------------------------------------------------------------- # Revision 0.1 03/04/98 # Initial release # Revision 1.1.1 08/04/06 # Added copyright/license #----------------------------------------------------------------------------- # Note: For full performance measurements, it is assumed that the library # and this program have both been compiled with the -DPERF flag. See the # Makefile in the ANN base directory for this flag. #----------------------------------------------------------------------------- #----------------------------------------------------------------------------- # Basic definitions # BASEDIR where include, src, lib, ... are # INCDIR include directory # LIBDIR library directory # BINDIR bin directory # LDFLAGS loader flags # ANNLIBS libraries #----------------------------------------------------------------------------- BASEDIR = .. INCDIR = $(BASEDIR)/include LIBDIR = $(BASEDIR)/lib BINDIR = $(BASEDIR)/bin LDFLAGS = -L$(LIBDIR) ANNLIBS = -lANN -lm #----------------------------------------------------------------------------- # Some more definitions # ANNSAMP name of sample program #----------------------------------------------------------------------------- ANNSAMP = ann_sample SAMPSOURCES = ann_sample.cpp SAMPOBJECTS = $(SAMPSOURCES:.cpp=.o) #----------------------------------------------------------------------------- # Make the program #----------------------------------------------------------------------------- default: @echo "Specify a target configuration" targets: $(BINDIR)/$(ANNSAMP) $(BINDIR)/$(ANNSAMP): $(SAMPOBJECTS) $(LIBDIR)/$(ANNLIB) $(C++) $(SAMPOBJECTS) -o $(ANNSAMP) $(LDFLAGS) $(ANNLIBS) mv $(ANNSAMP) $(BINDIR) #----------------------------------------------------------------------------- # configuration definitions #----------------------------------------------------------------------------- include ../Make-config #----------------------------------------------------------------------------- # Objects #----------------------------------------------------------------------------- ann_sample.o: ann_sample.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) ann_sample.cpp #----------------------------------------------------------------------------- # Cleaning #----------------------------------------------------------------------------- clean: -rm -f *.o *.out core realclean: clean ann-1.1.2+doc/sample/data.pts0000644000175000017500000000057111330212441016626 0ustar sylvestresylvestre-0.297462 0.176102 0.565538 -0.361496 0.909313 -0.182785 0.920712 0.478408 0.167682 0.0499836 0.305223 -0.0805835 0.114973 0.882453 0.742916 0.16376 0.0724605 -0.826775 0.690960 -0.559284 0.188485 -0.643934 0.749427 -0.942415 -0.970662 -0.223466 0.916110 0.879597 0.927417 -0.382593 -0.711327 0.278713 -0.519172 0.986146 0.135338 0.924588 -0.0837537 0.61687 0.0520465 0.896306 ann-1.1.2+doc/sample/sample.save0000644000175000017500000000216111330212441017323 0ustar sylvestresylvestreData Points: (-0.297462, 0.176102) (0.565538, -0.361496) (0.909313, -0.182785) (0.920712, 0.478408) (0.167682, 0.0499836) (0.305223, -0.0805835) (0.114973, 0.882453) (0.742916, 0.16376) (0.0724605, -0.826775) (0.69096, -0.559284) (0.188485, -0.643934) (0.749427, -0.942415) (-0.970662, -0.223466) (0.91611, 0.879597) (0.927417, -0.382593) (-0.711327, 0.278713) (-0.519172, 0.986146) (0.135338, 0.924588) (-0.0837537, 0.61687) (0.0520465, 0.896306) Query point: (0.0902484, -0.207129) NN: Index Distance 0 5 0.249455 Query point: (-0.419567, 0.485743) NN: Index Distance 0 0 0.332847 Query point: (0.826225, -0.30962) NN: Index Distance 0 14 0.124759 Query point: (0.694758, 0.987088) NN: Index Distance 0 13 0.246071 Query point: (-0.410807, -0.465182) NN: Index Distance 0 8 0.60357 Query point: (-0.836501, 0.490184) NN: Index Distance 0 15 0.245741 Query point: (0.588289, 0.656408) NN: Index Distance 0 3 0.37708 Query point: (0.325807, 0.38721) NN: Index Distance 0 4 0.372458 Query point: (-0.532226, -0.727036) NN: Index Distance 0 8 0.612857 Query point: (-0.52506, -0.853508) NN: Index Distance 0 8 0.598118 ann-1.1.2+doc/sample/query.pts0000644000175000017500000000027411330212441017062 0ustar sylvestresylvestre0.0902484 -0.207129 -0.419567 0.485743 0.826225 -0.30962 0.694758 0.987088 -0.410807 -0.465182 -0.836501 0.490184 0.588289 0.656408 0.325807 0.38721 -0.532226 -0.727036 -0.52506 -0.853508 ann-1.1.2+doc/sample/ann_sample.cpp0000644000175000017500000001512511330212441020007 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: ann_sample.cpp // Programmer: Sunil Arya and David Mount // Last modified: 03/04/98 (Release 0.1) // Description: Sample program for ANN //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- #include // C standard library #include // C I/O (for sscanf) #include // string manipulation #include // file I/O #include // ANN declarations using namespace std; // make std:: accessible //---------------------------------------------------------------------- // ann_sample // // This is a simple sample program for the ANN library. After compiling, // it can be run as follows. // // ann_sample [-d dim] [-max mpts] [-nn k] [-e eps] [-df data] [-qf query] // // where // dim is the dimension of the space (default = 2) // mpts maximum number of data points (default = 1000) // k number of nearest neighbors per query (default 1) // eps is the error bound (default = 0.0) // data file containing data points // query file containing query points // // Results are sent to the standard output. //---------------------------------------------------------------------- //---------------------------------------------------------------------- // Parameters that are set in getArgs() //---------------------------------------------------------------------- void getArgs(int argc, char **argv); // get command-line arguments int k = 1; // number of nearest neighbors int dim = 2; // dimension double eps = 0; // error bound int maxPts = 1000; // maximum number of data points istream* dataIn = NULL; // input for data points istream* queryIn = NULL; // input for query points bool readPt(istream &in, ANNpoint p) // read point (false on EOF) { for (int i = 0; i < dim; i++) { if(!(in >> p[i])) return false; } return true; } void printPt(ostream &out, ANNpoint p) // print point { out << "(" << p[0]; for (int i = 1; i < dim; i++) { out << ", " << p[i]; } out << ")\n"; } int main(int argc, char **argv) { int nPts; // actual number of data points ANNpointArray dataPts; // data points ANNpoint queryPt; // query point ANNidxArray nnIdx; // near neighbor indices ANNdistArray dists; // near neighbor distances ANNkd_tree* kdTree; // search structure getArgs(argc, argv); // read command-line arguments queryPt = annAllocPt(dim); // allocate query point dataPts = annAllocPts(maxPts, dim); // allocate data points nnIdx = new ANNidx[k]; // allocate near neigh indices dists = new ANNdist[k]; // allocate near neighbor dists nPts = 0; // read data points cout << "Data Points:\n"; while (nPts < maxPts && readPt(*dataIn, dataPts[nPts])) { printPt(cout, dataPts[nPts]); nPts++; } kdTree = new ANNkd_tree( // build search structure dataPts, // the data points nPts, // number of points dim); // dimension of space while (readPt(*queryIn, queryPt)) { // read query points cout << "Query point: "; // echo query point printPt(cout, queryPt); kdTree->annkSearch( // search queryPt, // query point k, // number of near neighbors nnIdx, // nearest neighbors (returned) dists, // distance (returned) eps); // error bound cout << "\tNN:\tIndex\tDistance\n"; for (int i = 0; i < k; i++) { // print summary dists[i] = sqrt(dists[i]); // unsquare distance cout << "\t" << i << "\t" << nnIdx[i] << "\t" << dists[i] << "\n"; } } delete [] nnIdx; // clean things up delete [] dists; delete kdTree; annClose(); // done with ANN return EXIT_SUCCESS; } //---------------------------------------------------------------------- // getArgs - get command line arguments //---------------------------------------------------------------------- void getArgs(int argc, char **argv) { static ifstream dataStream; // data file stream static ifstream queryStream; // query file stream if (argc <= 1) { // no arguments cerr << "Usage:\n\n" << " ann_sample [-d dim] [-max m] [-nn k] [-e eps] [-df data]" " [-qf query]\n\n" << " where:\n" << " dim dimension of the space (default = 2)\n" << " m maximum number of data points (default = 1000)\n" << " k number of nearest neighbors per query (default 1)\n" << " eps the error bound (default = 0.0)\n" << " data name of file containing data points\n" << " query name of file containing query points\n\n" << " Results are sent to the standard output.\n" << "\n" << " To run this demo use:\n" << " ann_sample -df data.pts -qf query.pts\n"; exit(0); } int i = 1; while (i < argc) { // read arguments if (!strcmp(argv[i], "-d")) { // -d option dim = atoi(argv[++i]); // get dimension to dump } else if (!strcmp(argv[i], "-max")) { // -max option maxPts = atoi(argv[++i]); // get max number of points } else if (!strcmp(argv[i], "-nn")) { // -nn option k = atoi(argv[++i]); // get number of near neighbors } else if (!strcmp(argv[i], "-e")) { // -e option sscanf(argv[++i], "%lf", &eps); // get error bound } else if (!strcmp(argv[i], "-df")) { // -df option dataStream.open(argv[++i], ios::in);// open data file if (!dataStream) { cerr << "Cannot open data file\n"; exit(1); } dataIn = &dataStream; // make this the data stream } else if (!strcmp(argv[i], "-qf")) { // -qf option queryStream.open(argv[++i], ios::in);// open query file if (!queryStream) { cerr << "Cannot open query file\n"; exit(1); } queryIn = &queryStream; // make this query stream } else { // illegal syntax cerr << "Unrecognized option.\n"; exit(1); } i++; } if (dataIn == NULL || queryIn == NULL) { cerr << "-df and -qf options must be specified\n"; exit(1); } } ann-1.1.2+doc/src/0000755000175000017500000000000011330212441014470 5ustar sylvestresylvestreann-1.1.2+doc/src/kd_fix_rad_search.h0000644000175000017500000000340611330212441020263 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_fix_rad_search.h // Programmer: Sunil Arya and David Mount // Description: Standard kd-tree fixed-radius kNN search // Last modified: 05/03/05 (Version 1.1) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 1.1 05/03/05 // Initial release //---------------------------------------------------------------------- #ifndef ANN_kd_fix_rad_search_H #define ANN_kd_fix_rad_search_H #include "kd_tree.h" // kd-tree declarations #include "kd_util.h" // kd-tree utilities #include "pr_queue_k.h" // k-element priority queue #include // performance evaluation //---------------------------------------------------------------------- // Global variables // These are active for the life of each call to // annRangeSearch(). They are set to save the number of // variables that need to be passed among the various search // procedures. //---------------------------------------------------------------------- extern ANNpoint ANNkdFRQ; // query point (static copy) #endif ann-1.1.2+doc/src/kd_fix_rad_search.cpp0000644000175000017500000001624111330212441020617 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_fix_rad_search.cpp // Programmer: Sunil Arya and David Mount // Description: Standard kd-tree fixed-radius kNN search // Last modified: 05/03/05 (Version 1.1) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 1.1 05/03/05 // Initial release //---------------------------------------------------------------------- #include "kd_fix_rad_search.h" // kd fixed-radius search decls //---------------------------------------------------------------------- // Approximate fixed-radius k nearest neighbor search // The squared radius is provided, and this procedure finds the // k nearest neighbors within the radius, and returns the total // number of points lying within the radius. // // The method used for searching the kd-tree is a variation of the // nearest neighbor search used in kd_search.cpp, except that the // radius of the search ball is known. We refer the reader to that // file for the explanation of the recursive search procedure. //---------------------------------------------------------------------- //---------------------------------------------------------------------- // To keep argument lists short, a number of global variables // are maintained which are common to all the recursive calls. // These are given below. //---------------------------------------------------------------------- int ANNkdFRDim; // dimension of space ANNpoint ANNkdFRQ; // query point ANNdist ANNkdFRSqRad; // squared radius search bound double ANNkdFRMaxErr; // max tolerable squared error ANNpointArray ANNkdFRPts; // the points ANNmin_k* ANNkdFRPointMK; // set of k closest points int ANNkdFRPtsVisited; // total points visited int ANNkdFRPtsInRange; // number of points in the range //---------------------------------------------------------------------- // annkFRSearch - fixed radius search for k nearest neighbors //---------------------------------------------------------------------- int ANNkd_tree::annkFRSearch( ANNpoint q, // the query point ANNdist sqRad, // squared radius search bound int k, // number of near neighbors to return ANNidxArray nn_idx, // nearest neighbor indices (returned) ANNdistArray dd, // the approximate nearest neighbor double eps) // the error bound { ANNkdFRDim = dim; // copy arguments to static equivs ANNkdFRQ = q; ANNkdFRSqRad = sqRad; ANNkdFRPts = pts; ANNkdFRPtsVisited = 0; // initialize count of points visited ANNkdFRPtsInRange = 0; // ...and points in the range ANNkdFRMaxErr = ANN_POW(1.0 + eps); ANN_FLOP(2) // increment floating op count ANNkdFRPointMK = new ANNmin_k(k); // create set for closest k points // search starting at the root root->ann_FR_search(annBoxDistance(q, bnd_box_lo, bnd_box_hi, dim)); for (int i = 0; i < k; i++) { // extract the k-th closest points if (dd != NULL) dd[i] = ANNkdFRPointMK->ith_smallest_key(i); if (nn_idx != NULL) nn_idx[i] = ANNkdFRPointMK->ith_smallest_info(i); } delete ANNkdFRPointMK; // deallocate closest point set return ANNkdFRPtsInRange; // return final point count } //---------------------------------------------------------------------- // kd_split::ann_FR_search - search a splitting node // Note: This routine is similar in structure to the standard kNN // search. It visits the subtree that is closer to the query point // first. For fixed-radius search, there is no benefit in visiting // one subtree before the other, but we maintain the same basic // code structure for the sake of uniformity. //---------------------------------------------------------------------- void ANNkd_split::ann_FR_search(ANNdist box_dist) { // check dist calc term condition if (ANNmaxPtsVisited != 0 && ANNkdFRPtsVisited > ANNmaxPtsVisited) return; // distance to cutting plane ANNcoord cut_diff = ANNkdFRQ[cut_dim] - cut_val; if (cut_diff < 0) { // left of cutting plane child[ANN_LO]->ann_FR_search(box_dist);// visit closer child first ANNcoord box_diff = cd_bnds[ANN_LO] - ANNkdFRQ[cut_dim]; if (box_diff < 0) // within bounds - ignore box_diff = 0; // distance to further box box_dist = (ANNdist) ANN_SUM(box_dist, ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff))); // visit further child if in range if (box_dist * ANNkdFRMaxErr <= ANNkdFRSqRad) child[ANN_HI]->ann_FR_search(box_dist); } else { // right of cutting plane child[ANN_HI]->ann_FR_search(box_dist);// visit closer child first ANNcoord box_diff = ANNkdFRQ[cut_dim] - cd_bnds[ANN_HI]; if (box_diff < 0) // within bounds - ignore box_diff = 0; // distance to further box box_dist = (ANNdist) ANN_SUM(box_dist, ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff))); // visit further child if close enough if (box_dist * ANNkdFRMaxErr <= ANNkdFRSqRad) child[ANN_LO]->ann_FR_search(box_dist); } ANN_FLOP(13) // increment floating ops ANN_SPL(1) // one more splitting node visited } //---------------------------------------------------------------------- // kd_leaf::ann_FR_search - search points in a leaf node // Note: The unreadability of this code is the result of // some fine tuning to replace indexing by pointer operations. //---------------------------------------------------------------------- void ANNkd_leaf::ann_FR_search(ANNdist box_dist) { register ANNdist dist; // distance to data point register ANNcoord* pp; // data coordinate pointer register ANNcoord* qq; // query coordinate pointer register ANNcoord t; register int d; for (int i = 0; i < n_pts; i++) { // check points in bucket pp = ANNkdFRPts[bkt[i]]; // first coord of next data point qq = ANNkdFRQ; // first coord of query point dist = 0; for(d = 0; d < ANNkdFRDim; d++) { ANN_COORD(1) // one more coordinate hit ANN_FLOP(5) // increment floating ops t = *(qq++) - *(pp++); // compute length and adv coordinate // exceeds dist to k-th smallest? if( (dist = ANN_SUM(dist, ANN_POW(t))) > ANNkdFRSqRad) { break; } } if (d >= ANNkdFRDim && // among the k best? (ANN_ALLOW_SELF_MATCH || dist!=0)) { // and no self-match problem // add it to the list ANNkdFRPointMK->insert(dist, bkt[i]); ANNkdFRPtsInRange++; // increment point count } } ANN_LEAF(1) // one more leaf node visited ANN_PTS(n_pts) // increment points visited ANNkdFRPtsVisited += n_pts; // increment number of points visited } ann-1.1.2+doc/src/kd_tree.h0000644000175000017500000001746211330212441016270 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_tree.h // Programmer: Sunil Arya and David Mount // Description: Declarations for standard kd-tree routines // Last modified: 05/03/05 (Version 1.1) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.1 05/03/05 // Added fixed radius kNN search //---------------------------------------------------------------------- #ifndef ANN_kd_tree_H #define ANN_kd_tree_H #include // all ANN includes using namespace std; // make std:: available //---------------------------------------------------------------------- // Generic kd-tree node // // Nodes in kd-trees are of two types, splitting nodes which contain // splitting information (a splitting hyperplane orthogonal to one // of the coordinate axes) and leaf nodes which contain point // information (an array of points stored in a bucket). This is // handled by making a generic class kd_node, which is essentially an // empty shell, and then deriving the leaf and splitting nodes from // this. //---------------------------------------------------------------------- class ANNkd_node{ // generic kd-tree node (empty shell) public: virtual ~ANNkd_node() {} // virtual distroyer virtual void ann_search(ANNdist) = 0; // tree search virtual void ann_pri_search(ANNdist) = 0; // priority search virtual void ann_FR_search(ANNdist) = 0; // fixed-radius search virtual void getStats( // get tree statistics int dim, // dimension of space ANNkdStats &st, // statistics ANNorthRect &bnd_box) = 0; // bounding box // print node virtual void print(int level, ostream &out) = 0; virtual void dump(ostream &out) = 0; // dump node friend class ANNkd_tree; // allow kd-tree to access us }; //---------------------------------------------------------------------- // kd-splitting function: // kd_splitter is a pointer to a splitting routine for preprocessing. // Different splitting procedures result in different strategies // for building the tree. //---------------------------------------------------------------------- typedef void (*ANNkd_splitter)( // splitting routine for kd-trees ANNpointArray pa, // point array (unaltered) ANNidxArray pidx, // point indices (permuted on return) const ANNorthRect &bnds, // bounding rectangle for cell int n, // number of points int dim, // dimension of space int &cut_dim, // cutting dimension (returned) ANNcoord &cut_val, // cutting value (returned) int &n_lo); // num of points on low side (returned) //---------------------------------------------------------------------- // Leaf kd-tree node // Leaf nodes of the kd-tree store the set of points associated // with this bucket, stored as an array of point indices. These // are indices in the array points, which resides with the // root of the kd-tree. We also store the number of points // that reside in this bucket. //---------------------------------------------------------------------- class ANNkd_leaf: public ANNkd_node // leaf node for kd-tree { int n_pts; // no. points in bucket ANNidxArray bkt; // bucket of points public: ANNkd_leaf( // constructor int n, // number of points ANNidxArray b) // bucket { n_pts = n; // number of points in bucket bkt = b; // the bucket } ~ANNkd_leaf() { } // destructor (none) virtual void getStats( // get tree statistics int dim, // dimension of space ANNkdStats &st, // statistics ANNorthRect &bnd_box); // bounding box virtual void print(int level, ostream &out);// print node virtual void dump(ostream &out); // dump node virtual void ann_search(ANNdist); // standard search virtual void ann_pri_search(ANNdist); // priority search virtual void ann_FR_search(ANNdist); // fixed-radius search }; //---------------------------------------------------------------------- // KD_TRIVIAL is a special pointer to an empty leaf node. Since // some splitting rules generate many (more than 50%) trivial // leaves, we use this one shared node to save space. // // The pointer is initialized to NULL, but whenever a kd-tree is // created, we allocate this node, if it has not already been // allocated. This node is *never* deallocated, so it produces // a small memory leak. //---------------------------------------------------------------------- extern ANNkd_leaf *KD_TRIVIAL; // trivial (empty) leaf node //---------------------------------------------------------------------- // kd-tree splitting node. // Splitting nodes contain a cutting dimension and a cutting value. // These indicate the axis-parellel plane which subdivide the // box for this node. The extent of the bounding box along the // cutting dimension is maintained (this is used to speed up point // to box distance calculations) [we do not store the entire bounding // box since this may be wasteful of space in high dimensions]. // We also store pointers to the 2 children. //---------------------------------------------------------------------- class ANNkd_split : public ANNkd_node // splitting node of a kd-tree { int cut_dim; // dim orthogonal to cutting plane ANNcoord cut_val; // location of cutting plane ANNcoord cd_bnds[2]; // lower and upper bounds of // rectangle along cut_dim ANNkd_ptr child[2]; // left and right children public: ANNkd_split( // constructor int cd, // cutting dimension ANNcoord cv, // cutting value ANNcoord lv, ANNcoord hv, // low and high values ANNkd_ptr lc=NULL, ANNkd_ptr hc=NULL) // children { cut_dim = cd; // cutting dimension cut_val = cv; // cutting value cd_bnds[ANN_LO] = lv; // lower bound for rectangle cd_bnds[ANN_HI] = hv; // upper bound for rectangle child[ANN_LO] = lc; // left child child[ANN_HI] = hc; // right child } ~ANNkd_split() // destructor { if (child[ANN_LO]!= NULL && child[ANN_LO]!= KD_TRIVIAL) delete child[ANN_LO]; if (child[ANN_HI]!= NULL && child[ANN_HI]!= KD_TRIVIAL) delete child[ANN_HI]; } virtual void getStats( // get tree statistics int dim, // dimension of space ANNkdStats &st, // statistics ANNorthRect &bnd_box); // bounding box virtual void print(int level, ostream &out);// print node virtual void dump(ostream &out); // dump node virtual void ann_search(ANNdist); // standard search virtual void ann_pri_search(ANNdist); // priority search virtual void ann_FR_search(ANNdist); // fixed-radius search }; //---------------------------------------------------------------------- // External entry points //---------------------------------------------------------------------- ANNkd_ptr rkd_tree( // recursive construction of kd-tree ANNpointArray pa, // point array (unaltered) ANNidxArray pidx, // point indices to store in subtree int n, // number of points int dim, // dimension of space int bsp, // bucket space ANNorthRect &bnd_box, // bounding box for current node ANNkd_splitter splitter); // splitting routine #endif ann-1.1.2+doc/src/kd_dump.cpp0000644000175000017500000004044111330212441016622 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_dump.cc // Programmer: David Mount // Description: Dump and Load for kd- and bd-trees // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.0 04/01/05 // Moved dump out of kd_tree.cc into this file. // Added kd-tree load constructor. //---------------------------------------------------------------------- // This file contains routines for dumping kd-trees and bd-trees and // reloading them. (It is an abuse of policy to include both kd- and // bd-tree routines in the same file, sorry. There should be no problem // in deleting the bd- versions of the routines if they are not // desired.) //---------------------------------------------------------------------- #include "kd_tree.h" // kd-tree declarations #include "bd_tree.h" // bd-tree declarations using namespace std; // make std:: available //---------------------------------------------------------------------- // Constants //---------------------------------------------------------------------- const int STRING_LEN = 500; // maximum string length const double EPSILON = 1E-5; // small number for float comparison enum ANNtreeType {KD_TREE, BD_TREE}; // tree types (used in loading) //---------------------------------------------------------------------- // Procedure declarations //---------------------------------------------------------------------- static ANNkd_ptr annReadDump( // read dump file istream &in, // input stream ANNtreeType tree_type, // type of tree expected ANNpointArray &the_pts, // new points (if applic) ANNidxArray &the_pidx, // point indices (returned) int &the_dim, // dimension (returned) int &the_n_pts, // number of points (returned) int &the_bkt_size, // bucket size (returned) ANNpoint &the_bnd_box_lo, // low bounding point ANNpoint &the_bnd_box_hi); // high bounding point static ANNkd_ptr annReadTree( // read tree-part of dump file istream &in, // input stream ANNtreeType tree_type, // type of tree expected ANNidxArray the_pidx, // point indices (modified) int &next_idx); // next index (modified) //---------------------------------------------------------------------- // ANN kd- and bd-tree Dump Format // The dump file begins with a header containing the version of // ANN, an optional section containing the points, followed by // a description of the tree. The tree is printed in preorder. // // Format: // #ANN [END_OF_LINE] // points (point coordinates: this is optional) // 0 ... (point indices and coordinates) // 1 ... // ... // tree // ... (lower end of bounding box) // ... (upper end of bounding box) // If the tree is null, then a single line "null" is // output. Otherwise the nodes of the tree are printed // one per line in preorder. Leaves and splitting nodes // have the following formats: // Leaf node: // leaf ... // Splitting nodes: // split // // For bd-trees: // // Shrinking nodes: // shrink // // // ... (repeated n_bnds times) //---------------------------------------------------------------------- void ANNkd_tree::Dump( // dump entire tree ANNbool with_pts, // print points as well? ostream &out) // output stream { out << "#ANN " << ANNversion << "\n"; out.precision(ANNcoordPrec); // use full precision in dumping if (with_pts) { // print point coordinates out << "points " << dim << " " << n_pts << "\n"; for (int i = 0; i < n_pts; i++) { out << i << " "; annPrintPt(pts[i], dim, out); out << "\n"; } } out << "tree " // print tree elements << dim << " " << n_pts << " " << bkt_size << "\n"; annPrintPt(bnd_box_lo, dim, out); // print lower bound out << "\n"; annPrintPt(bnd_box_hi, dim, out); // print upper bound out << "\n"; if (root == NULL) // empty tree? out << "null\n"; else { root->dump(out); // invoke printing at root } out.precision(0); // restore default precision } void ANNkd_split::dump( // dump a splitting node ostream &out) // output stream { out << "split " << cut_dim << " " << cut_val << " "; out << cd_bnds[ANN_LO] << " " << cd_bnds[ANN_HI] << "\n"; child[ANN_LO]->dump(out); // print low child child[ANN_HI]->dump(out); // print high child } void ANNkd_leaf::dump( // dump a leaf node ostream &out) // output stream { if (this == KD_TRIVIAL) { // canonical trivial leaf node out << "leaf 0\n"; // leaf no points } else{ out << "leaf " << n_pts; for (int j = 0; j < n_pts; j++) { out << " " << bkt[j]; } out << "\n"; } } void ANNbd_shrink::dump( // dump a shrinking node ostream &out) // output stream { out << "shrink " << n_bnds << "\n"; for (int j = 0; j < n_bnds; j++) { out << bnds[j].cd << " " << bnds[j].cv << " " << bnds[j].sd << "\n"; } child[ANN_IN]->dump(out); // print in-child child[ANN_OUT]->dump(out); // print out-child } //---------------------------------------------------------------------- // Load kd-tree from dump file // This rebuilds a kd-tree which was dumped to a file. The dump // file contains all the basic tree information according to a // preorder traversal. We assume that the dump file also contains // point data. (This is to guarantee the consistency of the tree.) // If not, then an error is generated. // // Indirectly, this procedure allocates space for points, point // indices, all nodes in the tree, and the bounding box for the // tree. When the tree is destroyed, all but the points are // deallocated. // // This routine calls annReadDump to do all the work. //---------------------------------------------------------------------- ANNkd_tree::ANNkd_tree( // build from dump file istream &in) // input stream for dump file { int the_dim; // local dimension int the_n_pts; // local number of points int the_bkt_size; // local number of points ANNpoint the_bnd_box_lo; // low bounding point ANNpoint the_bnd_box_hi; // high bounding point ANNpointArray the_pts; // point storage ANNidxArray the_pidx; // point index storage ANNkd_ptr the_root; // root of the tree the_root = annReadDump( // read the dump file in, // input stream KD_TREE, // expecting a kd-tree the_pts, // point array (returned) the_pidx, // point indices (returned) the_dim, the_n_pts, the_bkt_size, // basic tree info (returned) the_bnd_box_lo, the_bnd_box_hi); // bounding box info (returned) // create a skeletal tree SkeletonTree(the_n_pts, the_dim, the_bkt_size, the_pts, the_pidx); bnd_box_lo = the_bnd_box_lo; bnd_box_hi = the_bnd_box_hi; root = the_root; // set the root } ANNbd_tree::ANNbd_tree( // build bd-tree from dump file istream &in) : ANNkd_tree() // input stream for dump file { int the_dim; // local dimension int the_n_pts; // local number of points int the_bkt_size; // local number of points ANNpoint the_bnd_box_lo; // low bounding point ANNpoint the_bnd_box_hi; // high bounding point ANNpointArray the_pts; // point storage ANNidxArray the_pidx; // point index storage ANNkd_ptr the_root; // root of the tree the_root = annReadDump( // read the dump file in, // input stream BD_TREE, // expecting a bd-tree the_pts, // point array (returned) the_pidx, // point indices (returned) the_dim, the_n_pts, the_bkt_size, // basic tree info (returned) the_bnd_box_lo, the_bnd_box_hi); // bounding box info (returned) // create a skeletal tree SkeletonTree(the_n_pts, the_dim, the_bkt_size, the_pts, the_pidx); bnd_box_lo = the_bnd_box_lo; bnd_box_hi = the_bnd_box_hi; root = the_root; // set the root } //---------------------------------------------------------------------- // annReadDump - read a dump file // // This procedure reads a dump file, constructs a kd-tree // and returns all the essential information needed to actually // construct the tree. Because this procedure is used for // constructing both kd-trees and bd-trees, the second argument // is used to indicate which type of tree we are expecting. //---------------------------------------------------------------------- static ANNkd_ptr annReadDump( istream &in, // input stream ANNtreeType tree_type, // type of tree expected ANNpointArray &the_pts, // new points (returned) ANNidxArray &the_pidx, // point indices (returned) int &the_dim, // dimension (returned) int &the_n_pts, // number of points (returned) int &the_bkt_size, // bucket size (returned) ANNpoint &the_bnd_box_lo, // low bounding point (ret'd) ANNpoint &the_bnd_box_hi) // high bounding point (ret'd) { int j; char str[STRING_LEN]; // storage for string char version[STRING_LEN]; // ANN version number ANNkd_ptr the_root = NULL; //------------------------------------------------------------------ // Input file header //------------------------------------------------------------------ in >> str; // input header if (strcmp(str, "#ANN") != 0) { // incorrect header annError("Incorrect header for dump file", ANNabort); } in.getline(version, STRING_LEN); // get version (ignore) //------------------------------------------------------------------ // Input the points // An array the_pts is allocated and points are read from // the dump file. //------------------------------------------------------------------ in >> str; // get major heading if (strcmp(str, "points") == 0) { // points section in >> the_dim; // input dimension in >> the_n_pts; // number of points // allocate point storage the_pts = annAllocPts(the_n_pts, the_dim); for (int i = 0; i < the_n_pts; i++) { // input point coordinates ANNidx idx; // point index in >> idx; // input point index if (idx < 0 || idx >= the_n_pts) { annError("Point index is out of range", ANNabort); } for (j = 0; j < the_dim; j++) { in >> the_pts[idx][j]; // read point coordinates } } in >> str; // get next major heading } else { // no points were input annError("Points must be supplied in the dump file", ANNabort); } //------------------------------------------------------------------ // Input the tree // After the basic header information, we invoke annReadTree // to do all the heavy work. We create our own array of // point indices (so we can pass them to annReadTree()) // but we do not deallocate them. They will be deallocated // when the tree is destroyed. //------------------------------------------------------------------ if (strcmp(str, "tree") == 0) { // tree section in >> the_dim; // read dimension in >> the_n_pts; // number of points in >> the_bkt_size; // bucket size the_bnd_box_lo = annAllocPt(the_dim); // allocate bounding box pts the_bnd_box_hi = annAllocPt(the_dim); for (j = 0; j < the_dim; j++) { // read bounding box low in >> the_bnd_box_lo[j]; } for (j = 0; j < the_dim; j++) { // read bounding box low in >> the_bnd_box_hi[j]; } the_pidx = new ANNidx[the_n_pts]; // allocate point index array int next_idx = 0; // number of indices filled // read the tree and indices the_root = annReadTree(in, tree_type, the_pidx, next_idx); if (next_idx != the_n_pts) { // didn't see all the points? annError("Didn't see as many points as expected", ANNwarn); } } else { annError("Illegal dump format. Expecting section heading", ANNabort); } return the_root; } //---------------------------------------------------------------------- // annReadTree - input tree and return pointer // // annReadTree reads in a node of the tree, makes any recursive // calls as needed to input the children of this node (if internal). // It returns a pointer to the node that was created. An array // of point indices is given along with a pointer to the next // available location in the array. As leaves are read, their // point indices are stored here, and the point buckets point // to the first entry in the array. // // Recall that these are the formats. The tree is given in // preorder. // // Leaf node: // leaf ... // Splitting nodes: // split // // For bd-trees: // // Shrinking nodes: // shrink // // // ... (repeated n_bnds times) //---------------------------------------------------------------------- static ANNkd_ptr annReadTree( istream &in, // input stream ANNtreeType tree_type, // type of tree expected ANNidxArray the_pidx, // point indices (modified) int &next_idx) // next index (modified) { char tag[STRING_LEN]; // tag (leaf, split, shrink) int n_pts; // number of points in leaf int cd; // cut dimension ANNcoord cv; // cut value ANNcoord lb; // low bound ANNcoord hb; // high bound int n_bnds; // number of bounding sides int sd; // which side in >> tag; // input node tag if (strcmp(tag, "null") == 0) { // null tree return NULL; } //------------------------------------------------------------------ // Read a leaf //------------------------------------------------------------------ if (strcmp(tag, "leaf") == 0) { // leaf node in >> n_pts; // input number of points int old_idx = next_idx; // save next_idx if (n_pts == 0) { // trivial leaf return KD_TRIVIAL; } else { for (int i = 0; i < n_pts; i++) { // input point indices in >> the_pidx[next_idx++]; // store in array of indices } } return new ANNkd_leaf(n_pts, &the_pidx[old_idx]); } //------------------------------------------------------------------ // Read a splitting node //------------------------------------------------------------------ else if (strcmp(tag, "split") == 0) { // splitting node in >> cd >> cv >> lb >> hb; // read low and high subtrees ANNkd_ptr lc = annReadTree(in, tree_type, the_pidx, next_idx); ANNkd_ptr hc = annReadTree(in, tree_type, the_pidx, next_idx); // create new node and return return new ANNkd_split(cd, cv, lb, hb, lc, hc); } //------------------------------------------------------------------ // Read a shrinking node (bd-tree only) //------------------------------------------------------------------ else if (strcmp(tag, "shrink") == 0) { // shrinking node if (tree_type != BD_TREE) { annError("Shrinking node not allowed in kd-tree", ANNabort); } in >> n_bnds; // number of bounding sides // allocate bounds array ANNorthHSArray bds = new ANNorthHalfSpace[n_bnds]; for (int i = 0; i < n_bnds; i++) { in >> cd >> cv >> sd; // input bounding halfspace // copy to array bds[i] = ANNorthHalfSpace(cd, cv, sd); } // read inner and outer subtrees ANNkd_ptr ic = annReadTree(in, tree_type, the_pidx, next_idx); ANNkd_ptr oc = annReadTree(in, tree_type, the_pidx, next_idx); // create new node and return return new ANNbd_shrink(n_bnds, bds, ic, oc); } else { annError("Illegal node type in dump file", ANNabort); exit(0); // to keep the compiler happy } } ann-1.1.2+doc/src/Makefile0000644000175000017500000000743711330212441016143 0ustar sylvestresylvestre#----------------------------------------------------------------------------- # Makefile for ANN library #---------------------------------------------------------------------- # Copyright (c) 1997-2005 University of Maryland and Sunil Arya and # David Mount. All Rights Reserved. # # This software and related documentation is part of the Approximate # Nearest Neighbor Library (ANN). This software is provided under # the provisions of the Lesser GNU Public License (LGPL). See the # file ../ReadMe.txt for further information. # # The University of Maryland (U.M.) and the authors make no # representations about the suitability or fitness of this software for # any purpose. It is provided "as is" without express or implied # warranty. #---------------------------------------------------------------------- # History: # Revision 0.1 03/04/98 # Initial release # Revision 1.0 04/01/05 # Renamed files from .cc to .cpp for Microsoft Visual C++ # Added kd_dump.cpp # Revision 1.1 05/03/05 # Added kd_fix_rad_search.cpp and bd_fix_rad_search.cpp #---------------------------------------------------------------------- #----------------------------------------------------------------------------- # Some basic definitions: # BASEDIR where include, src, lib, ... are # INCLIB include directory # LIBLIB library directory #----------------------------------------------------------------------------- BASEDIR = .. INCDIR = $(BASEDIR)/include LIBDIR = $(BASEDIR)/lib SOURCES = ANN.cpp brute.cpp kd_tree.cpp kd_util.cpp kd_split.cpp \ kd_dump.cpp kd_search.cpp kd_pr_search.cpp kd_fix_rad_search.cpp \ bd_tree.cpp bd_search.cpp bd_pr_search.cpp bd_fix_rad_search.cpp \ perf.cpp HEADERS = kd_tree.h kd_split.h kd_util.h kd_search.h \ kd_pr_search.h kd_fix_rad_search.h perf.h pr_queue.h pr_queue_k.h OBJECTS = $(SOURCES:.cpp=.o) #----------------------------------------------------------------------------- # Make the library #----------------------------------------------------------------------------- default: @echo "Specify a target configuration" targets: $(LIBDIR)/$(ANNLIB) $(LIBDIR)/$(ANNLIB): $(OBJECTS) $(MAKELIB) $(ANNLIB) $(OBJECTS) $(RANLIB) $(ANNLIB) mv $(ANNLIB) $(LIBDIR) #----------------------------------------------------------------------------- # Make object files #----------------------------------------------------------------------------- ANN.o: ANN.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) ANN.cpp brute.o: brute.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) brute.cpp kd_tree.o: kd_tree.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) kd_tree.cpp kd_util.o: kd_util.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) kd_util.cpp kd_split.o: kd_split.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) kd_split.cpp kd_search.o: kd_search.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) kd_search.cpp kd_pr_search.o: kd_pr_search.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) kd_pr_search.cpp kd_fix_rad_search.o: kd_fix_rad_search.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) kd_fix_rad_search.cpp kd_dump.o: kd_dump.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) kd_dump.cpp bd_tree.o: bd_tree.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) bd_tree.cpp bd_search.o: bd_search.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) bd_search.cpp bd_pr_search.o: bd_pr_search.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) bd_pr_search.cpp bd_fix_rad_search.o: bd_fix_rad_search.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) bd_fix_rad_search.cpp perf.o: perf.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) perf.cpp #----------------------------------------------------------------------------- # Configuration definitions #----------------------------------------------------------------------------- include ../Make-config #----------------------------------------------------------------------------- # Cleaning #----------------------------------------------------------------------------- clean: -rm -f *.o core realclean: clean ann-1.1.2+doc/src/kd_tree.cpp0000644000175000017500000003566611330212441016631 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_tree.cpp // Programmer: Sunil Arya and David Mount // Description: Basic methods for kd-trees. // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.0 04/01/05 // Increased aspect ratio bound (ANN_AR_TOOBIG) from 100 to 1000. // Fixed leaf counts to count trivial leaves. // Added optional pa, pi arguments to Skeleton kd_tree constructor // for use in load constructor. // Added annClose() to eliminate KD_TRIVIAL memory leak. //---------------------------------------------------------------------- #include "kd_tree.h" // kd-tree declarations #include "kd_split.h" // kd-tree splitting rules #include "kd_util.h" // kd-tree utilities #include // performance evaluation //---------------------------------------------------------------------- // Global data // // For some splitting rules, especially with small bucket sizes, // it is possible to generate a large number of empty leaf nodes. // To save storage we allocate a single trivial leaf node which // contains no points. For messy coding reasons it is convenient // to have it reference a trivial point index. // // KD_TRIVIAL is allocated when the first kd-tree is created. It // must *never* deallocated (since it may be shared by more than // one tree). //---------------------------------------------------------------------- static int IDX_TRIVIAL[] = {0}; // trivial point index ANNkd_leaf *KD_TRIVIAL = NULL; // trivial leaf node //---------------------------------------------------------------------- // Printing the kd-tree // These routines print a kd-tree in reverse inorder (high then // root then low). (This is so that if you look at the output // from the right side it appear from left to right in standard // inorder.) When outputting leaves we output only the point // indices rather than the point coordinates. There is an option // to print the point coordinates separately. // // The tree printing routine calls the printing routines on the // individual nodes of the tree, passing in the level or depth // in the tree. The level in the tree is used to print indentation // for readability. //---------------------------------------------------------------------- void ANNkd_split::print( // print splitting node int level, // depth of node in tree ostream &out) // output stream { child[ANN_HI]->print(level+1, out); // print high child out << " "; for (int i = 0; i < level; i++) // print indentation out << ".."; out << "Split cd=" << cut_dim << " cv=" << cut_val; out << " lbnd=" << cd_bnds[ANN_LO]; out << " hbnd=" << cd_bnds[ANN_HI]; out << "\n"; child[ANN_LO]->print(level+1, out); // print low child } void ANNkd_leaf::print( // print leaf node int level, // depth of node in tree ostream &out) // output stream { out << " "; for (int i = 0; i < level; i++) // print indentation out << ".."; if (this == KD_TRIVIAL) { // canonical trivial leaf node out << "Leaf (trivial)\n"; } else{ out << "Leaf n=" << n_pts << " <"; for (int j = 0; j < n_pts; j++) { out << bkt[j]; if (j < n_pts-1) out << ","; } out << ">\n"; } } void ANNkd_tree::Print( // print entire tree ANNbool with_pts, // print points as well? ostream &out) // output stream { out << "ANN Version " << ANNversion << "\n"; if (with_pts) { // print point coordinates out << " Points:\n"; for (int i = 0; i < n_pts; i++) { out << "\t" << i << ": "; annPrintPt(pts[i], dim, out); out << "\n"; } } if (root == NULL) // empty tree? out << " Null tree.\n"; else { root->print(0, out); // invoke printing at root } } //---------------------------------------------------------------------- // kd_tree statistics (for performance evaluation) // This routine compute various statistics information for // a kd-tree. It is used by the implementors for performance // evaluation of the data structure. //---------------------------------------------------------------------- #define MAX(a,b) ((a) > (b) ? (a) : (b)) void ANNkdStats::merge(const ANNkdStats &st) // merge stats from child { n_lf += st.n_lf; n_tl += st.n_tl; n_spl += st.n_spl; n_shr += st.n_shr; depth = MAX(depth, st.depth); sum_ar += st.sum_ar; } //---------------------------------------------------------------------- // Update statistics for nodes //---------------------------------------------------------------------- const double ANN_AR_TOOBIG = 1000; // too big an aspect ratio void ANNkd_leaf::getStats( // get subtree statistics int dim, // dimension of space ANNkdStats &st, // stats (modified) ANNorthRect &bnd_box) // bounding box { st.reset(); st.n_lf = 1; // count this leaf if (this == KD_TRIVIAL) st.n_tl = 1; // count trivial leaf double ar = annAspectRatio(dim, bnd_box); // aspect ratio of leaf // incr sum (ignore outliers) st.sum_ar += float(ar < ANN_AR_TOOBIG ? ar : ANN_AR_TOOBIG); } void ANNkd_split::getStats( // get subtree statistics int dim, // dimension of space ANNkdStats &st, // stats (modified) ANNorthRect &bnd_box) // bounding box { ANNkdStats ch_stats; // stats for children // get stats for low child ANNcoord hv = bnd_box.hi[cut_dim]; // save box bounds bnd_box.hi[cut_dim] = cut_val; // upper bound for low child ch_stats.reset(); // reset child[ANN_LO]->getStats(dim, ch_stats, bnd_box); st.merge(ch_stats); // merge them bnd_box.hi[cut_dim] = hv; // restore bound // get stats for high child ANNcoord lv = bnd_box.lo[cut_dim]; // save box bounds bnd_box.lo[cut_dim] = cut_val; // lower bound for high child ch_stats.reset(); // reset child[ANN_HI]->getStats(dim, ch_stats, bnd_box); st.merge(ch_stats); // merge them bnd_box.lo[cut_dim] = lv; // restore bound st.depth++; // increment depth st.n_spl++; // increment number of splits } //---------------------------------------------------------------------- // getStats // Collects a number of statistics related to kd_tree or // bd_tree. //---------------------------------------------------------------------- void ANNkd_tree::getStats( // get tree statistics ANNkdStats &st) // stats (modified) { st.reset(dim, n_pts, bkt_size); // reset stats // create bounding box ANNorthRect bnd_box(dim, bnd_box_lo, bnd_box_hi); if (root != NULL) { // if nonempty tree root->getStats(dim, st, bnd_box); // get statistics st.avg_ar = st.sum_ar / st.n_lf; // average leaf asp ratio } } //---------------------------------------------------------------------- // kd_tree destructor // The destructor just frees the various elements that were // allocated in the construction process. //---------------------------------------------------------------------- ANNkd_tree::~ANNkd_tree() // tree destructor { if (root != NULL) delete root; if (pidx != NULL) delete [] pidx; if (bnd_box_lo != NULL) annDeallocPt(bnd_box_lo); if (bnd_box_hi != NULL) annDeallocPt(bnd_box_hi); } //---------------------------------------------------------------------- // This is called with all use of ANN is finished. It eliminates the // minor memory leak caused by the allocation of KD_TRIVIAL. //---------------------------------------------------------------------- void annClose() // close use of ANN { if (KD_TRIVIAL != NULL) { delete KD_TRIVIAL; KD_TRIVIAL = NULL; } } //---------------------------------------------------------------------- // kd_tree constructors // There is a skeleton kd-tree constructor which sets up a // trivial empty tree. The last optional argument allows // the routine to be passed a point index array which is // assumed to be of the proper size (n). Otherwise, one is // allocated and initialized to the identity. Warning: In // either case the destructor will deallocate this array. // // As a kludge, we need to allocate KD_TRIVIAL if one has not // already been allocated. (This is because I'm too dumb to // figure out how to cause a pointer to be allocated at load // time.) //---------------------------------------------------------------------- void ANNkd_tree::SkeletonTree( // construct skeleton tree int n, // number of points int dd, // dimension int bs, // bucket size ANNpointArray pa, // point array ANNidxArray pi) // point indices { dim = dd; // initialize basic elements n_pts = n; bkt_size = bs; pts = pa; // initialize points array root = NULL; // no associated tree yet if (pi == NULL) { // point indices provided? pidx = new ANNidx[n]; // no, allocate space for point indices for (int i = 0; i < n; i++) { pidx[i] = i; // initially identity } } else { pidx = pi; // yes, use them } bnd_box_lo = bnd_box_hi = NULL; // bounding box is nonexistent if (KD_TRIVIAL == NULL) // no trivial leaf node yet? KD_TRIVIAL = new ANNkd_leaf(0, IDX_TRIVIAL); // allocate it } ANNkd_tree::ANNkd_tree( // basic constructor int n, // number of points int dd, // dimension int bs) // bucket size { SkeletonTree(n, dd, bs); } // construct skeleton tree //---------------------------------------------------------------------- // rkd_tree - recursive procedure to build a kd-tree // // Builds a kd-tree for points in pa as indexed through the // array pidx[0..n-1] (typically a subarray of the array used in // the top-level call). This routine permutes the array pidx, // but does not alter pa[]. // // The construction is based on a standard algorithm for constructing // the kd-tree (see Friedman, Bentley, and Finkel, ``An algorithm for // finding best matches in logarithmic expected time,'' ACM Transactions // on Mathematical Software, 3(3):209-226, 1977). The procedure // operates by a simple divide-and-conquer strategy, which determines // an appropriate orthogonal cutting plane (see below), and splits // the points. When the number of points falls below the bucket size, // we simply store the points in a leaf node's bucket. // // One of the arguments is a pointer to a splitting routine, // whose prototype is: // // void split( // ANNpointArray pa, // complete point array // ANNidxArray pidx, // point array (permuted on return) // ANNorthRect &bnds, // bounds of current cell // int n, // number of points // int dim, // dimension of space // int &cut_dim, // cutting dimension // ANNcoord &cut_val, // cutting value // int &n_lo) // no. of points on low side of cut // // This procedure selects a cutting dimension and cutting value, // partitions pa about these values, and returns the number of // points on the low side of the cut. //---------------------------------------------------------------------- ANNkd_ptr rkd_tree( // recursive construction of kd-tree ANNpointArray pa, // point array ANNidxArray pidx, // point indices to store in subtree int n, // number of points int dim, // dimension of space int bsp, // bucket space ANNorthRect &bnd_box, // bounding box for current node ANNkd_splitter splitter) // splitting routine { if (n <= bsp) { // n small, make a leaf node if (n == 0) // empty leaf node return KD_TRIVIAL; // return (canonical) empty leaf else // construct the node and return return new ANNkd_leaf(n, pidx); } else { // n large, make a splitting node int cd; // cutting dimension ANNcoord cv; // cutting value int n_lo; // number on low side of cut ANNkd_node *lo, *hi; // low and high children // invoke splitting procedure (*splitter)(pa, pidx, bnd_box, n, dim, cd, cv, n_lo); ANNcoord lv = bnd_box.lo[cd]; // save bounds for cutting dimension ANNcoord hv = bnd_box.hi[cd]; bnd_box.hi[cd] = cv; // modify bounds for left subtree lo = rkd_tree( // build left subtree pa, pidx, n_lo, // ...from pidx[0..n_lo-1] dim, bsp, bnd_box, splitter); bnd_box.hi[cd] = hv; // restore bounds bnd_box.lo[cd] = cv; // modify bounds for right subtree hi = rkd_tree( // build right subtree pa, pidx + n_lo, n-n_lo,// ...from pidx[n_lo..n-1] dim, bsp, bnd_box, splitter); bnd_box.lo[cd] = lv; // restore bounds // create the splitting node ANNkd_split *ptr = new ANNkd_split(cd, cv, lv, hv, lo, hi); return ptr; // return pointer to this node } } //---------------------------------------------------------------------- // kd-tree constructor // This is the main constructor for kd-trees given a set of points. // It first builds a skeleton tree, then computes the bounding box // of the data points, and then invokes rkd_tree() to actually // build the tree, passing it the appropriate splitting routine. //---------------------------------------------------------------------- ANNkd_tree::ANNkd_tree( // construct from point array ANNpointArray pa, // point array (with at least n pts) int n, // number of points int dd, // dimension int bs, // bucket size ANNsplitRule split) // splitting method { SkeletonTree(n, dd, bs); // set up the basic stuff pts = pa; // where the points are if (n == 0) return; // no points--no sweat ANNorthRect bnd_box(dd); // bounding box for points annEnclRect(pa, pidx, n, dd, bnd_box);// construct bounding rectangle // copy to tree structure bnd_box_lo = annCopyPt(dd, bnd_box.lo); bnd_box_hi = annCopyPt(dd, bnd_box.hi); switch (split) { // build by rule case ANN_KD_STD: // standard kd-splitting rule root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, kd_split); break; case ANN_KD_MIDPT: // midpoint split root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, midpt_split); break; case ANN_KD_FAIR: // fair split root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, fair_split); break; case ANN_KD_SUGGEST: // best (in our opinion) case ANN_KD_SL_MIDPT: // sliding midpoint split root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, sl_midpt_split); break; case ANN_KD_SL_FAIR: // sliding fair split root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, sl_fair_split); break; default: annError("Illegal splitting method", ANNabort); } } ann-1.1.2+doc/src/kd_util.cpp0000644000175000017500000003534311330212441016637 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_util.cpp // Programmer: Sunil Arya and David Mount // Description: Common utilities for kd-trees // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release //---------------------------------------------------------------------- #include "kd_util.h" // kd-utility declarations #include // performance evaluation //---------------------------------------------------------------------- // The following routines are utility functions for manipulating // points sets, used in determining splitting planes for kd-tree // construction. //---------------------------------------------------------------------- //---------------------------------------------------------------------- // NOTE: Virtually all point indexing is done through an index (i.e. // permutation) array pidx. Consequently, a reference to the d-th // coordinate of the i-th point is pa[pidx[i]][d]. The macro PA(i,d) // is a shorthand for this. //---------------------------------------------------------------------- // standard 2-d indirect indexing #define PA(i,d) (pa[pidx[(i)]][(d)]) // accessing a single point #define PP(i) (pa[pidx[(i)]]) //---------------------------------------------------------------------- // annAspectRatio // Compute the aspect ratio (ratio of longest to shortest side) // of a rectangle. //---------------------------------------------------------------------- double annAspectRatio( int dim, // dimension const ANNorthRect &bnd_box) // bounding cube { ANNcoord length = bnd_box.hi[0] - bnd_box.lo[0]; ANNcoord min_length = length; // min side length ANNcoord max_length = length; // max side length for (int d = 0; d < dim; d++) { length = bnd_box.hi[d] - bnd_box.lo[d]; if (length < min_length) min_length = length; if (length > max_length) max_length = length; } return max_length/min_length; } //---------------------------------------------------------------------- // annEnclRect, annEnclCube // These utilities compute the smallest rectangle and cube enclosing // a set of points, respectively. //---------------------------------------------------------------------- void annEnclRect( ANNpointArray pa, // point array ANNidxArray pidx, // point indices int n, // number of points int dim, // dimension ANNorthRect &bnds) // bounding cube (returned) { for (int d = 0; d < dim; d++) { // find smallest enclosing rectangle ANNcoord lo_bnd = PA(0,d); // lower bound on dimension d ANNcoord hi_bnd = PA(0,d); // upper bound on dimension d for (int i = 0; i < n; i++) { if (PA(i,d) < lo_bnd) lo_bnd = PA(i,d); else if (PA(i,d) > hi_bnd) hi_bnd = PA(i,d); } bnds.lo[d] = lo_bnd; bnds.hi[d] = hi_bnd; } } void annEnclCube( // compute smallest enclosing cube ANNpointArray pa, // point array ANNidxArray pidx, // point indices int n, // number of points int dim, // dimension ANNorthRect &bnds) // bounding cube (returned) { int d; // compute smallest enclosing rect annEnclRect(pa, pidx, n, dim, bnds); ANNcoord max_len = 0; // max length of any side for (d = 0; d < dim; d++) { // determine max side length ANNcoord len = bnds.hi[d] - bnds.lo[d]; if (len > max_len) { // update max_len if longest max_len = len; } } for (d = 0; d < dim; d++) { // grow sides to match max ANNcoord len = bnds.hi[d] - bnds.lo[d]; ANNcoord half_diff = (max_len - len) / 2; bnds.lo[d] -= half_diff; bnds.hi[d] += half_diff; } } //---------------------------------------------------------------------- // annBoxDistance - utility routine which computes distance from point to // box (Note: most distances to boxes are computed using incremental // distance updates, not this function.) //---------------------------------------------------------------------- ANNdist annBoxDistance( // compute distance from point to box const ANNpoint q, // the point const ANNpoint lo, // low point of box const ANNpoint hi, // high point of box int dim) // dimension of space { register ANNdist dist = 0.0; // sum of squared distances register ANNdist t; for (register int d = 0; d < dim; d++) { if (q[d] < lo[d]) { // q is left of box t = ANNdist(lo[d]) - ANNdist(q[d]); dist = ANN_SUM(dist, ANN_POW(t)); } else if (q[d] > hi[d]) { // q is right of box t = ANNdist(q[d]) - ANNdist(hi[d]); dist = ANN_SUM(dist, ANN_POW(t)); } } ANN_FLOP(4*dim) // increment floating op count return dist; } //---------------------------------------------------------------------- // annSpread - find spread along given dimension // annMinMax - find min and max coordinates along given dimension // annMaxSpread - find dimension of max spread //---------------------------------------------------------------------- ANNcoord annSpread( // compute point spread along dimension ANNpointArray pa, // point array ANNidxArray pidx, // point indices int n, // number of points int d) // dimension to check { ANNcoord min = PA(0,d); // compute max and min coords ANNcoord max = PA(0,d); for (int i = 1; i < n; i++) { ANNcoord c = PA(i,d); if (c < min) min = c; else if (c > max) max = c; } return (max - min); // total spread is difference } void annMinMax( // compute min and max coordinates along dim ANNpointArray pa, // point array ANNidxArray pidx, // point indices int n, // number of points int d, // dimension to check ANNcoord &min, // minimum value (returned) ANNcoord &max) // maximum value (returned) { min = PA(0,d); // compute max and min coords max = PA(0,d); for (int i = 1; i < n; i++) { ANNcoord c = PA(i,d); if (c < min) min = c; else if (c > max) max = c; } } int annMaxSpread( // compute dimension of max spread ANNpointArray pa, // point array ANNidxArray pidx, // point indices int n, // number of points int dim) // dimension of space { int max_dim = 0; // dimension of max spread ANNcoord max_spr = 0; // amount of max spread if (n == 0) return max_dim; // no points, who cares? for (int d = 0; d < dim; d++) { // compute spread along each dim ANNcoord spr = annSpread(pa, pidx, n, d); if (spr > max_spr) { // bigger than current max max_spr = spr; max_dim = d; } } return max_dim; } //---------------------------------------------------------------------- // annMedianSplit - split point array about its median // Splits a subarray of points pa[0..n] about an element of given // rank (median: n_lo = n/2) with respect to dimension d. It places // the element of rank n_lo-1 correctly (because our splitting rule // takes the mean of these two). On exit, the array is permuted so // that: // // pa[0..n_lo-2][d] <= pa[n_lo-1][d] <= pa[n_lo][d] <= pa[n_lo+1..n-1][d]. // // The mean of pa[n_lo-1][d] and pa[n_lo][d] is returned as the // splitting value. // // All indexing is done indirectly through the index array pidx. // // This function uses the well known selection algorithm due to // C.A.R. Hoare. //---------------------------------------------------------------------- // swap two points in pa array #define PASWAP(a,b) { int tmp = pidx[a]; pidx[a] = pidx[b]; pidx[b] = tmp; } void annMedianSplit( ANNpointArray pa, // points to split ANNidxArray pidx, // point indices int n, // number of points int d, // dimension along which to split ANNcoord &cv, // cutting value int n_lo) // split into n_lo and n-n_lo { int l = 0; // left end of current subarray int r = n-1; // right end of current subarray while (l < r) { register int i = (r+l)/2; // select middle as pivot register int k; if (PA(i,d) > PA(r,d)) // make sure last > pivot PASWAP(i,r) PASWAP(l,i); // move pivot to first position ANNcoord c = PA(l,d); // pivot value i = l; k = r; for(;;) { // pivot about c while (PA(++i,d) < c) ; while (PA(--k,d) > c) ; if (i < k) PASWAP(i,k) else break; } PASWAP(l,k); // pivot winds up in location k if (k > n_lo) r = k-1; // recurse on proper subarray else if (k < n_lo) l = k+1; else break; // got the median exactly } if (n_lo > 0) { // search for next smaller item ANNcoord c = PA(0,d); // candidate for max int k = 0; // candidate's index for (int i = 1; i < n_lo; i++) { if (PA(i,d) > c) { c = PA(i,d); k = i; } } PASWAP(n_lo-1, k); // max among pa[0..n_lo-1] to pa[n_lo-1] } // cut value is midpoint value cv = (PA(n_lo-1,d) + PA(n_lo,d))/2.0; } //---------------------------------------------------------------------- // annPlaneSplit - split point array about a cutting plane // Split the points in an array about a given plane along a // given cutting dimension. On exit, br1 and br2 are set so // that: // // pa[ 0 ..br1-1] < cv // pa[br1..br2-1] == cv // pa[br2.. n -1] > cv // // All indexing is done indirectly through the index array pidx. // //---------------------------------------------------------------------- void annPlaneSplit( // split points by a plane ANNpointArray pa, // points to split ANNidxArray pidx, // point indices int n, // number of points int d, // dimension along which to split ANNcoord cv, // cutting value int &br1, // first break (values < cv) int &br2) // second break (values == cv) { int l = 0; int r = n-1; for(;;) { // partition pa[0..n-1] about cv while (l < n && PA(l,d) < cv) l++; while (r >= 0 && PA(r,d) >= cv) r--; if (l > r) break; PASWAP(l,r); l++; r--; } br1 = l; // now: pa[0..br1-1] < cv <= pa[br1..n-1] r = n-1; for(;;) { // partition pa[br1..n-1] about cv while (l < n && PA(l,d) <= cv) l++; while (r >= br1 && PA(r,d) > cv) r--; if (l > r) break; PASWAP(l,r); l++; r--; } br2 = l; // now: pa[br1..br2-1] == cv < pa[br2..n-1] } //---------------------------------------------------------------------- // annBoxSplit - split point array about a orthogonal rectangle // Split the points in an array about a given orthogonal // rectangle. On exit, n_in is set to the number of points // that are inside (or on the boundary of) the rectangle. // // All indexing is done indirectly through the index array pidx. // //---------------------------------------------------------------------- void annBoxSplit( // split points by a box ANNpointArray pa, // points to split ANNidxArray pidx, // point indices int n, // number of points int dim, // dimension of space ANNorthRect &box, // the box int &n_in) // number of points inside (returned) { int l = 0; int r = n-1; for(;;) { // partition pa[0..n-1] about box while (l < n && box.inside(dim, PP(l))) l++; while (r >= 0 && !box.inside(dim, PP(r))) r--; if (l > r) break; PASWAP(l,r); l++; r--; } n_in = l; // now: pa[0..n_in-1] inside and rest outside } //---------------------------------------------------------------------- // annSplitBalance - compute balance factor for a given plane split // Balance factor is defined as the number of points lying // below the splitting value minus n/2 (median). Thus, a // median split has balance 0, left of this is negative and // right of this is positive. (The points are unchanged.) //---------------------------------------------------------------------- int annSplitBalance( // determine balance factor of a split ANNpointArray pa, // points to split ANNidxArray pidx, // point indices int n, // number of points int d, // dimension along which to split ANNcoord cv) // cutting value { int n_lo = 0; for(int i = 0; i < n; i++) { // count number less than cv if (PA(i,d) < cv) n_lo++; } return n_lo - n/2; } //---------------------------------------------------------------------- // annBox2Bnds - convert bounding box to list of bounds // Given two boxes, an inner box enclosed within a bounding // box, this routine determines all the sides for which the // inner box is strictly contained with the bounding box, // and adds an appropriate entry to a list of bounds. Then // we allocate storage for the final list of bounds, and return // the resulting list and its size. //---------------------------------------------------------------------- void annBox2Bnds( // convert inner box to bounds const ANNorthRect &inner_box, // inner box const ANNorthRect &bnd_box, // enclosing box int dim, // dimension of space int &n_bnds, // number of bounds (returned) ANNorthHSArray &bnds) // bounds array (returned) { int i; n_bnds = 0; // count number of bounds for (i = 0; i < dim; i++) { if (inner_box.lo[i] > bnd_box.lo[i]) // low bound is inside n_bnds++; if (inner_box.hi[i] < bnd_box.hi[i]) // high bound is inside n_bnds++; } bnds = new ANNorthHalfSpace[n_bnds]; // allocate appropriate size int j = 0; for (i = 0; i < dim; i++) { // fill the array if (inner_box.lo[i] > bnd_box.lo[i]) { bnds[j].cd = i; bnds[j].cv = inner_box.lo[i]; bnds[j].sd = +1; j++; } if (inner_box.hi[i] < bnd_box.hi[i]) { bnds[j].cd = i; bnds[j].cv = inner_box.hi[i]; bnds[j].sd = -1; j++; } } } //---------------------------------------------------------------------- // annBnds2Box - convert list of bounds to bounding box // Given an enclosing box and a list of bounds, this routine // computes the corresponding inner box. It is assumed that // the box points have been allocated already. //---------------------------------------------------------------------- void annBnds2Box( const ANNorthRect &bnd_box, // enclosing box int dim, // dimension of space int n_bnds, // number of bounds ANNorthHSArray bnds, // bounds array ANNorthRect &inner_box) // inner box (returned) { annAssignRect(dim, inner_box, bnd_box); // copy bounding box to inner for (int i = 0; i < n_bnds; i++) { bnds[i].project(inner_box.lo); // project each endpoint bnds[i].project(inner_box.hi); } } ann-1.1.2+doc/src/kd_split.h0000644000175000017500000000720111330212441016452 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_split.h // Programmer: Sunil Arya and David Mount // Description: Methods for splitting kd-trees // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release //---------------------------------------------------------------------- #ifndef ANN_KD_SPLIT_H #define ANN_KD_SPLIT_H #include "kd_tree.h" // kd-tree definitions //---------------------------------------------------------------------- // External entry points // These are all splitting procedures for kd-trees. //---------------------------------------------------------------------- void kd_split( // standard (optimized) kd-splitter ANNpointArray pa, // point array (unaltered) ANNidxArray pidx, // point indices (permuted on return) const ANNorthRect &bnds, // bounding rectangle for cell int n, // number of points int dim, // dimension of space int &cut_dim, // cutting dimension (returned) ANNcoord &cut_val, // cutting value (returned) int &n_lo); // num of points on low side (returned) void midpt_split( // midpoint kd-splitter ANNpointArray pa, // point array (unaltered) ANNidxArray pidx, // point indices (permuted on return) const ANNorthRect &bnds, // bounding rectangle for cell int n, // number of points int dim, // dimension of space int &cut_dim, // cutting dimension (returned) ANNcoord &cut_val, // cutting value (returned) int &n_lo); // num of points on low side (returned) void sl_midpt_split( // sliding midpoint kd-splitter ANNpointArray pa, // point array (unaltered) ANNidxArray pidx, // point indices (permuted on return) const ANNorthRect &bnds, // bounding rectangle for cell int n, // number of points int dim, // dimension of space int &cut_dim, // cutting dimension (returned) ANNcoord &cut_val, // cutting value (returned) int &n_lo); // num of points on low side (returned) void fair_split( // fair-split kd-splitter ANNpointArray pa, // point array (unaltered) ANNidxArray pidx, // point indices (permuted on return) const ANNorthRect &bnds, // bounding rectangle for cell int n, // number of points int dim, // dimension of space int &cut_dim, // cutting dimension (returned) ANNcoord &cut_val, // cutting value (returned) int &n_lo); // num of points on low side (returned) void sl_fair_split( // sliding fair-split kd-splitter ANNpointArray pa, // point array (unaltered) ANNidxArray pidx, // point indices (permuted on return) const ANNorthRect &bnds, // bounding rectangle for cell int n, // number of points int dim, // dimension of space int &cut_dim, // cutting dimension (returned) ANNcoord &cut_val, // cutting value (returned) int &n_lo); // num of points on low side (returned) #endif ann-1.1.2+doc/src/pr_queue_k.h0000644000175000017500000001045011330212441017000 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: pr_queue_k.h // Programmer: Sunil Arya and David Mount // Description: Include file for priority queue with k items. // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release //---------------------------------------------------------------------- #ifndef PR_QUEUE_K_H #define PR_QUEUE_K_H #include // all ANN includes #include // performance evaluation //---------------------------------------------------------------------- // Basic types //---------------------------------------------------------------------- typedef ANNdist PQKkey; // key field is distance typedef int PQKinfo; // info field is int //---------------------------------------------------------------------- // Constants // The NULL key value is used to initialize the priority queue, and // so it should be larger than any valid distance, so that it will // be replaced as legal distance values are inserted. The NULL // info value must be a nonvalid array index, we use ANN_NULL_IDX, // which is guaranteed to be negative. //---------------------------------------------------------------------- const PQKkey PQ_NULL_KEY = ANN_DIST_INF; // nonexistent key value const PQKinfo PQ_NULL_INFO = ANN_NULL_IDX; // nonexistent info value //---------------------------------------------------------------------- // ANNmin_k // An ANNmin_k structure is one which maintains the smallest // k values (of type PQKkey) and associated information (of type // PQKinfo). The special info and key values PQ_NULL_INFO and // PQ_NULL_KEY means that thise entry is empty. // // It is currently implemented using an array with k items. // Items are stored in increasing sorted order, and insertions // are made through standard insertion sort. (This is quite // inefficient, but current applications call for small values // of k and relatively few insertions.) // // Note that the list contains k+1 entries, but the last entry // is used as a simple placeholder and is otherwise ignored. //---------------------------------------------------------------------- class ANNmin_k { struct mk_node { // node in min_k structure PQKkey key; // key value PQKinfo info; // info field (user defined) }; int k; // max number of keys to store int n; // number of keys currently active mk_node *mk; // the list itself public: ANNmin_k(int max) // constructor (given max size) { n = 0; // initially no items k = max; // maximum number of items mk = new mk_node[max+1]; // sorted array of keys } ~ANNmin_k() // destructor { delete [] mk; } PQKkey ANNmin_key() // return minimum key { return (n > 0 ? mk[0].key : PQ_NULL_KEY); } PQKkey max_key() // return maximum key { return (n == k ? mk[k-1].key : PQ_NULL_KEY); } PQKkey ith_smallest_key(int i) // ith smallest key (i in [0..n-1]) { return (i < n ? mk[i].key : PQ_NULL_KEY); } PQKinfo ith_smallest_info(int i) // info for ith smallest (i in [0..n-1]) { return (i < n ? mk[i].info : PQ_NULL_INFO); } inline void insert( // insert item (inlined for speed) PQKkey kv, // key value PQKinfo inf) // item info { register int i; // slide larger values up for (i = n; i > 0; i--) { if (mk[i-1].key > kv) mk[i] = mk[i-1]; else break; } mk[i].key = kv; // store element here mk[i].info = inf; if (n < k) n++; // increment number of items ANN_FLOP(k-i+1) // increment floating ops } }; #endif ann-1.1.2+doc/src/brute.cpp0000644000175000017500000000777511330212441016335 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: brute.cpp // Programmer: Sunil Arya and David Mount // Description: Brute-force nearest neighbors // Last modified: 05/03/05 (Version 1.1) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.1 05/03/05 // Added fixed-radius kNN search //---------------------------------------------------------------------- #include // all ANN includes #include "pr_queue_k.h" // k element priority queue //---------------------------------------------------------------------- // Brute-force search simply stores a pointer to the list of // data points and searches linearly for the nearest neighbor. // The k nearest neighbors are stored in a k-element priority // queue (which is implemented in a pretty dumb way as well). // // If ANN_ALLOW_SELF_MATCH is ANNfalse then data points at distance // zero are not considered. // // Note that the error bound eps is passed in, but it is ignored. // These routines compute exact nearest neighbors (which is needed // for validation purposes in ann_test.cpp). //---------------------------------------------------------------------- ANNbruteForce::ANNbruteForce( // constructor from point array ANNpointArray pa, // point array int n, // number of points int dd) // dimension { dim = dd; n_pts = n; pts = pa; } ANNbruteForce::~ANNbruteForce() { } // destructor (empty) void ANNbruteForce::annkSearch( // approx k near neighbor search ANNpoint q, // query point int k, // number of near neighbors to return ANNidxArray nn_idx, // nearest neighbor indices (returned) ANNdistArray dd, // dist to near neighbors (returned) double eps) // error bound (ignored) { ANNmin_k mk(k); // construct a k-limited priority queue int i; if (k > n_pts) { // too many near neighbors? annError("Requesting more near neighbors than data points", ANNabort); } // run every point through queue for (i = 0; i < n_pts; i++) { // compute distance to point ANNdist sqDist = annDist(dim, pts[i], q); if (ANN_ALLOW_SELF_MATCH || sqDist != 0) mk.insert(sqDist, i); } for (i = 0; i < k; i++) { // extract the k closest points dd[i] = mk.ith_smallest_key(i); nn_idx[i] = mk.ith_smallest_info(i); } } int ANNbruteForce::annkFRSearch( // approx fixed-radius kNN search ANNpoint q, // query point ANNdist sqRad, // squared radius int k, // number of near neighbors to return ANNidxArray nn_idx, // nearest neighbor array (returned) ANNdistArray dd, // dist to near neighbors (returned) double eps) // error bound { ANNmin_k mk(k); // construct a k-limited priority queue int i; int pts_in_range = 0; // number of points in query range // run every point through queue for (i = 0; i < n_pts; i++) { // compute distance to point ANNdist sqDist = annDist(dim, pts[i], q); if (sqDist <= sqRad && // within radius bound (ANN_ALLOW_SELF_MATCH || sqDist != 0)) { // ...and no self match mk.insert(sqDist, i); pts_in_range++; } } for (i = 0; i < k; i++) { // extract the k closest points if (dd != NULL) dd[i] = mk.ith_smallest_key(i); if (nn_idx != NULL) nn_idx[i] = mk.ith_smallest_info(i); } return pts_in_range; } ann-1.1.2+doc/src/kd_search.h0000644000175000017500000000400111330212441016557 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_search.h // Programmer: Sunil Arya and David Mount // Description: Standard kd-tree search // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release //---------------------------------------------------------------------- #ifndef ANN_kd_search_H #define ANN_kd_search_H #include "kd_tree.h" // kd-tree declarations #include "kd_util.h" // kd-tree utilities #include "pr_queue_k.h" // k-element priority queue #include // performance evaluation //---------------------------------------------------------------------- // More global variables // These are active for the life of each call to annkSearch(). They // are set to save the number of variables that need to be passed // among the various search procedures. //---------------------------------------------------------------------- extern int ANNkdDim; // dimension of space (static copy) extern ANNpoint ANNkdQ; // query point (static copy) extern double ANNkdMaxErr; // max tolerable squared error extern ANNpointArray ANNkdPts; // the points (static copy) extern ANNmin_k *ANNkdPointMK; // set of k closest points extern int ANNptsVisited; // number of points visited #endif ann-1.1.2+doc/src/ANN.cpp0000644000175000017500000001462211330212441015615 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: ANN.cpp // Programmer: Sunil Arya and David Mount // Description: Methods for ANN.h and ANNx.h // Last modified: 01/27/10 (Version 1.1.2) //---------------------------------------------------------------------- // Copyright (c) 1997-2010 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.0 04/01/05 // Added performance counting to annDist() // Revision 1.1.2 01/27/10 // Fixed minor compilation bugs for new versions of gcc //---------------------------------------------------------------------- #include // C standard lib defs #include // all ANN includes #include // ANN performance using namespace std; // make std:: accessible //---------------------------------------------------------------------- // Point methods //---------------------------------------------------------------------- //---------------------------------------------------------------------- // Distance utility. // (Note: In the nearest neighbor search, most distances are // computed using partial distance calculations, not this // procedure.) //---------------------------------------------------------------------- ANNdist annDist( // interpoint squared distance int dim, ANNpoint p, ANNpoint q) { register int d; register ANNcoord diff; register ANNcoord dist; dist = 0; for (d = 0; d < dim; d++) { diff = p[d] - q[d]; dist = ANN_SUM(dist, ANN_POW(diff)); } ANN_FLOP(3*dim) // performance counts ANN_PTS(1) ANN_COORD(dim) return dist; } //---------------------------------------------------------------------- // annPrintPoint() prints a point to a given output stream. //---------------------------------------------------------------------- void annPrintPt( // print a point ANNpoint pt, // the point int dim, // the dimension std::ostream &out) // output stream { for (int j = 0; j < dim; j++) { out << pt[j]; if (j < dim-1) out << " "; } } //---------------------------------------------------------------------- // Point allocation/deallocation: // // Because points (somewhat like strings in C) are stored // as pointers. Consequently, creating and destroying // copies of points may require storage allocation. These // procedures do this. // // annAllocPt() and annDeallocPt() allocate a deallocate // storage for a single point, and return a pointer to it. // // annAllocPts() allocates an array of points as well a place // to store their coordinates, and initializes the points to // point to their respective coordinates. It allocates point // storage in a contiguous block large enough to store all the // points. It performs no initialization. // // annDeallocPts() should only be used on point arrays allocated // by annAllocPts since it assumes that points are allocated in // a block. // // annCopyPt() copies a point taking care to allocate storage // for the new point. // // annAssignRect() assigns the coordinates of one rectangle to // another. The two rectangles must have the same dimension // (and it is not possible to test this here). //---------------------------------------------------------------------- ANNpoint annAllocPt(int dim, ANNcoord c) // allocate 1 point { ANNpoint p = new ANNcoord[dim]; for (int i = 0; i < dim; i++) p[i] = c; return p; } ANNpointArray annAllocPts(int n, int dim) // allocate n pts in dim { ANNpointArray pa = new ANNpoint[n]; // allocate points ANNpoint p = new ANNcoord[n*dim]; // allocate space for coords for (int i = 0; i < n; i++) { pa[i] = &(p[i*dim]); } return pa; } void annDeallocPt(ANNpoint &p) // deallocate 1 point { delete [] p; p = NULL; } void annDeallocPts(ANNpointArray &pa) // deallocate points { delete [] pa[0]; // dealloc coordinate storage delete [] pa; // dealloc points pa = NULL; } ANNpoint annCopyPt(int dim, ANNpoint source) // copy point { ANNpoint p = new ANNcoord[dim]; for (int i = 0; i < dim; i++) p[i] = source[i]; return p; } // assign one rect to another void annAssignRect(int dim, ANNorthRect &dest, const ANNorthRect &source) { for (int i = 0; i < dim; i++) { dest.lo[i] = source.lo[i]; dest.hi[i] = source.hi[i]; } } // is point inside rectangle? ANNbool ANNorthRect::inside(int dim, ANNpoint p) { for (int i = 0; i < dim; i++) { if (p[i] < lo[i] || p[i] > hi[i]) return ANNfalse; } return ANNtrue; } //---------------------------------------------------------------------- // Error handler //---------------------------------------------------------------------- void annError(const char* msg, ANNerr level) { if (level == ANNabort) { cerr << "ANN: ERROR------->" << msg << "<-------------ERROR\n"; exit(1); } else { cerr << "ANN: WARNING----->" << msg << "<-------------WARNING\n"; } } //---------------------------------------------------------------------- // Limit on number of points visited // We have an option for terminating the search early if the // number of points visited exceeds some threshold. If the // threshold is 0 (its default) this means there is no limit // and the algorithm applies its normal termination condition. // This is for applications where there are real time constraints // on the running time of the algorithm. //---------------------------------------------------------------------- int ANNmaxPtsVisited = 0; // maximum number of pts visited int ANNptsVisited; // number of pts visited in search //---------------------------------------------------------------------- // Global function declarations //---------------------------------------------------------------------- void annMaxPtsVisit( // set limit on max. pts to visit in search int maxPts) // the limit { ANNmaxPtsVisited = maxPts; } ann-1.1.2+doc/src/bd_tree.h0000644000175000017500000000757511330212441016263 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: bd_tree.h // Programmer: David Mount // Description: Declarations for standard bd-tree routines // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.0 04/01/05 // Changed IN, OUT to ANN_IN, ANN_OUT //---------------------------------------------------------------------- #ifndef ANN_bd_tree_H #define ANN_bd_tree_H #include // all ANN includes #include "kd_tree.h" // kd-tree includes //---------------------------------------------------------------------- // bd-tree shrinking node. // The main addition in the bd-tree is the shrinking node, which // is declared here. // // Shrinking nodes are defined by list of orthogonal halfspaces. // These halfspaces define a (possibly unbounded) orthogonal // rectangle. There are two children, in and out. Points that // lie within this rectangle are stored in the in-child, and the // other points are stored in the out-child. // // We use a list of orthogonal halfspaces rather than an // orthogonal rectangle object because typically the number of // sides of the shrinking box will be much smaller than the // worst case bound of 2*dim. // // BEWARE: Note that constructor just copies the pointer to the // bounding array, but the destructor deallocates it. This is // rather poor practice, but happens to be convenient. The list // is allocated in the bd-tree building procedure rbd_tree() just // prior to construction, and is used for no other purposes. // // WARNING: In the near neighbor searching code it is assumed that // the list of bounding halfspaces is irredundant, meaning that there // are no two distinct halfspaces in the list with the same outward // pointing normals. //---------------------------------------------------------------------- class ANNbd_shrink : public ANNkd_node // splitting node of a kd-tree { int n_bnds; // number of bounding halfspaces ANNorthHSArray bnds; // list of bounding halfspaces ANNkd_ptr child[2]; // in and out children public: ANNbd_shrink( // constructor int nb, // number of bounding halfspaces ANNorthHSArray bds, // list of bounding halfspaces ANNkd_ptr ic=NULL, ANNkd_ptr oc=NULL) // children { n_bnds = nb; // cutting dimension bnds = bds; // assign bounds child[ANN_IN] = ic; // set children child[ANN_OUT] = oc; } ~ANNbd_shrink() // destructor { if (child[ANN_IN]!= NULL && child[ANN_IN]!= KD_TRIVIAL) delete child[ANN_IN]; if (child[ANN_OUT]!= NULL&& child[ANN_OUT]!= KD_TRIVIAL) delete child[ANN_OUT]; if (bnds != NULL) delete [] bnds; // delete bounds } virtual void getStats( // get tree statistics int dim, // dimension of space ANNkdStats &st, // statistics ANNorthRect &bnd_box); // bounding box virtual void print(int level, ostream &out);// print node virtual void dump(ostream &out); // dump node virtual void ann_search(ANNdist); // standard search virtual void ann_pri_search(ANNdist); // priority search virtual void ann_FR_search(ANNdist); // fixed-radius search }; #endif ann-1.1.2+doc/src/kd_split.cpp0000644000175000017500000004075611330212441017021 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_split.cpp // Programmer: Sunil Arya and David Mount // Description: Methods for splitting kd-trees // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.0 04/01/05 //---------------------------------------------------------------------- #include "kd_tree.h" // kd-tree definitions #include "kd_util.h" // kd-tree utilities #include "kd_split.h" // splitting functions //---------------------------------------------------------------------- // Constants //---------------------------------------------------------------------- const double ERR = 0.001; // a small value const double FS_ASPECT_RATIO = 3.0; // maximum allowed aspect ratio // in fair split. Must be >= 2. //---------------------------------------------------------------------- // kd_split - Bentley's standard splitting routine for kd-trees // Find the dimension of the greatest spread, and split // just before the median point along this dimension. //---------------------------------------------------------------------- void kd_split( ANNpointArray pa, // point array (permuted on return) ANNidxArray pidx, // point indices const ANNorthRect &bnds, // bounding rectangle for cell int n, // number of points int dim, // dimension of space int &cut_dim, // cutting dimension (returned) ANNcoord &cut_val, // cutting value (returned) int &n_lo) // num of points on low side (returned) { // find dimension of maximum spread cut_dim = annMaxSpread(pa, pidx, n, dim); n_lo = n/2; // median rank // split about median annMedianSplit(pa, pidx, n, cut_dim, cut_val, n_lo); } //---------------------------------------------------------------------- // midpt_split - midpoint splitting rule for box-decomposition trees // // This is the simplest splitting rule that guarantees boxes // of bounded aspect ratio. It simply cuts the box with the // longest side through its midpoint. If there are ties, it // selects the dimension with the maximum point spread. // // WARNING: This routine (while simple) doesn't seem to work // well in practice in high dimensions, because it tends to // generate a large number of trivial and/or unbalanced splits. // Either kd_split(), sl_midpt_split(), or fair_split() are // recommended, instead. //---------------------------------------------------------------------- void midpt_split( ANNpointArray pa, // point array ANNidxArray pidx, // point indices (permuted on return) const ANNorthRect &bnds, // bounding rectangle for cell int n, // number of points int dim, // dimension of space int &cut_dim, // cutting dimension (returned) ANNcoord &cut_val, // cutting value (returned) int &n_lo) // num of points on low side (returned) { int d; ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; for (d = 1; d < dim; d++) { // find length of longest box side ANNcoord length = bnds.hi[d] - bnds.lo[d]; if (length > max_length) { max_length = length; } } ANNcoord max_spread = -1; // find long side with most spread for (d = 0; d < dim; d++) { // is it among longest? if (double(bnds.hi[d] - bnds.lo[d]) >= (1-ERR)*max_length) { // compute its spread ANNcoord spr = annSpread(pa, pidx, n, d); if (spr > max_spread) { // is it max so far? max_spread = spr; cut_dim = d; } } } // split along cut_dim at midpoint cut_val = (bnds.lo[cut_dim] + bnds.hi[cut_dim]) / 2; // permute points accordingly int br1, br2; annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); //------------------------------------------------------------------ // On return: pa[0..br1-1] < cut_val // pa[br1..br2-1] == cut_val // pa[br2..n-1] > cut_val // // We can set n_lo to any value in the range [br1..br2]. // We choose split so that points are most evenly divided. //------------------------------------------------------------------ if (br1 > n/2) n_lo = br1; else if (br2 < n/2) n_lo = br2; else n_lo = n/2; } //---------------------------------------------------------------------- // sl_midpt_split - sliding midpoint splitting rule // // This is a modification of midpt_split, which has the nonsensical // name "sliding midpoint". The idea is that we try to use the // midpoint rule, by bisecting the longest side. If there are // ties, the dimension with the maximum spread is selected. If, // however, the midpoint split produces a trivial split (no points // on one side of the splitting plane) then we slide the splitting // (maintaining its orientation) until it produces a nontrivial // split. For example, if the splitting plane is along the x-axis, // and all the data points have x-coordinate less than the x-bisector, // then the split is taken along the maximum x-coordinate of the // data points. // // Intuitively, this rule cannot generate trivial splits, and // hence avoids midpt_split's tendency to produce trees with // a very large number of nodes. // //---------------------------------------------------------------------- void sl_midpt_split( ANNpointArray pa, // point array ANNidxArray pidx, // point indices (permuted on return) const ANNorthRect &bnds, // bounding rectangle for cell int n, // number of points int dim, // dimension of space int &cut_dim, // cutting dimension (returned) ANNcoord &cut_val, // cutting value (returned) int &n_lo) // num of points on low side (returned) { int d; ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; for (d = 1; d < dim; d++) { // find length of longest box side ANNcoord length = bnds.hi[d] - bnds.lo[d]; if (length > max_length) { max_length = length; } } ANNcoord max_spread = -1; // find long side with most spread for (d = 0; d < dim; d++) { // is it among longest? if ((bnds.hi[d] - bnds.lo[d]) >= (1-ERR)*max_length) { // compute its spread ANNcoord spr = annSpread(pa, pidx, n, d); if (spr > max_spread) { // is it max so far? max_spread = spr; cut_dim = d; } } } // ideal split at midpoint ANNcoord ideal_cut_val = (bnds.lo[cut_dim] + bnds.hi[cut_dim])/2; ANNcoord min, max; annMinMax(pa, pidx, n, cut_dim, min, max); // find min/max coordinates if (ideal_cut_val < min) // slide to min or max as needed cut_val = min; else if (ideal_cut_val > max) cut_val = max; else cut_val = ideal_cut_val; // permute points accordingly int br1, br2; annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); //------------------------------------------------------------------ // On return: pa[0..br1-1] < cut_val // pa[br1..br2-1] == cut_val // pa[br2..n-1] > cut_val // // We can set n_lo to any value in the range [br1..br2] to satisfy // the exit conditions of the procedure. // // if ideal_cut_val < min (implying br2 >= 1), // then we select n_lo = 1 (so there is one point on left) and // if ideal_cut_val > max (implying br1 <= n-1), // then we select n_lo = n-1 (so there is one point on right). // Otherwise, we select n_lo as close to n/2 as possible within // [br1..br2]. //------------------------------------------------------------------ if (ideal_cut_val < min) n_lo = 1; else if (ideal_cut_val > max) n_lo = n-1; else if (br1 > n/2) n_lo = br1; else if (br2 < n/2) n_lo = br2; else n_lo = n/2; } //---------------------------------------------------------------------- // fair_split - fair-split splitting rule // // This is a compromise between the kd-tree splitting rule (which // always splits data points at their median) and the midpoint // splitting rule (which always splits a box through its center. // The goal of this procedure is to achieve both nicely balanced // splits, and boxes of bounded aspect ratio. // // A constant FS_ASPECT_RATIO is defined. Given a box, those sides // which can be split so that the ratio of the longest to shortest // side does not exceed ASPECT_RATIO are identified. Among these // sides, we select the one in which the points have the largest // spread. We then split the points in a manner which most evenly // distributes the points on either side of the splitting plane, // subject to maintaining the bound on the ratio of long to short // sides. To determine that the aspect ratio will be preserved, // we determine the longest side (other than this side), and // determine how narrowly we can cut this side, without causing the // aspect ratio bound to be exceeded (small_piece). // // This procedure is more robust than either kd_split or midpt_split, // but is more complicated as well. When point distribution is // extremely skewed, this degenerates to midpt_split (actually // 1/3 point split), and when the points are most evenly distributed, // this degenerates to kd-split. //---------------------------------------------------------------------- void fair_split( ANNpointArray pa, // point array ANNidxArray pidx, // point indices (permuted on return) const ANNorthRect &bnds, // bounding rectangle for cell int n, // number of points int dim, // dimension of space int &cut_dim, // cutting dimension (returned) ANNcoord &cut_val, // cutting value (returned) int &n_lo) // num of points on low side (returned) { int d; ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; cut_dim = 0; for (d = 1; d < dim; d++) { // find length of longest box side ANNcoord length = bnds.hi[d] - bnds.lo[d]; if (length > max_length) { max_length = length; cut_dim = d; } } ANNcoord max_spread = 0; // find legal cut with max spread cut_dim = 0; for (d = 0; d < dim; d++) { ANNcoord length = bnds.hi[d] - bnds.lo[d]; // is this side midpoint splitable // without violating aspect ratio? if (((double) max_length)*2.0/((double) length) <= FS_ASPECT_RATIO) { // compute spread along this dim ANNcoord spr = annSpread(pa, pidx, n, d); if (spr > max_spread) { // best spread so far max_spread = spr; cut_dim = d; // this is dimension to cut } } } max_length = 0; // find longest side other than cut_dim for (d = 0; d < dim; d++) { ANNcoord length = bnds.hi[d] - bnds.lo[d]; if (d != cut_dim && length > max_length) max_length = length; } // consider most extreme splits ANNcoord small_piece = max_length / FS_ASPECT_RATIO; ANNcoord lo_cut = bnds.lo[cut_dim] + small_piece;// lowest legal cut ANNcoord hi_cut = bnds.hi[cut_dim] - small_piece;// highest legal cut int br1, br2; // is median below lo_cut ? if (annSplitBalance(pa, pidx, n, cut_dim, lo_cut) >= 0) { cut_val = lo_cut; // cut at lo_cut annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); n_lo = br1; } // is median above hi_cut? else if (annSplitBalance(pa, pidx, n, cut_dim, hi_cut) <= 0) { cut_val = hi_cut; // cut at hi_cut annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); n_lo = br2; } else { // median cut preserves asp ratio n_lo = n/2; // split about median annMedianSplit(pa, pidx, n, cut_dim, cut_val, n_lo); } } //---------------------------------------------------------------------- // sl_fair_split - sliding fair split splitting rule // // Sliding fair split is a splitting rule that combines the // strengths of both fair split with sliding midpoint split. // Fair split tends to produce balanced splits when the points // are roughly uniformly distributed, but it can produce many // trivial splits when points are highly clustered. Sliding // midpoint never produces trivial splits, and shrinks boxes // nicely if points are highly clustered, but it may produce // rather unbalanced splits when points are unclustered but not // quite uniform. // // Sliding fair split is based on the theory that there are two // types of splits that are "good": balanced splits that produce // fat boxes, and unbalanced splits provided the cell with fewer // points is fat. // // This splitting rule operates by first computing the longest // side of the current bounding box. Then it asks which sides // could be split (at the midpoint) and still satisfy the aspect // ratio bound with respect to this side. Among these, it selects // the side with the largest spread (as fair split would). It // then considers the most extreme cuts that would be allowed by // the aspect ratio bound. This is done by dividing the longest // side of the box by the aspect ratio bound. If the median cut // lies between these extreme cuts, then we use the median cut. // If not, then consider the extreme cut that is closer to the // median. If all the points lie to one side of this cut, then // we slide the cut until it hits the first point. This may // violate the aspect ratio bound, but will never generate empty // cells. However the sibling of every such skinny cell is fat, // and hence packing arguments still apply. // //---------------------------------------------------------------------- void sl_fair_split( ANNpointArray pa, // point array ANNidxArray pidx, // point indices (permuted on return) const ANNorthRect &bnds, // bounding rectangle for cell int n, // number of points int dim, // dimension of space int &cut_dim, // cutting dimension (returned) ANNcoord &cut_val, // cutting value (returned) int &n_lo) // num of points on low side (returned) { int d; ANNcoord min, max; // min/max coordinates int br1, br2; // split break points ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; cut_dim = 0; for (d = 1; d < dim; d++) { // find length of longest box side ANNcoord length = bnds.hi[d] - bnds.lo[d]; if (length > max_length) { max_length = length; cut_dim = d; } } ANNcoord max_spread = 0; // find legal cut with max spread cut_dim = 0; for (d = 0; d < dim; d++) { ANNcoord length = bnds.hi[d] - bnds.lo[d]; // is this side midpoint splitable // without violating aspect ratio? if (((double) max_length)*2.0/((double) length) <= FS_ASPECT_RATIO) { // compute spread along this dim ANNcoord spr = annSpread(pa, pidx, n, d); if (spr > max_spread) { // best spread so far max_spread = spr; cut_dim = d; // this is dimension to cut } } } max_length = 0; // find longest side other than cut_dim for (d = 0; d < dim; d++) { ANNcoord length = bnds.hi[d] - bnds.lo[d]; if (d != cut_dim && length > max_length) max_length = length; } // consider most extreme splits ANNcoord small_piece = max_length / FS_ASPECT_RATIO; ANNcoord lo_cut = bnds.lo[cut_dim] + small_piece;// lowest legal cut ANNcoord hi_cut = bnds.hi[cut_dim] - small_piece;// highest legal cut // find min and max along cut_dim annMinMax(pa, pidx, n, cut_dim, min, max); // is median below lo_cut? if (annSplitBalance(pa, pidx, n, cut_dim, lo_cut) >= 0) { if (max > lo_cut) { // are any points above lo_cut? cut_val = lo_cut; // cut at lo_cut annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); n_lo = br1; // balance if there are ties } else { // all points below lo_cut cut_val = max; // cut at max value annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); n_lo = n-1; } } // is median above hi_cut? else if (annSplitBalance(pa, pidx, n, cut_dim, hi_cut) <= 0) { if (min < hi_cut) { // are any points below hi_cut? cut_val = hi_cut; // cut at hi_cut annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); n_lo = br2; // balance if there are ties } else { // all points above hi_cut cut_val = min; // cut at min value annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); n_lo = 1; } } else { // median cut is good enough n_lo = n/2; // split about median annMedianSplit(pa, pidx, n, cut_dim, cut_val, n_lo); } } ann-1.1.2+doc/src/bd_tree.cpp0000644000175000017500000003754011330212441016611 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: bd_tree.cpp // Programmer: David Mount // Description: Basic methods for bd-trees. // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision l.0 04/01/05 // Fixed centroid shrink threshold condition to depend on the // dimension. // Moved dump routine to kd_dump.cpp. //---------------------------------------------------------------------- #include "bd_tree.h" // bd-tree declarations #include "kd_util.h" // kd-tree utilities #include "kd_split.h" // kd-tree splitting rules #include // performance evaluation //---------------------------------------------------------------------- // Printing a bd-tree // These routines print a bd-tree. See the analogous procedure // in kd_tree.cpp for more information. //---------------------------------------------------------------------- void ANNbd_shrink::print( // print shrinking node int level, // depth of node in tree ostream &out) // output stream { child[ANN_OUT]->print(level+1, out); // print out-child out << " "; for (int i = 0; i < level; i++) // print indentation out << ".."; out << "Shrink"; for (int j = 0; j < n_bnds; j++) { // print sides, 2 per line if (j % 2 == 0) { out << "\n"; // newline and indentation for (int i = 0; i < level+2; i++) out << " "; } out << " ([" << bnds[j].cd << "]" << (bnds[j].sd > 0 ? ">=" : "< ") << bnds[j].cv << ")"; } out << "\n"; child[ANN_IN]->print(level+1, out); // print in-child } //---------------------------------------------------------------------- // kd_tree statistics utility (for performance evaluation) // This routine computes various statistics information for // shrinking nodes. See file kd_tree.cpp for more information. //---------------------------------------------------------------------- void ANNbd_shrink::getStats( // get subtree statistics int dim, // dimension of space ANNkdStats &st, // stats (modified) ANNorthRect &bnd_box) // bounding box { ANNkdStats ch_stats; // stats for children ANNorthRect inner_box(dim); // inner box of shrink annBnds2Box(bnd_box, // enclosing box dim, // dimension n_bnds, // number of bounds bnds, // bounds array inner_box); // inner box (modified) // get stats for inner child ch_stats.reset(); // reset child[ANN_IN]->getStats(dim, ch_stats, inner_box); st.merge(ch_stats); // merge them // get stats for outer child ch_stats.reset(); // reset child[ANN_OUT]->getStats(dim, ch_stats, bnd_box); st.merge(ch_stats); // merge them st.depth++; // increment depth st.n_shr++; // increment number of shrinks } //---------------------------------------------------------------------- // bd-tree constructor // This is the main constructor for bd-trees given a set of points. // It first builds a skeleton kd-tree as a basis, then computes the // bounding box of the data points, and then invokes rbd_tree() to // actually build the tree, passing it the appropriate splitting // and shrinking information. //---------------------------------------------------------------------- ANNkd_ptr rbd_tree( // recursive construction of bd-tree ANNpointArray pa, // point array ANNidxArray pidx, // point indices to store in subtree int n, // number of points int dim, // dimension of space int bsp, // bucket space ANNorthRect &bnd_box, // bounding box for current node ANNkd_splitter splitter, // splitting routine ANNshrinkRule shrink); // shrinking rule ANNbd_tree::ANNbd_tree( // construct from point array ANNpointArray pa, // point array (with at least n pts) int n, // number of points int dd, // dimension int bs, // bucket size ANNsplitRule split, // splitting rule ANNshrinkRule shrink) // shrinking rule : ANNkd_tree(n, dd, bs) // build skeleton base tree { pts = pa; // where the points are if (n == 0) return; // no points--no sweat ANNorthRect bnd_box(dd); // bounding box for points // construct bounding rectangle annEnclRect(pa, pidx, n, dd, bnd_box); // copy to tree structure bnd_box_lo = annCopyPt(dd, bnd_box.lo); bnd_box_hi = annCopyPt(dd, bnd_box.hi); switch (split) { // build by rule case ANN_KD_STD: // standard kd-splitting rule root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, kd_split, shrink); break; case ANN_KD_MIDPT: // midpoint split root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, midpt_split, shrink); break; case ANN_KD_SUGGEST: // best (in our opinion) case ANN_KD_SL_MIDPT: // sliding midpoint split root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, sl_midpt_split, shrink); break; case ANN_KD_FAIR: // fair split root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, fair_split, shrink); break; case ANN_KD_SL_FAIR: // sliding fair split root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, sl_fair_split, shrink); break; default: annError("Illegal splitting method", ANNabort); } } //---------------------------------------------------------------------- // Shrinking rules //---------------------------------------------------------------------- enum ANNdecomp {SPLIT, SHRINK}; // decomposition methods //---------------------------------------------------------------------- // trySimpleShrink - Attempt a simple shrink // // We compute the tight bounding box of the points, and compute // the 2*dim ``gaps'' between the sides of the tight box and the // bounding box. If any of the gaps is large enough relative to // the longest side of the tight bounding box, then we shrink // all sides whose gaps are large enough. (The reason for // comparing against the tight bounding box, is that after // shrinking the longest box size will decrease, and if we use // the standard bounding box, we may decide to shrink twice in // a row. Since the tight box is fixed, we cannot shrink twice // consecutively.) //---------------------------------------------------------------------- const float BD_GAP_THRESH = 0.5; // gap threshold (must be < 1) const int BD_CT_THRESH = 2; // min number of shrink sides ANNdecomp trySimpleShrink( // try a simple shrink ANNpointArray pa, // point array ANNidxArray pidx, // point indices to store in subtree int n, // number of points int dim, // dimension of space const ANNorthRect &bnd_box, // current bounding box ANNorthRect &inner_box) // inner box if shrinking (returned) { int i; // compute tight bounding box annEnclRect(pa, pidx, n, dim, inner_box); ANNcoord max_length = 0; // find longest box side for (i = 0; i < dim; i++) { ANNcoord length = inner_box.hi[i] - inner_box.lo[i]; if (length > max_length) { max_length = length; } } int shrink_ct = 0; // number of sides we shrunk for (i = 0; i < dim; i++) { // select which sides to shrink // gap between boxes ANNcoord gap_hi = bnd_box.hi[i] - inner_box.hi[i]; // big enough gap to shrink? if (gap_hi < max_length*BD_GAP_THRESH) inner_box.hi[i] = bnd_box.hi[i]; // no - expand else shrink_ct++; // yes - shrink this side // repeat for high side ANNcoord gap_lo = inner_box.lo[i] - bnd_box.lo[i]; if (gap_lo < max_length*BD_GAP_THRESH) inner_box.lo[i] = bnd_box.lo[i]; // no - expand else shrink_ct++; // yes - shrink this side } if (shrink_ct >= BD_CT_THRESH) // did we shrink enough sides? return SHRINK; else return SPLIT; } //---------------------------------------------------------------------- // tryCentroidShrink - Attempt a centroid shrink // // We repeatedly apply the splitting rule, always to the larger subset // of points, until the number of points decreases by the constant // fraction BD_FRACTION. If this takes more than dim*BD_MAX_SPLIT_FAC // splits for this to happen, then we shrink to the final inner box // Otherwise we split. //---------------------------------------------------------------------- const float BD_MAX_SPLIT_FAC = 0.5; // maximum number of splits allowed const float BD_FRACTION = 0.5; // ...to reduce points by this fraction // ...This must be < 1. ANNdecomp tryCentroidShrink( // try a centroid shrink ANNpointArray pa, // point array ANNidxArray pidx, // point indices to store in subtree int n, // number of points int dim, // dimension of space const ANNorthRect &bnd_box, // current bounding box ANNkd_splitter splitter, // splitting procedure ANNorthRect &inner_box) // inner box if shrinking (returned) { int n_sub = n; // number of points in subset int n_goal = (int) (n*BD_FRACTION); // number of point in goal int n_splits = 0; // number of splits needed // initialize inner box to bounding box annAssignRect(dim, inner_box, bnd_box); while (n_sub > n_goal) { // keep splitting until goal reached int cd; // cut dim from splitter (ignored) ANNcoord cv; // cut value from splitter (ignored) int n_lo; // number of points on low side // invoke splitting procedure (*splitter)(pa, pidx, inner_box, n_sub, dim, cd, cv, n_lo); n_splits++; // increment split count if (n_lo >= n_sub/2) { // most points on low side inner_box.hi[cd] = cv; // collapse high side n_sub = n_lo; // recurse on lower points } else { // most points on high side inner_box.lo[cd] = cv; // collapse low side pidx += n_lo; // recurse on higher points n_sub -= n_lo; } } if (n_splits > dim*BD_MAX_SPLIT_FAC)// took too many splits return SHRINK; // shrink to final subset else return SPLIT; } //---------------------------------------------------------------------- // selectDecomp - select which decomposition to use //---------------------------------------------------------------------- ANNdecomp selectDecomp( // select decomposition method ANNpointArray pa, // point array ANNidxArray pidx, // point indices to store in subtree int n, // number of points int dim, // dimension of space const ANNorthRect &bnd_box, // current bounding box ANNkd_splitter splitter, // splitting procedure ANNshrinkRule shrink, // shrinking rule ANNorthRect &inner_box) // inner box if shrinking (returned) { ANNdecomp decomp = SPLIT; // decomposition switch (shrink) { // check shrinking rule case ANN_BD_NONE: // no shrinking allowed decomp = SPLIT; break; case ANN_BD_SUGGEST: // author's suggestion case ANN_BD_SIMPLE: // simple shrink decomp = trySimpleShrink( pa, pidx, // points and indices n, dim, // number of points and dimension bnd_box, // current bounding box inner_box); // inner box if shrinking (returned) break; case ANN_BD_CENTROID: // centroid shrink decomp = tryCentroidShrink( pa, pidx, // points and indices n, dim, // number of points and dimension bnd_box, // current bounding box splitter, // splitting procedure inner_box); // inner box if shrinking (returned) break; default: annError("Illegal shrinking rule", ANNabort); } return decomp; } //---------------------------------------------------------------------- // rbd_tree - recursive procedure to build a bd-tree // // This is analogous to rkd_tree, but for bd-trees. See the // procedure rkd_tree() in kd_split.cpp for more information. // // If the number of points falls below the bucket size, then a // leaf node is created for the points. Otherwise we invoke the // procedure selectDecomp() which determines whether we are to // split or shrink. If splitting is chosen, then we essentially // do exactly as rkd_tree() would, and invoke the specified // splitting procedure to the points. Otherwise, the selection // procedure returns a bounding box, from which we extract the // appropriate shrinking bounds, and create a shrinking node. // Finally the points are subdivided, and the procedure is // invoked recursively on the two subsets to form the children. //---------------------------------------------------------------------- ANNkd_ptr rbd_tree( // recursive construction of bd-tree ANNpointArray pa, // point array ANNidxArray pidx, // point indices to store in subtree int n, // number of points int dim, // dimension of space int bsp, // bucket space ANNorthRect &bnd_box, // bounding box for current node ANNkd_splitter splitter, // splitting routine ANNshrinkRule shrink) // shrinking rule { ANNdecomp decomp; // decomposition method ANNorthRect inner_box(dim); // inner box (if shrinking) if (n <= bsp) { // n small, make a leaf node if (n == 0) // empty leaf node return KD_TRIVIAL; // return (canonical) empty leaf else // construct the node and return return new ANNkd_leaf(n, pidx); } decomp = selectDecomp( // select decomposition method pa, pidx, // points and indices n, dim, // number of points and dimension bnd_box, // current bounding box splitter, shrink, // splitting/shrinking methods inner_box); // inner box if shrinking (returned) if (decomp == SPLIT) { // split selected int cd; // cutting dimension ANNcoord cv; // cutting value int n_lo; // number on low side of cut // invoke splitting procedure (*splitter)(pa, pidx, bnd_box, n, dim, cd, cv, n_lo); ANNcoord lv = bnd_box.lo[cd]; // save bounds for cutting dimension ANNcoord hv = bnd_box.hi[cd]; bnd_box.hi[cd] = cv; // modify bounds for left subtree ANNkd_ptr lo = rbd_tree( // build left subtree pa, pidx, n_lo, // ...from pidx[0..n_lo-1] dim, bsp, bnd_box, splitter, shrink); bnd_box.hi[cd] = hv; // restore bounds bnd_box.lo[cd] = cv; // modify bounds for right subtree ANNkd_ptr hi = rbd_tree( // build right subtree pa, pidx + n_lo, n-n_lo,// ...from pidx[n_lo..n-1] dim, bsp, bnd_box, splitter, shrink); bnd_box.lo[cd] = lv; // restore bounds // create the splitting node return new ANNkd_split(cd, cv, lv, hv, lo, hi); } else { // shrink selected int n_in; // number of points in box int n_bnds; // number of bounding sides annBoxSplit( // split points around inner box pa, // points to split pidx, // point indices n, // number of points dim, // dimension inner_box, // inner box n_in); // number of points inside (returned) ANNkd_ptr in = rbd_tree( // build inner subtree pidx[0..n_in-1] pa, pidx, n_in, dim, bsp, inner_box, splitter, shrink); ANNkd_ptr out = rbd_tree( // build outer subtree pidx[n_in..n] pa, pidx+n_in, n - n_in, dim, bsp, bnd_box, splitter, shrink); ANNorthHSArray bnds = NULL; // bounds (alloc in Box2Bnds and // ...freed in bd_shrink destroyer) annBox2Bnds( // convert inner box to bounds inner_box, // inner box bnd_box, // enclosing box dim, // dimension n_bnds, // number of bounds (returned) bnds); // bounds array (modified) // return shrinking node return new ANNbd_shrink(n_bnds, bnds, in, out); } } ann-1.1.2+doc/src/kd_pr_search.h0000644000175000017500000000375311330212441017275 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_pr_search.h // Programmer: Sunil Arya and David Mount // Description: Priority kd-tree search // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release //---------------------------------------------------------------------- #ifndef ANN_kd_pr_search_H #define ANN_kd_pr_search_H #include "kd_tree.h" // kd-tree declarations #include "kd_util.h" // kd-tree utilities #include "pr_queue.h" // priority queue declarations #include "pr_queue_k.h" // k-element priority queue #include // performance evaluation //---------------------------------------------------------------------- // Global variables // Active for the life of each call to Appx_Near_Neigh() or // Appx_k_Near_Neigh(). //---------------------------------------------------------------------- extern double ANNprEps; // the error bound extern int ANNprDim; // dimension of space extern ANNpoint ANNprQ; // query point extern double ANNprMaxErr; // max tolerable squared error extern ANNpointArray ANNprPts; // the points extern ANNpr_queue *ANNprBoxPQ; // priority queue for boxes extern ANNmin_k *ANNprPointMK; // set of k closest points #endif ann-1.1.2+doc/src/bd_search.cpp0000644000175000017500000000515411330212441017113 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: bd_search.cpp // Programmer: David Mount // Description: Standard bd-tree search // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release //---------------------------------------------------------------------- #include "bd_tree.h" // bd-tree declarations #include "kd_search.h" // kd-tree search declarations //---------------------------------------------------------------------- // Approximate searching for bd-trees. // See the file kd_search.cpp for general information on the // approximate nearest neighbor search algorithm. Here we // include the extensions for shrinking nodes. //---------------------------------------------------------------------- //---------------------------------------------------------------------- // bd_shrink::ann_search - search a shrinking node //---------------------------------------------------------------------- void ANNbd_shrink::ann_search(ANNdist box_dist) { // check dist calc term cond. if (ANNmaxPtsVisited != 0 && ANNptsVisited > ANNmaxPtsVisited) return; ANNdist inner_dist = 0; // distance to inner box for (int i = 0; i < n_bnds; i++) { // is query point in the box? if (bnds[i].out(ANNkdQ)) { // outside this bounding side? // add to inner distance inner_dist = (ANNdist) ANN_SUM(inner_dist, bnds[i].dist(ANNkdQ)); } } if (inner_dist <= box_dist) { // if inner box is closer child[ANN_IN]->ann_search(inner_dist); // search inner child first child[ANN_OUT]->ann_search(box_dist); // ...then outer child } else { // if outer box is closer child[ANN_OUT]->ann_search(box_dist); // search outer child first child[ANN_IN]->ann_search(inner_dist); // ...then outer child } ANN_FLOP(3*n_bnds) // increment floating ops ANN_SHR(1) // one more shrinking node } ann-1.1.2+doc/src/pr_queue.h0000644000175000017500000001061711330212441016473 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: pr_queue.h // Programmer: Sunil Arya and David Mount // Description: Include file for priority queue and related // structures. // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release //---------------------------------------------------------------------- #ifndef PR_QUEUE_H #define PR_QUEUE_H #include // all ANN includes #include // performance evaluation //---------------------------------------------------------------------- // Basic types. //---------------------------------------------------------------------- typedef void *PQinfo; // info field is generic pointer typedef ANNdist PQkey; // key field is distance //---------------------------------------------------------------------- // Priority queue // A priority queue is a list of items, along with associated // priorities. The basic operations are insert and extract_minimum. // // The priority queue is maintained using a standard binary heap. // (Implementation note: Indexing is performed from [1..max] rather // than the C standard of [0..max-1]. This simplifies parent/child // computations.) User information consists of a void pointer, // and the user is responsible for casting this quantity into whatever // useful form is desired. // // Because the priority queue is so central to the efficiency of // query processing, all the code is inline. //---------------------------------------------------------------------- class ANNpr_queue { struct pq_node { // node in priority queue PQkey key; // key value PQinfo info; // info field }; int n; // number of items in queue int max_size; // maximum queue size pq_node *pq; // the priority queue (array of nodes) public: ANNpr_queue(int max) // constructor (given max size) { n = 0; // initially empty max_size = max; // maximum number of items pq = new pq_node[max+1]; // queue is array [1..max] of nodes } ~ANNpr_queue() // destructor { delete [] pq; } ANNbool empty() // is queue empty? { if (n==0) return ANNtrue; else return ANNfalse; } ANNbool non_empty() // is queue nonempty? { if (n==0) return ANNfalse; else return ANNtrue; } void reset() // make existing queue empty { n = 0; } inline void insert( // insert item (inlined for speed) PQkey kv, // key value PQinfo inf) // item info { if (++n > max_size) annError("Priority queue overflow.", ANNabort); register int r = n; while (r > 1) { // sift up new item register int p = r/2; ANN_FLOP(1) // increment floating ops if (pq[p].key <= kv) // in proper order break; pq[r] = pq[p]; // else swap with parent r = p; } pq[r].key = kv; // insert new item at final location pq[r].info = inf; } inline void extr_min( // extract minimum (inlined for speed) PQkey &kv, // key (returned) PQinfo &inf) // item info (returned) { kv = pq[1].key; // key of min item inf = pq[1].info; // information of min item register PQkey kn = pq[n--].key;// last item in queue register int p = 1; // p points to item out of position register int r = p<<1; // left child of p while (r <= n) { // while r is still within the heap ANN_FLOP(2) // increment floating ops // set r to smaller child of p if (r < n && pq[r].key > pq[r+1].key) r++; if (kn <= pq[r].key) // in proper order break; pq[p] = pq[r]; // else swap with child p = r; // advance pointers r = p<<1; } pq[p] = pq[n+1]; // insert last item in proper place } }; #endif ann-1.1.2+doc/src/bd_fix_rad_search.cpp0000644000175000017500000000522111330212441020602 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: bd_fix_rad_search.cpp // Programmer: David Mount // Description: Standard bd-tree search // Last modified: 05/03/05 (Version 1.1) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 1.1 05/03/05 // Initial release //---------------------------------------------------------------------- #include "bd_tree.h" // bd-tree declarations #include "kd_fix_rad_search.h" // kd-tree FR search declarations //---------------------------------------------------------------------- // Approximate searching for bd-trees. // See the file kd_FR_search.cpp for general information on the // approximate nearest neighbor search algorithm. Here we // include the extensions for shrinking nodes. //---------------------------------------------------------------------- //---------------------------------------------------------------------- // bd_shrink::ann_FR_search - search a shrinking node //---------------------------------------------------------------------- void ANNbd_shrink::ann_FR_search(ANNdist box_dist) { // check dist calc term cond. if (ANNmaxPtsVisited != 0 && ANNptsVisited > ANNmaxPtsVisited) return; ANNdist inner_dist = 0; // distance to inner box for (int i = 0; i < n_bnds; i++) { // is query point in the box? if (bnds[i].out(ANNkdFRQ)) { // outside this bounding side? // add to inner distance inner_dist = (ANNdist) ANN_SUM(inner_dist, bnds[i].dist(ANNkdFRQ)); } } if (inner_dist <= box_dist) { // if inner box is closer child[ANN_IN]->ann_FR_search(inner_dist);// search inner child first child[ANN_OUT]->ann_FR_search(box_dist);// ...then outer child } else { // if outer box is closer child[ANN_OUT]->ann_FR_search(box_dist);// search outer child first child[ANN_IN]->ann_FR_search(inner_dist);// ...then outer child } ANN_FLOP(3*n_bnds) // increment floating ops ANN_SHR(1) // one more shrinking node } ann-1.1.2+doc/src/perf.cpp0000644000175000017500000001236311330212441016135 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: perf.cpp // Programmer: Sunil Arya and David Mount // Description: Methods for performance stats // Last modified: 01/27/10 (Version 1.1.2) //---------------------------------------------------------------------- // Copyright (c) 1997-2010 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.0 04/01/05 // Changed names to avoid namespace conflicts. // Added flush after printing performance stats to fix bug // in Microsoft Windows version. // Revision 1.1.2 01/27/10 // Fixed minor compilation bugs for new versions of gcc //---------------------------------------------------------------------- #include // basic ANN includes #include // performance includes using namespace std; // make std:: available //---------------------------------------------------------------------- // Performance statistics // The following data and routines are used for computing // performance statistics for nearest neighbor searching. // Because these routines can slow the code down, they can be // activated and deactiviated by defining the PERF variable, // by compiling with the option: -DPERF //---------------------------------------------------------------------- //---------------------------------------------------------------------- // Global counters for performance measurement //---------------------------------------------------------------------- int ann_Ndata_pts = 0; // number of data points int ann_Nvisit_lfs = 0; // number of leaf nodes visited int ann_Nvisit_spl = 0; // number of splitting nodes visited int ann_Nvisit_shr = 0; // number of shrinking nodes visited int ann_Nvisit_pts = 0; // visited points for one query int ann_Ncoord_hts = 0; // coordinate hits for one query int ann_Nfloat_ops = 0; // floating ops for one query ANNsampStat ann_visit_lfs; // stats on leaf nodes visits ANNsampStat ann_visit_spl; // stats on splitting nodes visits ANNsampStat ann_visit_shr; // stats on shrinking nodes visits ANNsampStat ann_visit_nds; // stats on total nodes visits ANNsampStat ann_visit_pts; // stats on points visited ANNsampStat ann_coord_hts; // stats on coordinate hits ANNsampStat ann_float_ops; // stats on floating ops // ANNsampStat ann_average_err; // average error ANNsampStat ann_rank_err; // rank error //---------------------------------------------------------------------- // Routines for statistics. //---------------------------------------------------------------------- DLL_API void annResetStats(int data_size) // reset stats for a set of queries { ann_Ndata_pts = data_size; ann_visit_lfs.reset(); ann_visit_spl.reset(); ann_visit_shr.reset(); ann_visit_nds.reset(); ann_visit_pts.reset(); ann_coord_hts.reset(); ann_float_ops.reset(); ann_average_err.reset(); ann_rank_err.reset(); } DLL_API void annResetCounts() // reset counts for one query { ann_Nvisit_lfs = 0; ann_Nvisit_spl = 0; ann_Nvisit_shr = 0; ann_Nvisit_pts = 0; ann_Ncoord_hts = 0; ann_Nfloat_ops = 0; } DLL_API void annUpdateStats() // update stats with current counts { ann_visit_lfs += ann_Nvisit_lfs; ann_visit_nds += ann_Nvisit_spl + ann_Nvisit_lfs; ann_visit_spl += ann_Nvisit_spl; ann_visit_shr += ann_Nvisit_shr; ann_visit_pts += ann_Nvisit_pts; ann_coord_hts += ann_Ncoord_hts; ann_float_ops += ann_Nfloat_ops; } // print a single statistic void print_one_stat(const char* title, ANNsampStat s, double div) { cout << title << "= [ "; cout.width(9); cout << s.mean()/div << " : "; cout.width(9); cout << s.stdDev()/div << " ]<"; cout.width(9); cout << s.min()/div << " , "; cout.width(9); cout << s.max()/div << " >\n"; } DLL_API void annPrintStats( // print statistics for a run ANNbool validate) // true if average errors desired { cout.precision(4); // set floating precision cout << " (Performance stats: " << " [ mean : stddev ]< min , max >\n"; print_one_stat(" leaf_nodes ", ann_visit_lfs, 1); print_one_stat(" splitting_nodes ", ann_visit_spl, 1); print_one_stat(" shrinking_nodes ", ann_visit_shr, 1); print_one_stat(" total_nodes ", ann_visit_nds, 1); print_one_stat(" points_visited ", ann_visit_pts, 1); print_one_stat(" coord_hits/pt ", ann_coord_hts, ann_Ndata_pts); print_one_stat(" floating_ops_(K) ", ann_float_ops, 1000); if (validate) { print_one_stat(" average_error ", ann_average_err, 1); print_one_stat(" rank_error ", ann_rank_err, 1); } cout.precision(0); // restore the default cout << " )\n"; cout.flush(); } ann-1.1.2+doc/src/kd_search.cpp0000644000175000017500000002072611330212441017126 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_search.cpp // Programmer: Sunil Arya and David Mount // Description: Standard kd-tree search // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.0 04/01/05 // Changed names LO, HI to ANN_LO, ANN_HI //---------------------------------------------------------------------- #include "kd_search.h" // kd-search declarations //---------------------------------------------------------------------- // Approximate nearest neighbor searching by kd-tree search // The kd-tree is searched for an approximate nearest neighbor. // The point is returned through one of the arguments, and the // distance returned is the squared distance to this point. // // The method used for searching the kd-tree is an approximate // adaptation of the search algorithm described by Friedman, // Bentley, and Finkel, ``An algorithm for finding best matches // in logarithmic expected time,'' ACM Transactions on Mathematical // Software, 3(3):209-226, 1977). // // The algorithm operates recursively. When first encountering a // node of the kd-tree we first visit the child which is closest to // the query point. On return, we decide whether we want to visit // the other child. If the box containing the other child exceeds // 1/(1+eps) times the current best distance, then we skip it (since // any point found in this child cannot be closer to the query point // by more than this factor.) Otherwise, we visit it recursively. // The distance between a box and the query point is computed exactly // (not approximated as is often done in kd-tree), using incremental // distance updates, as described by Arya and Mount in ``Algorithms // for fast vector quantization,'' Proc. of DCC '93: Data Compression // Conference, eds. J. A. Storer and M. Cohn, IEEE Press, 1993, // 381-390. // // The main entry points is annkSearch() which sets things up and // then call the recursive routine ann_search(). This is a recursive // routine which performs the processing for one node in the kd-tree. // There are two versions of this virtual procedure, one for splitting // nodes and one for leaves. When a splitting node is visited, we // determine which child to visit first (the closer one), and visit // the other child on return. When a leaf is visited, we compute // the distances to the points in the buckets, and update information // on the closest points. // // Some trickery is used to incrementally update the distance from // a kd-tree rectangle to the query point. This comes about from // the fact that which each successive split, only one component // (along the dimension that is split) of the squared distance to // the child rectangle is different from the squared distance to // the parent rectangle. //---------------------------------------------------------------------- //---------------------------------------------------------------------- // To keep argument lists short, a number of global variables // are maintained which are common to all the recursive calls. // These are given below. //---------------------------------------------------------------------- int ANNkdDim; // dimension of space ANNpoint ANNkdQ; // query point double ANNkdMaxErr; // max tolerable squared error ANNpointArray ANNkdPts; // the points ANNmin_k *ANNkdPointMK; // set of k closest points //---------------------------------------------------------------------- // annkSearch - search for the k nearest neighbors //---------------------------------------------------------------------- void ANNkd_tree::annkSearch( ANNpoint q, // the query point int k, // number of near neighbors to return ANNidxArray nn_idx, // nearest neighbor indices (returned) ANNdistArray dd, // the approximate nearest neighbor double eps) // the error bound { ANNkdDim = dim; // copy arguments to static equivs ANNkdQ = q; ANNkdPts = pts; ANNptsVisited = 0; // initialize count of points visited if (k > n_pts) { // too many near neighbors? annError("Requesting more near neighbors than data points", ANNabort); } ANNkdMaxErr = ANN_POW(1.0 + eps); ANN_FLOP(2) // increment floating op count ANNkdPointMK = new ANNmin_k(k); // create set for closest k points // search starting at the root root->ann_search(annBoxDistance(q, bnd_box_lo, bnd_box_hi, dim)); for (int i = 0; i < k; i++) { // extract the k-th closest points dd[i] = ANNkdPointMK->ith_smallest_key(i); nn_idx[i] = ANNkdPointMK->ith_smallest_info(i); } delete ANNkdPointMK; // deallocate closest point set } //---------------------------------------------------------------------- // kd_split::ann_search - search a splitting node //---------------------------------------------------------------------- void ANNkd_split::ann_search(ANNdist box_dist) { // check dist calc term condition if (ANNmaxPtsVisited != 0 && ANNptsVisited > ANNmaxPtsVisited) return; // distance to cutting plane ANNcoord cut_diff = ANNkdQ[cut_dim] - cut_val; if (cut_diff < 0) { // left of cutting plane child[ANN_LO]->ann_search(box_dist);// visit closer child first ANNcoord box_diff = cd_bnds[ANN_LO] - ANNkdQ[cut_dim]; if (box_diff < 0) // within bounds - ignore box_diff = 0; // distance to further box box_dist = (ANNdist) ANN_SUM(box_dist, ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff))); // visit further child if close enough if (box_dist * ANNkdMaxErr < ANNkdPointMK->max_key()) child[ANN_HI]->ann_search(box_dist); } else { // right of cutting plane child[ANN_HI]->ann_search(box_dist);// visit closer child first ANNcoord box_diff = ANNkdQ[cut_dim] - cd_bnds[ANN_HI]; if (box_diff < 0) // within bounds - ignore box_diff = 0; // distance to further box box_dist = (ANNdist) ANN_SUM(box_dist, ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff))); // visit further child if close enough if (box_dist * ANNkdMaxErr < ANNkdPointMK->max_key()) child[ANN_LO]->ann_search(box_dist); } ANN_FLOP(10) // increment floating ops ANN_SPL(1) // one more splitting node visited } //---------------------------------------------------------------------- // kd_leaf::ann_search - search points in a leaf node // Note: The unreadability of this code is the result of // some fine tuning to replace indexing by pointer operations. //---------------------------------------------------------------------- void ANNkd_leaf::ann_search(ANNdist box_dist) { register ANNdist dist; // distance to data point register ANNcoord* pp; // data coordinate pointer register ANNcoord* qq; // query coordinate pointer register ANNdist min_dist; // distance to k-th closest point register ANNcoord t; register int d; min_dist = ANNkdPointMK->max_key(); // k-th smallest distance so far for (int i = 0; i < n_pts; i++) { // check points in bucket pp = ANNkdPts[bkt[i]]; // first coord of next data point qq = ANNkdQ; // first coord of query point dist = 0; for(d = 0; d < ANNkdDim; d++) { ANN_COORD(1) // one more coordinate hit ANN_FLOP(4) // increment floating ops t = *(qq++) - *(pp++); // compute length and adv coordinate // exceeds dist to k-th smallest? if( (dist = ANN_SUM(dist, ANN_POW(t))) > min_dist) { break; } } if (d >= ANNkdDim && // among the k best? (ANN_ALLOW_SELF_MATCH || dist!=0)) { // and no self-match problem // add it to the list ANNkdPointMK->insert(dist, bkt[i]); min_dist = ANNkdPointMK->max_key(); } } ANN_LEAF(1) // one more leaf node visited ANN_PTS(n_pts) // increment points visited ANNptsVisited += n_pts; // increment number of points visited } ann-1.1.2+doc/src/kd_util.h0000644000175000017500000001121711330212441016276 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_util.h // Programmer: Sunil Arya and David Mount // Description: Common utilities for kd- trees // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release //---------------------------------------------------------------------- #ifndef ANN_kd_util_H #define ANN_kd_util_H #include "kd_tree.h" // kd-tree declarations //---------------------------------------------------------------------- // externally accessible functions //---------------------------------------------------------------------- double annAspectRatio( // compute aspect ratio of box int dim, // dimension const ANNorthRect &bnd_box); // bounding cube void annEnclRect( // compute smallest enclosing rectangle ANNpointArray pa, // point array ANNidxArray pidx, // point indices int n, // number of points int dim, // dimension ANNorthRect &bnds); // bounding cube (returned) void annEnclCube( // compute smallest enclosing cube ANNpointArray pa, // point array ANNidxArray pidx, // point indices int n, // number of points int dim, // dimension ANNorthRect &bnds); // bounding cube (returned) ANNdist annBoxDistance( // compute distance from point to box const ANNpoint q, // the point const ANNpoint lo, // low point of box const ANNpoint hi, // high point of box int dim); // dimension of space ANNcoord annSpread( // compute point spread along dimension ANNpointArray pa, // point array ANNidxArray pidx, // point indices int n, // number of points int d); // dimension to check void annMinMax( // compute min and max coordinates along dim ANNpointArray pa, // point array ANNidxArray pidx, // point indices int n, // number of points int d, // dimension to check ANNcoord& min, // minimum value (returned) ANNcoord& max); // maximum value (returned) int annMaxSpread( // compute dimension of max spread ANNpointArray pa, // point array ANNidxArray pidx, // point indices int n, // number of points int dim); // dimension of space void annMedianSplit( // split points along median value ANNpointArray pa, // points to split ANNidxArray pidx, // point indices int n, // number of points int d, // dimension along which to split ANNcoord &cv, // cutting value int n_lo); // split into n_lo and n-n_lo void annPlaneSplit( // split points by a plane ANNpointArray pa, // points to split ANNidxArray pidx, // point indices int n, // number of points int d, // dimension along which to split ANNcoord cv, // cutting value int &br1, // first break (values < cv) int &br2); // second break (values == cv) void annBoxSplit( // split points by a box ANNpointArray pa, // points to split ANNidxArray pidx, // point indices int n, // number of points int dim, // dimension of space ANNorthRect &box, // the box int &n_in); // number of points inside (returned) int annSplitBalance( // determine balance factor of a split ANNpointArray pa, // points to split ANNidxArray pidx, // point indices int n, // number of points int d, // dimension along which to split ANNcoord cv); // cutting value void annBox2Bnds( // convert inner box to bounds const ANNorthRect &inner_box, // inner box const ANNorthRect &bnd_box, // enclosing box int dim, // dimension of space int &n_bnds, // number of bounds (returned) ANNorthHSArray &bnds); // bounds array (returned) void annBnds2Box( // convert bounds to inner box const ANNorthRect &bnd_box, // enclosing box int dim, // dimension of space int n_bnds, // number of bounds ANNorthHSArray bnds, // bounds array ANNorthRect &inner_box); // inner box (returned) #endif ann-1.1.2+doc/src/kd_pr_search.cpp0000644000175000017500000002131511330212441017622 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: kd_pr_search.cpp // Programmer: Sunil Arya and David Mount // Description: Priority search for kd-trees // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release //---------------------------------------------------------------------- #include "kd_pr_search.h" // kd priority search declarations //---------------------------------------------------------------------- // Approximate nearest neighbor searching by priority search. // The kd-tree is searched for an approximate nearest neighbor. // The point is returned through one of the arguments, and the // distance returned is the SQUARED distance to this point. // // The method used for searching the kd-tree is called priority // search. (It is described in Arya and Mount, ``Algorithms for // fast vector quantization,'' Proc. of DCC '93: Data Compression // Conference}, eds. J. A. Storer and M. Cohn, IEEE Press, 1993, // 381--390.) // // The cell of the kd-tree containing the query point is located, // and cells are visited in increasing order of distance from the // query point. This is done by placing each subtree which has // NOT been visited in a priority queue, according to the closest // distance of the corresponding enclosing rectangle from the // query point. The search stops when the distance to the nearest // remaining rectangle exceeds the distance to the nearest point // seen by a factor of more than 1/(1+eps). (Implying that any // point found subsequently in the search cannot be closer by more // than this factor.) // // The main entry point is annkPriSearch() which sets things up and // then call the recursive routine ann_pri_search(). This is a // recursive routine which performs the processing for one node in // the kd-tree. There are two versions of this virtual procedure, // one for splitting nodes and one for leaves. When a splitting node // is visited, we determine which child to continue the search on // (the closer one), and insert the other child into the priority // queue. When a leaf is visited, we compute the distances to the // points in the buckets, and update information on the closest // points. // // Some trickery is used to incrementally update the distance from // a kd-tree rectangle to the query point. This comes about from // the fact that which each successive split, only one component // (along the dimension that is split) of the squared distance to // the child rectangle is different from the squared distance to // the parent rectangle. //---------------------------------------------------------------------- //---------------------------------------------------------------------- // To keep argument lists short, a number of global variables // are maintained which are common to all the recursive calls. // These are given below. //---------------------------------------------------------------------- double ANNprEps; // the error bound int ANNprDim; // dimension of space ANNpoint ANNprQ; // query point double ANNprMaxErr; // max tolerable squared error ANNpointArray ANNprPts; // the points ANNpr_queue *ANNprBoxPQ; // priority queue for boxes ANNmin_k *ANNprPointMK; // set of k closest points //---------------------------------------------------------------------- // annkPriSearch - priority search for k nearest neighbors //---------------------------------------------------------------------- void ANNkd_tree::annkPriSearch( ANNpoint q, // query point int k, // number of near neighbors to return ANNidxArray nn_idx, // nearest neighbor indices (returned) ANNdistArray dd, // dist to near neighbors (returned) double eps) // error bound (ignored) { // max tolerable squared error ANNprMaxErr = ANN_POW(1.0 + eps); ANN_FLOP(2) // increment floating ops ANNprDim = dim; // copy arguments to static equivs ANNprQ = q; ANNprPts = pts; ANNptsVisited = 0; // initialize count of points visited ANNprPointMK = new ANNmin_k(k); // create set for closest k points // distance to root box ANNdist box_dist = annBoxDistance(q, bnd_box_lo, bnd_box_hi, dim); ANNprBoxPQ = new ANNpr_queue(n_pts);// create priority queue for boxes ANNprBoxPQ->insert(box_dist, root); // insert root in priority queue while (ANNprBoxPQ->non_empty() && (!(ANNmaxPtsVisited != 0 && ANNptsVisited > ANNmaxPtsVisited))) { ANNkd_ptr np; // next box from prior queue // extract closest box from queue ANNprBoxPQ->extr_min(box_dist, (void *&) np); ANN_FLOP(2) // increment floating ops if (box_dist*ANNprMaxErr >= ANNprPointMK->max_key()) break; np->ann_pri_search(box_dist); // search this subtree. } for (int i = 0; i < k; i++) { // extract the k-th closest points dd[i] = ANNprPointMK->ith_smallest_key(i); nn_idx[i] = ANNprPointMK->ith_smallest_info(i); } delete ANNprPointMK; // deallocate closest point set delete ANNprBoxPQ; // deallocate priority queue } //---------------------------------------------------------------------- // kd_split::ann_pri_search - search a splitting node //---------------------------------------------------------------------- void ANNkd_split::ann_pri_search(ANNdist box_dist) { ANNdist new_dist; // distance to child visited later // distance to cutting plane ANNcoord cut_diff = ANNprQ[cut_dim] - cut_val; if (cut_diff < 0) { // left of cutting plane ANNcoord box_diff = cd_bnds[ANN_LO] - ANNprQ[cut_dim]; if (box_diff < 0) // within bounds - ignore box_diff = 0; // distance to further box new_dist = (ANNdist) ANN_SUM(box_dist, ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff))); if (child[ANN_HI] != KD_TRIVIAL)// enqueue if not trivial ANNprBoxPQ->insert(new_dist, child[ANN_HI]); // continue with closer child child[ANN_LO]->ann_pri_search(box_dist); } else { // right of cutting plane ANNcoord box_diff = ANNprQ[cut_dim] - cd_bnds[ANN_HI]; if (box_diff < 0) // within bounds - ignore box_diff = 0; // distance to further box new_dist = (ANNdist) ANN_SUM(box_dist, ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff))); if (child[ANN_LO] != KD_TRIVIAL)// enqueue if not trivial ANNprBoxPQ->insert(new_dist, child[ANN_LO]); // continue with closer child child[ANN_HI]->ann_pri_search(box_dist); } ANN_SPL(1) // one more splitting node visited ANN_FLOP(8) // increment floating ops } //---------------------------------------------------------------------- // kd_leaf::ann_pri_search - search points in a leaf node // // This is virtually identical to the ann_search for standard search. //---------------------------------------------------------------------- void ANNkd_leaf::ann_pri_search(ANNdist box_dist) { register ANNdist dist; // distance to data point register ANNcoord* pp; // data coordinate pointer register ANNcoord* qq; // query coordinate pointer register ANNdist min_dist; // distance to k-th closest point register ANNcoord t; register int d; min_dist = ANNprPointMK->max_key(); // k-th smallest distance so far for (int i = 0; i < n_pts; i++) { // check points in bucket pp = ANNprPts[bkt[i]]; // first coord of next data point qq = ANNprQ; // first coord of query point dist = 0; for(d = 0; d < ANNprDim; d++) { ANN_COORD(1) // one more coordinate hit ANN_FLOP(4) // increment floating ops t = *(qq++) - *(pp++); // compute length and adv coordinate // exceeds dist to k-th smallest? if( (dist = ANN_SUM(dist, ANN_POW(t))) > min_dist) { break; } } if (d >= ANNprDim && // among the k best? (ANN_ALLOW_SELF_MATCH || dist!=0)) { // and no self-match problem // add it to the list ANNprPointMK->insert(dist, bkt[i]); min_dist = ANNprPointMK->max_key(); } } ANN_LEAF(1) // one more leaf node visited ANN_PTS(n_pts) // increment points visited ANNptsVisited += n_pts; // increment number of points visited } ann-1.1.2+doc/src/bd_pr_search.cpp0000644000175000017500000000525311330212441017614 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: bd_pr_search.cpp // Programmer: David Mount // Description: Priority search for bd-trees // Last modified: 01/04/05 (Version 1.0) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- //History: // Revision 0.1 03/04/98 // Initial release //---------------------------------------------------------------------- #include "bd_tree.h" // bd-tree declarations #include "kd_pr_search.h" // kd priority search declarations //---------------------------------------------------------------------- // Approximate priority searching for bd-trees. // See the file kd_pr_search.cc for general information on the // approximate nearest neighbor priority search algorithm. Here // we include the extensions for shrinking nodes. //---------------------------------------------------------------------- //---------------------------------------------------------------------- // bd_shrink::ann_search - search a shrinking node //---------------------------------------------------------------------- void ANNbd_shrink::ann_pri_search(ANNdist box_dist) { ANNdist inner_dist = 0; // distance to inner box for (int i = 0; i < n_bnds; i++) { // is query point in the box? if (bnds[i].out(ANNprQ)) { // outside this bounding side? // add to inner distance inner_dist = (ANNdist) ANN_SUM(inner_dist, bnds[i].dist(ANNprQ)); } } if (inner_dist <= box_dist) { // if inner box is closer if (child[ANN_OUT] != KD_TRIVIAL) // enqueue outer if not trivial ANNprBoxPQ->insert(box_dist,child[ANN_OUT]); // continue with inner child child[ANN_IN]->ann_pri_search(inner_dist); } else { // if outer box is closer if (child[ANN_IN] != KD_TRIVIAL) // enqueue inner if not trivial ANNprBoxPQ->insert(inner_dist,child[ANN_IN]); // continue with outer child child[ANN_OUT]->ann_pri_search(box_dist); } ANN_FLOP(3*n_bnds) // increment floating ops ANN_SHR(1) // one more shrinking node } ann-1.1.2+doc/Makefile0000644000175000017500000001101111330212441015333 0ustar sylvestresylvestre#----------------------------------------------------------------------------- # Top-level Makefile for ANN. # # ANN: Approximate Nearest Neighbors # Version: 1.1 05/03/05 #----------------------------------------------------------------------------- # Copyright (c) 1997-2005 University of Maryland and Sunil Arya and # David Mount. All Rights Reserved. # # This software and related documentation is part of the Approximate # Nearest Neighbor Library (ANN). This software is provided under # the provisions of the Lesser GNU Public License (LGPL). See the # file ../ReadMe.txt for further information. # # The University of Maryland (U.M.) and the authors make no # representations about the suitability or fitness of this software for # any purpose. It is provided "as is" without express or implied # warranty. #----------------------------------------------------------------------------- # Revision 0.1 09/06/97 # alpha release # Revision 0.2 06/26/98 # Minor changes to fix compilation errors on SGI systems. # Revision 1.0 04/01/05 # Initial release (finally!) # Added linux-g++ target # Revision 1.1 05/03/05 # Added macosx-g++ target #----------------------------------------------------------------------------- #----------------------------------------------------------------------------- # default: list the options # The following legacy targets are also available. # make sunos4 for Sun with SunOS 4.x # make sunos4-g++ for Sun with SunOS 4.x and g++ # make alpha-g++ for DEC Alpha and g++ # The following targets are used for internal development only # make authors-debug author's debugging # make authors-perf author's performance evaluations # make distribution author's generation of distribution file #----------------------------------------------------------------------------- default: @echo "Enter one of the following:" @echo " make linux-g++ for Linux and g++" @echo " make macosx-g++ for Mac OS X and g++" @echo " make sunos5 for Sun with SunOS 5.x" @echo " make sunos5-sl for Sun with SunOS 5.x, make shared libs" @echo " make sunos5-g++ for Sun with SunOS 5.x and g++" @echo " make sunos5-g++-sl for Sun with SunOS 5.x, g++, make shared libs" @echo " make clean remove .o files" @echo " make realclean remove .o, library and executable files" @echo " " @echo "See file Makefile for other compilation options, such as disabling" @echo "performance measurement code." #----------------------------------------------------------------------------- # main make entry point #----------------------------------------------------------------------------- alpha-g++ macosx-g++ linux-g++ sgi sunos4 sunos4-g++ sunos5 sunos5-g++ sunos5-g++-sl authors-debug authors-perf: cd src ; $(MAKE) $@ cd test ; $(MAKE) $@ cd sample ; $(MAKE) $@ cd ann2fig ; $(MAKE) $@ #----------------------------------------------------------------------------- # Remove .o files and core files #----------------------------------------------------------------------------- clean: cd src ; $(MAKE) clean cd test ; $(MAKE) clean cd sample ; $(MAKE) clean cd ann2fig ; $(MAKE) clean cd doc ; $(MAKE) clean cd MS_Win32; $(MAKE) clean cd validate ; $(MAKE) clean #----------------------------------------------------------------------------- # Remove everthing that can be remade #----------------------------------------------------------------------------- realclean: -rm -f lib/* -rm -f bin/* cd src ; $(MAKE) realclean cd test ; $(MAKE) realclean cd sample ; $(MAKE) realclean cd ann2fig ; $(MAKE) realclean cd doc ; $(MAKE) realclean cd MS_Win32; $(MAKE) realclean cd validate ; $(MAKE) realclean #----------------------------------------------------------------------------- # Make distribution package (for use by authors only) #----------------------------------------------------------------------------- DISTR = ann_1.1.2 distribution: realclean cd .. ; mv -f $(DISTR) $(DISTR)-old; mkdir $(DISTR) cp Copyright.txt ../$(DISTR) cp License.txt ../$(DISTR) cp Make-config ../$(DISTR) cp Makefile ../$(DISTR) cp ReadMe.txt ../$(DISTR) cp -r MS_Win32 ../$(DISTR) # cd ..; mv -f $(DISTR)_MS_Win32_bin $(DISTR)_MS_Win32_bin-old cp -r MS_Win32_bin ../$(DISTR)_MS_Win32_bin cp -r bin ../$(DISTR) cp -r include ../$(DISTR) cp -r lib ../$(DISTR) cp -r src ../$(DISTR) cp -r test ../$(DISTR) cp -r sample ../$(DISTR) cp -r ann2fig ../$(DISTR) cd ../$(DISTR); mkdir doc cp doc/*.pdf ../$(DISTR)/doc # cd .. ; tar -cfv $(DISTR).tar $(DISTR) ; gzip $(DISTR).tar ann-1.1.2+doc/test/0000755000175000017500000000000011330212441014660 5ustar sylvestresylvestreann-1.1.2+doc/test/ann_test.cpp0000644000175000017500000017263711330212441017217 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: ann_test.cpp // Programmer: Sunil Arya and David Mount // Description: test program for ANN (approximate nearest neighbors) // Last modified: 01/27/10 (Version 1.1.2) //---------------------------------------------------------------------- // Copyright (c) 1997-2010 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 0.2 06/26/98 // Added CLOCKS_PER_SEC definition if needed // Revision 1.0 04/01/05 // Added comments (from "#" to eol) // Added clus_orth_flats and clus_ellipsoids distributions // Fixed order of fair and midpt in split_table // Added dump/load operations // Cleaned up C++ for modern compilers // Revision 1.1 05/03/05 // Added fixed radius kNN search // Revision 1.1.1 08/04/06 // Added planted distribution // Revision 1.1.2 01/27/10 // Fixed minor compilation bugs for new versions of gcc // Allow round-off error in validation test //---------------------------------------------------------------------- #include // clock #include // math routines #include // C string ops #include // file I/O #include // ANN declarations #include // more ANN declarations #include // performance evaluation #include "rand.h" // random point generation #ifndef CLOCKS_PER_SEC // define clocks-per-second if needed #define CLOCKS_PER_SEC 1000000 #endif using namespace std; // make std:: available //---------------------------------------------------------------------- // ann_test // // This program is a driver for testing and evaluating the ANN library // for computing approximate nearest neighbors. It allows the user to // generate data and query sets of various sizes, dimensions, and // distributions, to build kd- and bbd-trees of various types, and then // run queries and outputting various performance statistics. // // Overview: // --------- // The test program is run as follows: // // ann_test < test_input > test_output // // where the test_input file contains a list of directives as described // below. Directives consist of a directive name, followed by list of // arguments (depending on the directive). Arguments and directives are // separated by white space (blank, tab, and newline). String arguments // are not quoted, and consist of a string of nonwhite chacters. A // character "#" denotes a comment. The following characters up to // the end of line are ignored. Comments may only be inserted between // directives (not within the argument list of a directive). // // Basic operations: // ----------------- // The test program can perform the following operations. How these // operations are performed depends on the options which are described // later. // // Data Generation: // ---------------- // read_data_pts Create a set of data points whose // coordinates are input from file . // gen_data_pts Create a set of data points whose // coordinates are generated from the // current point distribution. // // Building the tree: // ------------------ // build_ann Generate an approximate nearest neighbor // structure for the current data set, using // the selected splitting rules. Any existing // tree will be destroyed. // // Query Generation/Searching: // --------------------------- // read_query_pts Create a set of query points whose // coordinates are input from file . // gen_query_pts Create a set of query points whose // coordinates are generated from the // current point distribution. // run_queries Apply nearest neighbor searching to the // query points using the approximate nearest // neighbor structure and the given search // strategy. Possible strategies are: // standard = standard kd-tree search // priority = priority search // // Miscellaneous: // -------------- // output_label Output a label to the output file. // dump Dump the current structure to given file. // (The dump format is explained further in // the source file kd_tree.cc.) // load Load a tree from a data file which was // created by the dump operation. Any // existing tree will be destroyed. // // Options: // -------- // How these operations are performed depends on a set of options. // If an option is not specified, a default value is used. An option // retains its value until it is set again. String inputs are not // enclosed in quotes, and must contain no embedded white space (sorry, // this is C++'s convention). // // Options affecting search tree structure: // ---------------------------------------- // split_rule Type of splitting rule to use in building // the search tree. Choices are: // kd = optimized kd-tree // midpt = midpoint split // fair = fair split // sl_midpt = sliding midpt split // sl_fair = sliding fair split // suggest = authors' choice for best // The default is "suggest". See the file // kd_split.cc for more detailed information. // // shrink_rule Type of shrinking rule to use in building // a bd-tree data structure. If "none" is // given, then no shrinking is performed and // the result is a kd-tree. Choices are: // none = perform no shrinking // simple = simple shrinking // centroid = centroid shrinking // suggest = authors' choice for best // The default is "none". See the file // bd_tree.cc for more information. // bucket_size Bucket size, that is, the maximum number of // points stored in each leaf node. // // Options affecting data and query point generation: // -------------------------------------------------- // dim Dimension of space. // seed Seed for random number generation. // data_size Number of data points. When reading data // points from a file, this indicates the // maximum number of points for storage // allocation. Default = 100. // query_size Same as data_size for query points. // std_dev Standard deviation (used in gauss, // planted, and clustered distributions). // This is the "small" distribution for // clus_ellipsoids. Default = 1. // std_dev_lo Low and high standard deviations (used in // std_dev_hi clus_ellipsoids). Default = 1. // corr_coef Correlation coefficient (used in co-gauss // and co_lapace distributions). Default = 0.05. // colors Number of color classes (clusters) (used // in the clustered distributions). Default = 5. // new_clust Once generated, cluster centers are not // normally regenerated. This is so that both // query points and data points can be generated // using the same set of clusters. This option // forces new cluster centers to be generated // with the next generation of either data or // query points. // max_clus_dim Maximum dimension of clusters (used in // clus_orth_flats and clus_ellipsoids). // Default = 1. // distribution Type of input distribution // uniform = uniform over cube [-1,1]^d. // gauss = Gaussian with mean 0 // laplace = Laplacian, mean 0 and var 1 // co_gauss = correlated Gaussian // co_laplace = correlated Laplacian // clus_gauss = clustered Gaussian // clus_orth_flats = clusters of orth flats // clus_ellipsoids = clusters of ellipsoids // planted = planted distribution // See the file rand.cpp for further information. // // Options affecting nearest neighbor search: // ------------------------------------------ // epsilon Error bound for approx. near neigh. search. // near_neigh Number of nearest neighbors to compute. // max_pts_visit Maximum number of points to visit before // terminating. (Used in applications where // real-time performance is important.) // (Default = 0, which means no limit.) // radius_bound Sets an upper bound on the nearest // neighbor search radius. If the bound is // positive, then fixed-radius nearest // neighbor searching is performed, and the // count of the number of points in the // range is returned. If the bound is // zero, then standard search is used. // This can only be used with standard, not // priority, search. (Default = 0, which // means standard search.) // // Options affection general program behavior: // ------------------------------------------- // stats Level of statistics output // silent = no output, // exec_time += execution time only // prep_stats += preprocessing statistics // query_stats += query performance stats // query_res += results of queries // show_pts += show the data points // show_struct += print search structure // validate Validate experiment and compute average // error. Since validation causes exact // nearest neighbors to be computed by the // brute force method, this can take a long // time. Valid arguments are: // on = turn validation on // off = turn validation off // true_near_neigh Number of true nearest neighbors to compute. // When validating, we compute the difference // in rank between each reported nearest neighbor // and the true nearest neighbor of the same // rank. Thus it is necessary to compute a // few more true nearest neighbors. By default // we compute 10 more than near_neigh. With // this option the exact number can be set. // (Used only when validating.) // // Example: // -------- // output_label test_run_0 # output label for this run // validate off # do not perform validation // dim 16 # points in dimension 16 // stats query_stats # output performance statistics for queries // seed 121212 # random number seed // data_size 1000 // distribution uniform // gen_data_pts # 1000 uniform data points in dim 16 // query_size 100 // std_dev 0.05 // distribution clus_gauss // gen_query_pts # 100 points in 10 clusters with std_dev 0.05 // bucket_size 2 // split_rule kd // shrink_rule none // build_ann # kd-tree, bucket size 2 // epsilon 0.1 // near_neigh 5 // max_pts_visit 100 # stop search if more than 100 points seen // run_queries standard # run queries; 5 nearest neighbors, 10% error // data_size 500 // read_data_pts data.in # read up to 500 points from file data.in // split_rule sl_midpt // shrink_rule simple // build_ann # bd-tree; simple shrink, sliding midpoint split // epsilon 0 // run_queries priority # run same queries; 0 allowable error // //------------------------------------------------------------------------ //------------------------------------------------------------------------ // Constants //------------------------------------------------------------------------ const int STRING_LEN = 500; // max string length const double ERR = 0.00001; // epsilon (for float compares) const double RND_OFF = 5E-16; // double round-off error //------------------------------------------------------------------------ // Enumerated values and conversions //------------------------------------------------------------------------ typedef enum {DATA, QUERY} PtType; // point types //------------------------------------------------------------------------ // Statistics output levels //------------------------------------------------------------------------ typedef enum { // stat levels SILENT, // no output EXEC_TIME, // just execution time PREP_STATS, // preprocessing info QUERY_STATS, // query performance QUERY_RES, // query results SHOW_PTS, // show data points SHOW_STRUCT, // show tree structure N_STAT_LEVELS} // number of levels StatLev; const char stat_table[N_STAT_LEVELS][STRING_LEN] = { "silent", // SILENT "exec_time", // EXEC_TIME "prep_stats", // PREP_STATS "query_stats", // QUERY_STATS "query_res", // QUERY_RES "show_pts", // SHOW_PTS "show_struct"}; // SHOW_STRUCT //------------------------------------------------------------------------ // Distributions //------------------------------------------------------------------------ typedef enum { // distributions UNIFORM, // uniform over cube [-1,1]^d. GAUSS, // Gaussian with mean 0 LAPLACE, // Laplacian, mean 0 and var 1 CO_GAUSS, // correlated Gaussian CO_LAPLACE, // correlated Laplacian CLUS_GAUSS, // clustered Gaussian CLUS_ORTH_FLATS, // clustered on orthog flats CLUS_ELLIPSOIDS, // clustered on ellipsoids PLANTED, // planted distribution N_DISTRIBS} Distrib; const char distr_table[N_DISTRIBS][STRING_LEN] = { "uniform", // UNIFORM "gauss", // GAUSS "laplace", // LAPLACE "co_gauss", // CO_GAUSS "co_laplace", // CO_LAPLACE "clus_gauss", // CLUS_GAUSS "clus_orth_flats", // CLUS_ORTH_FLATS "clus_ellipsoids", // CLUS_ELLIPSOIS "planted"}; // PLANTED //------------------------------------------------------------------------ // Splitting rules for kd-trees (see ANN.h for types) //------------------------------------------------------------------------ const int N_SPLIT_RULES = 6; const char split_table[N_SPLIT_RULES][STRING_LEN] = { "standard", // standard optimized kd-tree "midpt", // midpoint split "fair", // fair split "sl_midpt", // sliding midpt split "sl_fair", // sliding fair split "suggest"}; // authors' choice for best //------------------------------------------------------------------------ // Shrinking rules for bd-trees (see ANN.h for types) //------------------------------------------------------------------------ const int N_SHRINK_RULES = 4; const char shrink_table[N_SHRINK_RULES][STRING_LEN] = { "none", // perform no shrinking (kd-tree) "simple", // simple shrinking "centroid", // centroid shrinking "suggest"}; // authors' choice for best //---------------------------------------------------------------------- // Short utility functions // Error - general error routine // printPoint - print a point to standard output // lookUp - look up a name in table and return index //---------------------------------------------------------------------- void Error( // error routine const char* msg, // error message ANNerr level) // abort afterwards { if (level == ANNabort) { cerr << "ann_test: ERROR------->" << msg << "<-------------ERROR\n"; exit(1); } else { cerr << "ann_test: WARNING----->" << msg << "<-------------WARNING\n"; } } void printPoint( // print point ANNpoint p, // the point int dim) // the dimension { cout << "["; for (int i = 0; i < dim; i++) { cout << p[i]; if (i < dim-1) cout << ","; } cout << "]"; } int lookUp( // look up name in table const char* arg, // name to look up const char (*table)[STRING_LEN], // name table int size) // table size { int i; for (i = 0; i < size; i++) { if (!strcmp(arg, table[i])) return i; } return i; } //------------------------------------------------------------------------ // Function declarations //------------------------------------------------------------------------ void generatePts( // generate data/query points ANNpointArray &pa, // point array (returned) int n, // number of points PtType type, // point type ANNbool new_clust, // new cluster centers desired? ANNpointArray src = NULL, // source array (for PLANTED) int n_src = 0); // source size (for PLANTED) void readPts( // read data/query points from file ANNpointArray &pa, // point array (returned) int &n, // number of points char *file_nm, // file name PtType type); // point type (DATA, QUERY) void doValidation(); // perform validation void getTrueNN(); // compute true nearest neighbors void treeStats( // print statistics on kd- or bd-tree ostream &out, // output stream ANNbool verbose); // print stats //------------------------------------------------------------------------ // Default execution parameters //------------------------------------------------------------------------ const int extra_nn = 10; // how many extra true nn's? const int def_dim = 2; // def dimension const int def_data_size = 100; // def data size const int def_query_size = 100; // def number of queries const int def_n_color = 5; // def number of colors const ANNbool def_new_clust = ANNfalse; // def new clusters flag const int def_max_dim = 1; // def max flat dimension const Distrib def_distr = UNIFORM; // def distribution const double def_std_dev = 1.00; // def standard deviation const double def_corr_coef = 0.05; // def correlation coef const int def_bucket_size = 1; // def bucket size const double def_epsilon = 0.0; // def error bound const int def_near_neigh = 1; // def number of near neighbors const int def_max_visit = 0; // def number of points visited const int def_rad_bound = 0; // def radius bound // def number of true nn's const int def_true_nn = def_near_neigh + extra_nn; const int def_seed = 0; // def seed for random numbers const ANNbool def_validate = ANNfalse; // def validation flag // def statistics output level const StatLev def_stats = QUERY_STATS; const ANNsplitRule // def splitting rule def_split = ANN_KD_SUGGEST; const ANNshrinkRule // def shrinking rule def_shrink = ANN_BD_NONE; //------------------------------------------------------------------------ // Global variables - Execution options //------------------------------------------------------------------------ int dim; // dimension int data_size; // data size int query_size; // number of queries int n_color; // number of colors ANNbool new_clust; // generate new clusters? int max_dim; // maximum flat dimension Distrib distr; // distribution double corr_coef; // correlation coef double std_dev; // standard deviation double std_dev_lo; // low standard deviation double std_dev_hi; // high standard deviation int bucket_size; // bucket size double epsilon; // error bound int near_neigh; // number of near neighbors int max_pts_visit; // max number of points to visit double radius_bound; // maximum radius search bound int true_nn; // number of true nn's ANNbool validate; // validation flag StatLev stats; // statistics output level ANNsplitRule split; // splitting rule ANNshrinkRule shrink; // shrinking rule //------------------------------------------------------------------------ // More globals - pointers to dynamically allocated arrays and structures // // It is assumed that all these values are set to NULL when nothing // is allocated. // // data_pts, query_pts The data and query points // the_tree Points to the kd- or bd-tree for // nearest neighbor searching. // apx_nn_idx, apx_dists Record approximate near neighbor // indices and distances // apx_pts_in_range Counts of the number of points in // the in approx range, for fixed- // radius NN searching. // true_nn_idx, true_dists Record true near neighbor // indices and distances // min_pts_in_range, max_... Min and max counts of the number // of points in the in approximate // range. // valid_dirty To avoid repeated validation, // we only validate query results // once. This validation becomes // invalid, if a new tree, new data // points or new query points have // been generated. // tree_data_size The number of points in the // current tree. (This will be the // same a data_size unless points have // been added since the tree was // built.) // // The approximate and true nearest neighbor results are stored // in: apx_nn_idx, apx_dists, and true_nn_idx, true_dists. // They are really flattened 2-dimensional arrays. Each of these // arrays consists of query_size blocks, each of which contains // near_neigh (or true_nn) entries, one for each of the nearest // neighbors for a given query point. //------------------------------------------------------------------------ ANNpointArray data_pts; // data points ANNpointArray query_pts; // query points ANNbd_tree* the_tree; // kd- or bd-tree search structure ANNidxArray apx_nn_idx; // storage for near neighbor indices ANNdistArray apx_dists; // storage for near neighbor distances int* apx_pts_in_range; // storage for no. of points in range ANNidxArray true_nn_idx; // true near neighbor indices ANNdistArray true_dists; // true near neighbor distances int* min_pts_in_range; // min points in approx range int* max_pts_in_range; // max points in approx range ANNbool valid_dirty; // validation is no longer valid //------------------------------------------------------------------------ // Initialize global parameters //------------------------------------------------------------------------ void initGlobals() { dim = def_dim; // init execution parameters data_size = def_data_size; query_size = def_query_size; distr = def_distr; corr_coef = def_corr_coef; std_dev = def_std_dev; std_dev_lo = def_std_dev; std_dev_hi = def_std_dev; new_clust = def_new_clust; max_dim = def_max_dim; n_color = def_n_color; bucket_size = def_bucket_size; epsilon = def_epsilon; near_neigh = def_near_neigh; max_pts_visit = def_max_visit; radius_bound = def_rad_bound; true_nn = def_true_nn; validate = def_validate; stats = def_stats; split = def_split; shrink = def_shrink; annIdum = -def_seed; // init. global seed for ran0() data_pts = NULL; // initialize storage pointers query_pts = NULL; the_tree = NULL; apx_nn_idx = NULL; apx_dists = NULL; apx_pts_in_range = NULL; true_nn_idx = NULL; true_dists = NULL; min_pts_in_range = NULL; max_pts_in_range = NULL; valid_dirty = ANNtrue; // (validation must be done) } //------------------------------------------------------------------------ // getDirective - skip comments and read next directive // Returns ANNtrue if directive read, and ANNfalse if eof seen. //------------------------------------------------------------------------ ANNbool skipComment( // skip any comments istream &in) // input stream { char ch = 0; // skip whitespace do { in.get(ch); } while (isspace(ch) && !in.eof()); while (ch == '#' && !in.eof()) { // comment? // skip to end of line do { in.get(ch); } while(ch != '\n' && !in.eof()); // skip whitespace do { in.get(ch); } while(isspace(ch) && !in.eof()); } if (in.eof()) return ANNfalse; // end of file in.putback(ch); // put character back return ANNtrue; } ANNbool getDirective( istream &in, // input stream char *directive) // directive storage { if (!skipComment(in)) // skip comments return ANNfalse; // found eof along the way? in >> directive; // read directive return ANNtrue; } //------------------------------------------------------------------------ // main program - driver // The main program reads input options, invokes the necessary // routines to process them. //------------------------------------------------------------------------ int main(int argc, char** argv) { long clock0; // clock time char directive[STRING_LEN]; // input directive char arg[STRING_LEN]; // all-purpose argument cout << "------------------------------------------------------------\n" << "ann_test: Version " << ANNversion << " " << ANNversionCmt << "\n" << " Copyright: " << ANNcopyright << ".\n" << " Latest Revision: " << ANNlatestRev << ".\n" << "------------------------------------------------------------\n\n"; initGlobals(); // initialize global values //-------------------------------------------------------------------- // Main input loop //-------------------------------------------------------------------- // read input directive while (getDirective(cin, directive)) { //---------------------------------------------------------------- // Read options //---------------------------------------------------------------- if (!strcmp(directive,"dim")) { cin >> dim; } else if (!strcmp(directive,"colors")) { cin >> n_color; } else if (!strcmp(directive,"new_clust")) { new_clust = ANNtrue; } else if (!strcmp(directive,"max_clus_dim")) { cin >> max_dim; } else if (!strcmp(directive,"std_dev")) { cin >> std_dev; } else if (!strcmp(directive,"std_dev_lo")) { cin >> std_dev_lo; } else if (!strcmp(directive,"std_dev_hi")) { cin >> std_dev_hi; } else if (!strcmp(directive,"corr_coef")) { cin >> corr_coef; } else if (!strcmp(directive, "data_size")) { cin >> data_size; } else if (!strcmp(directive,"query_size")) { cin >> query_size; } else if (!strcmp(directive,"bucket_size")) { cin >> bucket_size; } else if (!strcmp(directive,"epsilon")) { cin >> epsilon; } else if (!strcmp(directive,"max_pts_visit")) { cin >> max_pts_visit; valid_dirty = ANNtrue; // validation must be redone } else if (!strcmp(directive,"radius_bound")) { cin >> radius_bound; valid_dirty = ANNtrue; // validation must be redone } else if (!strcmp(directive,"near_neigh")) { cin >> near_neigh; true_nn = near_neigh + extra_nn; // also reset true near neighs valid_dirty = ANNtrue; // validation must be redone } else if (!strcmp(directive,"true_near_neigh")) { cin >> true_nn; valid_dirty = ANNtrue; // validation must be redone } //---------------------------------------------------------------- // seed option // The seed is reset by setting the global annIdum to the // negation of the seed value. See rand.cpp. //---------------------------------------------------------------- else if (!strcmp(directive,"seed")) { cin >> annIdum; annIdum = -annIdum; } //---------------------------------------------------------------- // validate option //---------------------------------------------------------------- else if (!strcmp(directive,"validate")) { cin >> arg; // input argument if (!strcmp(arg, "on")) { validate = ANNtrue; cout << "validate = on " << "(Warning: this may slow execution time.)\n"; } else if (!strcmp(arg, "off")) { validate = ANNfalse; } else { cerr << "Argument: " << arg << "\n"; Error("validate argument must be \"on\" or \"off\"", ANNabort); } } //---------------------------------------------------------------- // distribution option //---------------------------------------------------------------- else if (!strcmp(directive,"distribution")) { cin >> arg; // input name and translate distr = (Distrib) lookUp(arg, distr_table, N_DISTRIBS); if (distr >= N_DISTRIBS) { // not something we recognize cerr << "Distribution: " << arg << "\n"; Error("Unknown distribution", ANNabort); } } //---------------------------------------------------------------- // stats option //---------------------------------------------------------------- else if (!strcmp(directive,"stats")) { cin >> arg; // input name and translate stats = (StatLev) lookUp(arg, stat_table, N_STAT_LEVELS); if (stats >= N_STAT_LEVELS) { // not something we recognize cerr << "Stats level: " << arg << "\n"; Error("Unknown statistics level", ANNabort); } if (stats > SILENT) cout << "stats = " << arg << "\n"; } //---------------------------------------------------------------- // split_rule option //---------------------------------------------------------------- else if (!strcmp(directive,"split_rule")) { cin >> arg; // input split_rule name split = (ANNsplitRule) lookUp(arg, split_table, N_SPLIT_RULES); if (split >= N_SPLIT_RULES) { // not something we recognize cerr << "Splitting rule: " << arg << "\n"; Error("Unknown splitting rule", ANNabort); } } //---------------------------------------------------------------- // shrink_rule option //---------------------------------------------------------------- else if (!strcmp(directive,"shrink_rule")) { cin >> arg; // input split_rule name shrink = (ANNshrinkRule) lookUp(arg, shrink_table, N_SHRINK_RULES); if (shrink >= N_SHRINK_RULES) { // not something we recognize cerr << "Shrinking rule: " << arg << "\n"; Error("Unknown shrinking rule", ANNabort); } } //---------------------------------------------------------------- // label operation //---------------------------------------------------------------- else if (!strcmp(directive,"output_label")) { cin >> arg; if (stats > SILENT) cout << "<" << arg << ">\n"; } //---------------------------------------------------------------- // gen_data_pts operation //---------------------------------------------------------------- else if (!strcmp(directive,"gen_data_pts")) { if (distr == PLANTED) { // planted distribution Error("Cannot use planted distribution for data points", ANNabort); } generatePts( // generate data points data_pts, // data points data_size, // data size DATA, // data points new_clust); // new clusters flag valid_dirty = ANNtrue; // validation must be redone new_clust = ANNfalse; // reset flag } //---------------------------------------------------------------- // gen_query_pts operation // If the distribution is PLANTED, then the query points // are planted near the data points (which must already be // generated). //---------------------------------------------------------------- else if (!strcmp(directive,"gen_query_pts")) { if (distr == PLANTED) { // planted distribution if (data_pts == NULL) { Error("Must generate data points before query points for planted distribution", ANNabort); } generatePts( // generate query points query_pts, // point array query_size, // number of query points QUERY, // query points new_clust, // new clusters flag data_pts, // plant around data pts data_size); } else { // all other distributions generatePts( // generate query points query_pts, // point array query_size, // number of query points QUERY, // query points new_clust); // new clusters flag } valid_dirty = ANNtrue; // validation must be redone new_clust = ANNfalse; // reset flag } //---------------------------------------------------------------- // read_data_pts operation //---------------------------------------------------------------- else if (!strcmp(directive,"read_data_pts")) { cin >> arg; // input file name readPts( data_pts, // point array data_size, // number of points arg, // file name DATA); // data points valid_dirty = ANNtrue; // validation must be redone } //---------------------------------------------------------------- // read_query_pts operation //---------------------------------------------------------------- else if (!strcmp(directive,"read_query_pts")) { cin >> arg; // input file name readPts( query_pts, // point array query_size, // number of points arg, // file name QUERY); // query points valid_dirty = ANNtrue; // validation must be redone } //---------------------------------------------------------------- // build_ann operation // We always invoke the constructor for bd-trees. Note // that when the shrinking rule is NONE (which is true by // default), then this constructs a kd-tree. //---------------------------------------------------------------- else if (!strcmp(directive,"build_ann")) { //------------------------------------------------------------ // Build the tree //------------------------------------------------------------ if (the_tree != NULL) { // tree exists already delete the_tree; // get rid of it } clock0 = clock(); // start time the_tree = new ANNbd_tree( // build it data_pts, // the data points data_size, // number of points dim, // dimension of space bucket_size, // maximum bucket size split, // splitting rule shrink); // shrinking rule //------------------------------------------------------------ // Print summary //------------------------------------------------------------ long prep_time = clock() - clock0; // end of prep time if (stats > SILENT) { cout << "[Build ann-structure:\n"; cout << " split_rule = " << split_table[split] << "\n"; cout << " shrink_rule = " << shrink_table[shrink] << "\n"; cout << " data_size = " << data_size << "\n"; cout << " dim = " << dim << "\n"; cout << " bucket_size = " << bucket_size << "\n"; if (stats >= EXEC_TIME) { // output processing time cout << " process_time = " << double(prep_time)/CLOCKS_PER_SEC << " sec\n"; } if (stats >= PREP_STATS) // output or check tree stats treeStats(cout, ANNtrue); // print tree stats else treeStats(cout, ANNfalse); // check stats if (stats >= SHOW_STRUCT) { // print the whole tree cout << " (Structure Contents:\n"; the_tree->Print(ANNfalse, cout); cout << " )\n"; } cout << "]\n"; } } //---------------------------------------------------------------- // dump operation //---------------------------------------------------------------- else if (!strcmp(directive,"dump")) { cin >> arg; // input file name if (the_tree == NULL) { // no tree Error("Cannot dump. No tree has been built yet", ANNwarn); } else { // there is a tree // try to open file ofstream out_dump_file(arg); if (!out_dump_file) { cerr << "File name: " << arg << "\n"; Error("Cannot open dump file", ANNabort); } // dump the tree and points the_tree->Dump(ANNtrue, out_dump_file); if (stats > SILENT) { cout << "(Tree has been dumped to file " << arg << ")\n"; } } } //---------------------------------------------------------------- // load operation // Since this not only loads a tree, but loads a new set // of data points. //---------------------------------------------------------------- else if (!strcmp(directive,"load")) { cin >> arg; // input file name if (the_tree != NULL) { // tree exists already delete the_tree; // get rid of it } if (data_pts != NULL) { // data points exist already delete data_pts; // get rid of them } ifstream in_dump_file(arg); // try to open file if (!in_dump_file) { cerr << "File name: " << arg << "\n"; Error("Cannot open file for loading", ANNabort); } // build tree by loading the_tree = new ANNbd_tree(in_dump_file); dim = the_tree->theDim(); // new dimension data_size = the_tree->nPoints(); // number of points data_pts = the_tree->thePoints(); // new points valid_dirty = ANNtrue; // validation must be redone if (stats > SILENT) { cout << "(Tree has been loaded from file " << arg << ")\n"; } if (stats >= SHOW_STRUCT) { // print the tree cout << " (Structure Contents:\n"; the_tree->Print(ANNfalse, cout); cout << " )\n"; } } //---------------------------------------------------------------- // run_queries operation // This section does all the query processing. It consists // of the following subsections: // // ** input the argument (standard or priority) and output // the header describing the essential information. // ** allocate space for the results to be stored. // ** run the queries by invoking the appropriate search // procedure on the query points. Print nearest neighbor // if requested. // ** print final summaries // // The approach for processing multiple nearest neighbors is // pretty crude. We allocate an array whose size is the // product of the total number of queries times the number of // nearest neighbors (k), and then use each k consecutive // entries to store the results of each query. //---------------------------------------------------------------- else if (!strcmp(directive,"run_queries")) { //------------------------------------------------------------ // Input arguments and print summary //------------------------------------------------------------ enum {STANDARD, PRIORITY} method; cin >> arg; // input argument if (!strcmp(arg, "standard")) { method = STANDARD; } else if (!strcmp(arg, "priority")) { method = PRIORITY; } else { cerr << "Search type: " << arg << "\n"; Error("Search type must be \"standard\" or \"priority\"", ANNabort); } if (data_pts == NULL || query_pts == NULL) { Error("Either data set and query set not constructed", ANNabort); } if (the_tree == NULL) { Error("No search tree built.", ANNabort); } //------------------------------------------------------------ // Set up everything //------------------------------------------------------------ #ifdef ANN_PERF // performance only annResetStats(data_size); // reset statistics #endif clock0 = clock(); // start time // deallocate existing storage if (apx_nn_idx != NULL) delete [] apx_nn_idx; if (apx_dists != NULL) delete [] apx_dists; if (apx_pts_in_range != NULL) delete [] apx_pts_in_range; // allocate apx answer storage apx_nn_idx = new ANNidx[near_neigh*query_size]; apx_dists = new ANNdist[near_neigh*query_size]; apx_pts_in_range = new int[query_size]; annMaxPtsVisit(max_pts_visit); // set max points to visit //------------------------------------------------------------ // Run the queries //------------------------------------------------------------ // pointers for current query ANNidxArray curr_nn_idx = apx_nn_idx; ANNdistArray curr_dists = apx_dists; for (int i = 0; i < query_size; i++) { #ifdef ANN_PERF annResetCounts(); // reset counters #endif apx_pts_in_range[i] = 0; if (radius_bound == 0) { // no radius bound if (method == STANDARD) { the_tree->annkSearch( query_pts[i], // query point near_neigh, // number of near neighbors curr_nn_idx, // nearest neighbors (returned) curr_dists, // distance (returned) epsilon); // error bound } else if (method == PRIORITY) { the_tree->annkPriSearch( query_pts[i], // query point near_neigh, // number of near neighbors curr_nn_idx, // nearest neighbors (returned) curr_dists, // distance (returned) epsilon); // error bound } else { Error("Internal error - invalid method", ANNabort); } } else { // use radius bound if (method != STANDARD) { Error("A nonzero radius bound assumes standard search", ANNwarn); } apx_pts_in_range[i] = the_tree->annkFRSearch( query_pts[i], // query point ANN_POW(radius_bound), // squared radius search bound near_neigh, // number of near neighbors curr_nn_idx, // nearest neighbors (returned) curr_dists, // distance (returned) epsilon); // error bound } curr_nn_idx += near_neigh; // increment current pointers curr_dists += near_neigh; #ifdef ANN_PERF annUpdateStats(); // update stats #endif } long query_time = clock() - clock0; // end of query time if (validate) { // validation requested if (valid_dirty) getTrueNN(); // get true near neighbors doValidation(); // validate } //------------------------------------------------------------ // Print summaries //------------------------------------------------------------ if (stats > SILENT) { cout << "[Run Queries:\n"; cout << " query_size = " << query_size << "\n"; cout << " dim = " << dim << "\n"; cout << " search_method = " << arg << "\n"; cout << " epsilon = " << epsilon << "\n"; cout << " near_neigh = " << near_neigh << "\n"; if (max_pts_visit != 0) cout << " max_pts_visit = " << max_pts_visit << "\n"; if (radius_bound != 0) cout << " radius_bound = " << radius_bound << "\n"; if (validate) cout << " true_nn = " << true_nn << "\n"; if (stats >= EXEC_TIME) { // print exec time summary cout << " query_time = " << double(query_time)/(query_size*CLOCKS_PER_SEC) << " sec/query"; #ifdef ANN_PERF cout << " (biased by perf measurements)"; #endif cout << "\n"; } if (stats >= QUERY_STATS) { // output performance stats #ifdef ANN_PERF cout.flush(); annPrintStats(validate); #else cout << " (Performance statistics unavailable.)\n"; #endif } if (stats >= QUERY_RES) { // output results cout << " (Query Results:\n"; cout << " Pt\tANN\tDist\n"; curr_nn_idx = apx_nn_idx; // subarray pointers curr_dists = apx_dists; // output nearest neighbors for (int i = 0; i < query_size; i++) { cout << " " << setw(4) << i; for (int j = 0; j < near_neigh; j++) { // exit if no more neighbors if (curr_nn_idx[j] == ANN_NULL_IDX) { cout << "\t[no other pts in radius bound]\n"; break; } else { // output point info cout << "\t" << curr_nn_idx[j] << "\t" << ANN_ROOT(curr_dists[j]) << "\n"; } } // output range count if (radius_bound != 0) { cout << " pts_in_radius_bound = " << apx_pts_in_range[i] << "\n"; } // increment subarray pointers curr_nn_idx += near_neigh; curr_dists += near_neigh; } cout << " )\n"; } cout << "]\n"; } } //---------------------------------------------------------------- // Unknown directive //---------------------------------------------------------------- else { cerr << "Directive: " << directive << "\n"; Error("Unknown directive", ANNabort); } } //-------------------------------------------------------------------- // End of input loop (deallocate stuff that was allocated) //-------------------------------------------------------------------- if (the_tree != NULL) delete the_tree; if (data_pts != NULL) annDeallocPts(data_pts); if (query_pts != NULL) annDeallocPts(query_pts); if (apx_nn_idx != NULL) delete [] apx_nn_idx; if (apx_dists != NULL) delete [] apx_dists; if (apx_pts_in_range != NULL) delete [] apx_pts_in_range; annClose(); // close ANN return EXIT_SUCCESS; } //------------------------------------------------------------------------ // generatePts - call appropriate routine to generate points of a // given distribution. //------------------------------------------------------------------------ void generatePts( ANNpointArray &pa, // point array (returned) int n, // number of points to generate PtType type, // point type ANNbool new_clust, // new cluster centers desired? ANNpointArray src, // source array (if distr=PLANTED) int n_src) // source size (if distr=PLANTED) { if (pa != NULL) annDeallocPts(pa); // get rid of any old points pa = annAllocPts(n, dim); // allocate point storage switch (distr) { case UNIFORM: // uniform over cube [-1,1]^d. annUniformPts(pa, n, dim); break; case GAUSS: // Gaussian with mean 0 annGaussPts(pa, n, dim, std_dev); break; case LAPLACE: // Laplacian, mean 0 and var 1 annLaplacePts(pa, n, dim); break; case CO_GAUSS: // correlated Gaussian annCoGaussPts(pa, n, dim, corr_coef); break; case CO_LAPLACE: // correlated Laplacian annCoLaplacePts(pa, n, dim, corr_coef); break; case CLUS_GAUSS: // clustered Gaussian annClusGaussPts(pa, n, dim, n_color, new_clust, std_dev); break; case CLUS_ORTH_FLATS: // clustered on orthog flats annClusOrthFlats(pa, n, dim, n_color, new_clust, std_dev, max_dim); break; case CLUS_ELLIPSOIDS: // clustered ellipsoids annClusEllipsoids(pa, n, dim, n_color, new_clust, std_dev, std_dev_lo, std_dev_hi, max_dim); break; case PLANTED: // planted distribution annPlanted(pa, n, dim, src, n_src, std_dev); break; default: Error("INTERNAL ERROR: Unknown distribution", ANNabort); break; } if (stats > SILENT) { if(type == DATA) cout << "[Generating Data Points:\n"; else cout << "[Generating Query Points:\n"; cout << " number = " << n << "\n"; cout << " dim = " << dim << "\n"; cout << " distribution = " << distr_table[distr] << "\n"; if (annIdum < 0) cout << " seed = " << annIdum << "\n"; if (distr == GAUSS || distr == CLUS_GAUSS || distr == CLUS_ORTH_FLATS) cout << " std_dev = " << std_dev << "\n"; if (distr == CLUS_ELLIPSOIDS) { cout << " std_dev = " << std_dev << " (small) \n"; cout << " std_dev_lo = " << std_dev_lo << "\n"; cout << " std_dev_hi = " << std_dev_hi << "\n"; } if (distr == CO_GAUSS || distr == CO_LAPLACE) cout << " corr_coef = " << corr_coef << "\n"; if (distr == CLUS_GAUSS || distr == CLUS_ORTH_FLATS || distr == CLUS_ELLIPSOIDS) { cout << " colors = " << n_color << "\n"; if (new_clust) cout << " (cluster centers regenerated)\n"; } if (distr == CLUS_ORTH_FLATS || distr == CLUS_ELLIPSOIDS) { cout << " max_dim = " << max_dim << "\n"; } } // want to see points? if ((type == DATA && stats >= SHOW_PTS) || (type == QUERY && stats >= QUERY_RES)) { if(type == DATA) cout << "(Data Points:\n"; else cout << "(Query Points:\n"; for (int i = 0; i < n; i++) { cout << " " << setw(4) << i << "\t"; printPoint(pa[i], dim); cout << "\n"; } cout << " )\n"; } cout << "]\n"; } //------------------------------------------------------------------------ // readPts - read a collection of data or query points. //------------------------------------------------------------------------ void readPts( ANNpointArray &pa, // point array (returned) int &n, // number of points char *file_nm, // file name PtType type) // point type (DATA, QUERY) { int i; //-------------------------------------------------------------------- // Open input file and read points //-------------------------------------------------------------------- ifstream in_file(file_nm); // try to open data file if (!in_file) { cerr << "File name: " << file_nm << "\n"; Error("Cannot open input data/query file", ANNabort); } // allocate storage for points if (pa != NULL) annDeallocPts(pa); // get rid of old points pa = annAllocPts(n, dim); for (i = 0; i < n; i++) { // read the data if (!(in_file >> pa[i][0])) break; for (int d = 1; d < dim; d++) { in_file >> pa[i][d]; } } char ignore_me; // character for EOF test in_file >> ignore_me; // try to get one more character if (!in_file.eof()) { // exhausted space before eof if (type == DATA) Error("`data_size' too small. Input file truncated.", ANNwarn); else Error("`query_size' too small. Input file truncated.", ANNwarn); } n = i; // number of points read //-------------------------------------------------------------------- // Print summary //-------------------------------------------------------------------- if (stats > SILENT) { if (type == DATA) { cout << "[Read Data Points:\n"; cout << " data_size = " << n << "\n"; } else { cout << "[Read Query Points:\n"; cout << " query_size = " << n << "\n"; } cout << " file_name = " << file_nm << "\n"; cout << " dim = " << dim << "\n"; // print if results requested if ((type == DATA && stats >= SHOW_PTS) || (type == QUERY && stats >= QUERY_RES)) { cout << " (Points:\n"; for (i = 0; i < n; i++) { cout << " " << i << "\t"; printPoint(pa[i], dim); cout << "\n"; } cout << " )\n"; } cout << "]\n"; } } //------------------------------------------------------------------------ // getTrueNN // Computes the true nearest neighbors. For purposes of validation, // this intentionally done in a rather dumb (but safe way), by // invoking the brute-force search. // // The number of true nearest neighbors is somewhat larger than // the number of nearest neighbors. This is so that the validation // can determine the expected difference in element ranks. // // This procedure is invoked just prior to running queries. Since // the operation takes a long time, it is performed only if needed. // In particular, once generated, it will be regenerated only if // new query or data points are generated, or if the requested number // of true near neighbors or approximate near neighbors has changed. // // To validate fixed-radius searching, we compute two counts, one // with the original query radius (trueSqRadius) and the other with // a radius shrunken by the error factor (minSqradius). We then // check that the count of points inside the approximate range is // between these two bounds. Because fixed-radius search is // allowed to ignore points within the shrunken radius, we only // compute exact neighbors within this smaller distance (for we // cannot guarantee that we will even visit the other points). //------------------------------------------------------------------------ void getTrueNN() // compute true nearest neighbors { if (stats > SILENT) { cout << "(Computing true nearest neighbors for validation. This may take time.)\n"; } // deallocate existing storage if (true_nn_idx != NULL) delete [] true_nn_idx; if (true_dists != NULL) delete [] true_dists; if (min_pts_in_range != NULL) delete [] min_pts_in_range; if (max_pts_in_range != NULL) delete [] max_pts_in_range; if (true_nn > data_size) { // can't get more nn than points true_nn = data_size; } // allocate true answer storage true_nn_idx = new ANNidx[true_nn*query_size]; true_dists = new ANNdist[true_nn*query_size]; min_pts_in_range = new int[query_size]; max_pts_in_range = new int[query_size]; ANNidxArray curr_nn_idx = true_nn_idx; // current locations in arrays ANNdistArray curr_dists = true_dists; // allocate search structure ANNbruteForce *the_brute = new ANNbruteForce(data_pts, data_size, dim); // compute nearest neighbors for (int i = 0; i < query_size; i++) { if (radius_bound == 0) { // standard kNN search the_brute->annkSearch( // compute true near neighbors query_pts[i], // query point true_nn, // number of nearest neighbors curr_nn_idx, // where to put indices curr_dists); // where to put distances } else { // fixed radius kNN search // search radii limits ANNdist trueSqRadius = ANN_POW(radius_bound); ANNdist minSqRadius = ANN_POW(radius_bound / (1+epsilon)); min_pts_in_range[i] = the_brute->annkFRSearch( query_pts[i], // query point minSqRadius, // shrunken search radius true_nn, // number of near neighbors curr_nn_idx, // nearest neighbors (returned) curr_dists); // distance (returned) max_pts_in_range[i] = the_brute->annkFRSearch( query_pts[i], // query point trueSqRadius, // true search radius 0, NULL, NULL); // (ignore kNN info) } curr_nn_idx += true_nn; // increment nn index pointer curr_dists += true_nn; // increment nn dist pointer } delete the_brute; // delete brute-force struct valid_dirty = ANNfalse; // validation good for now } //------------------------------------------------------------------------ // doValidation // Compares the approximate answers to the k-nearest neighbors // against the true nearest neighbors (computed earlier). It is // assumed that the true nearest neighbors and indices have been // computed earlier. // // First, we check that all the results are within their allowed // limits, and generate an internal error, if not. For the sake of // performance evaluation, we also compute the following two // quantities for nearest neighbors: // // Average Error // ------------- // The relative error between the distance to a reported nearest // neighbor and the true nearest neighbor (of the same rank), // // Rank Error // ---------- // The difference in rank between the reported nearest neighbor and // its position (if any) among the true nearest neighbors. If we // cannot find this point among the true nearest neighbors, then // it assumed that the rank of the true nearest neighbor is true_nn+1. // // Because of the possibility of duplicate distances, this is computed // as follows. For the j-th reported nearest neighbor, we count the // number of true nearest neighbors that are at least this close. Let // this be rnk. Then the rank error is max(0, j-rnk). (In the code // below, j is an array index and so the first item is 0, not 1. Thus // we take max(0, j+1-rnk) instead.) // // For the results of fixed-radious range count, we verify that the // reported number of points in the range lies between the actual // number of points in the shrunken and the true search radius. //------------------------------------------------------------------------ void doValidation() // perform validation { int* curr_apx_idx = apx_nn_idx; // approx index pointer ANNdistArray curr_apx_dst = apx_dists; // approx distance pointer int* curr_tru_idx = true_nn_idx; // true index pointer ANNdistArray curr_tru_dst = true_dists; // true distance pointer int i, j; if (true_nn < near_neigh) { Error("Cannot validate with fewer true near neighbors than actual", ANNabort); } for (i = 0; i < query_size; i++) { // validate each query //---------------------------------------------------------------- // Compute result errors // In fixed radius search it is possible that not all k // nearest neighbors were computed. Because the true // results are computed over the shrunken radius, we should // have at least as many true nearest neighbors as // approximate nearest neighbors. (If not, an infinite // error will be generated, and so an internal error will // will be generated. // // Because nearest neighbors are sorted in increasing order // of distance, as soon as we see a null index, we can // terminate the distance checking. The error in the // result should not exceed epsilon. However, if // max_pts_visit is nonzero (meaning that the search is // terminated early) this might happen. //---------------------------------------------------------------- for (j = 0; j < near_neigh; j++) { if (curr_tru_idx[j] == ANN_NULL_IDX)// no more true neighbors? break; // true i-th smallest distance double true_dist = ANN_ROOT(curr_tru_dst[j]); // reported i-th smallest double rept_dist = ANN_ROOT(curr_apx_dst[j]); // better than optimum? if (rept_dist < true_dist*(1-ERR)) { Error("INTERNAL ERROR: True nearest neighbor incorrect", ANNabort); } double resultErr; // result error if (true_dist == 0.0) { // let's not divide by zero if (rept_dist != 0.0) resultErr = ANN_DBL_MAX; else resultErr = 0.0; } else { resultErr = (rept_dist - true_dist) / ((double) true_dist); } if (resultErr > epsilon + RND_OFF && max_pts_visit == 0) { Error("INTERNAL ERROR: Actual error exceeds epsilon", ANNabort); } #ifdef ANN_PERF ann_average_err += resultErr; // update statistics error #endif } //-------------------------------------------------------------------- // Compute rank errors (only needed for perf measurements) //-------------------------------------------------------------------- #ifdef ANN_PERF for (j = 0; j < near_neigh; j++) { if (curr_tru_idx[i] == ANN_NULL_IDX) // no more true neighbors? break; double rnkErr = 0.0; // rank error // reported j-th distance ANNdist rept_dist = curr_apx_dst[j]; int rnk = 0; // compute rank of this item while (rnk < true_nn && curr_tru_dst[rnk] <= rept_dist) rnk++; if (j+1-rnk > 0) rnkErr = (double) (j+1-rnk); ann_rank_err += rnkErr; // update average rank error } #endif //---------------------------------------------------------------- // Check range counts from fixed-radius query //---------------------------------------------------------------- if (radius_bound != 0) { // fixed-radius search if (apx_pts_in_range[i] < min_pts_in_range[i] || apx_pts_in_range[i] > max_pts_in_range[i]) Error("INTERNAL ERROR: Invalid fixed-radius range count", ANNabort); } curr_apx_idx += near_neigh; curr_apx_dst += near_neigh; curr_tru_idx += true_nn; // increment current pointers curr_tru_dst += true_nn; } } //---------------------------------------------------------------------- // treeStats // Computes a number of statistics related to kd_trees and // bd_trees. These statistics are printed if in verbose mode, // and otherwise they are only printed if they are deemed to // be outside of reasonable operating bounds. //---------------------------------------------------------------------- #define log2(x) (log(x)/log(2.0)) // log base 2 void treeStats( ostream &out, // output stream ANNbool verbose) // print stats { const int MIN_PTS = 20; // min no. pts for checking const float MAX_FRAC_TL = 0.50; // max frac of triv leaves const float MAX_AVG_AR = 20; // max average aspect ratio ANNkdStats st; // statistics structure the_tree->getStats(st); // get statistics // total number of nodes int n_nodes = st.n_lf + st.n_spl + st.n_shr; // should be O(n/bs) int opt_n_nodes = (int) (2*(float(st.n_pts)/st.bkt_size)); int too_many_nodes = 10*opt_n_nodes; if (st.n_pts >= MIN_PTS && n_nodes > too_many_nodes) { out << "-----------------------------------------------------------\n"; out << "Warning: The tree has more than 10x as many nodes as points.\n"; out << "You may want to consider a different split or shrink method.\n"; out << "-----------------------------------------------------------\n"; verbose = ANNtrue; } // fraction of trivial leaves float frac_tl = (st.n_lf == 0 ? 0 : ((float) st.n_tl)/ st.n_lf); if (st.n_pts >= MIN_PTS && frac_tl > MAX_FRAC_TL) { out << "-----------------------------------------------------------\n"; out << "Warning: A significant fraction of leaves contain no points.\n"; out << "You may want to consider a different split or shrink method.\n"; out << "-----------------------------------------------------------\n"; verbose = ANNtrue; } // depth should be O(dim*log n) int too_many_levels = (int) (2.0 * st.dim * log2((double) st.n_pts)); int opt_levels = (int) log2(double(st.n_pts)/st.bkt_size); if (st.n_pts >= MIN_PTS && st.depth > too_many_levels) { out << "-----------------------------------------------------------\n"; out << "Warning: The tree is more than 2x as deep as (dim*log n).\n"; out << "You may want to consider a different split or shrink method.\n"; out << "-----------------------------------------------------------\n"; verbose = ANNtrue; } // average leaf aspect ratio if (st.n_pts >= MIN_PTS && st.avg_ar > MAX_AVG_AR) { out << "-----------------------------------------------------------\n"; out << "Warning: Average aspect ratio of cells is quite large.\n"; out << "This may slow queries depending on the point distribution.\n"; out << "-----------------------------------------------------------\n"; verbose = ANNtrue; } //------------------------------------------------------------------ // Print summaries if requested //------------------------------------------------------------------ if (verbose) { // output statistics out << " (Structure Statistics:\n"; out << " n_nodes = " << n_nodes << " (opt = " << opt_n_nodes << ", best if < " << too_many_nodes << ")\n" << " n_leaves = " << st.n_lf << " (" << st.n_tl << " contain no points)\n" << " n_splits = " << st.n_spl << "\n" << " n_shrinks = " << st.n_shr << "\n"; out << " empty_leaves = " << frac_tl*100 << " percent (best if < " << MAX_FRAC_TL*100 << " percent)\n"; out << " depth = " << st.depth << " (opt = " << opt_levels << ", best if < " << too_many_levels << ")\n"; out << " avg_aspect_ratio = " << st.avg_ar << " (best if < " << MAX_AVG_AR << ")\n"; out << " )\n"; } } ann-1.1.2+doc/test/test1-query.pts0000644000175000017500000000027411330212441017616 0ustar sylvestresylvestre0.0902484 -0.207129 -0.419567 0.485743 0.826225 -0.30962 0.694758 0.987088 -0.410807 -0.465182 -0.836501 0.490184 0.588289 0.656408 0.325807 0.38721 -0.532226 -0.727036 -0.52506 -0.853508 ann-1.1.2+doc/test/Makefile0000644000175000017500000000646311330212441016331 0ustar sylvestresylvestre#----------------------------------------------------------------------------- # Makefile for the test and evaluation program # # ANN: Approximate Nearest Neighbors # Version: 1.1.1 08/04/06 #----------------------------------------------------------------------------- # Copyright (c) 1997-2005 University of Maryland and Sunil Arya and # David Mount. All Rights Reserved. # # This software and related documentation is part of the Approximate # Nearest Neighbor Library (ANN). This software is provided under # the provisions of the Lesser GNU Public License (LGPL). See the # file ../ReadMe.txt for further information. # # The University of Maryland (U.M.) and the authors make no # representations about the suitability or fitness of this software for # any purpose. It is provided "as is" without express or implied # warranty. #----------------------------------------------------------------------------- # Revision 0.1 03/04/98 # Initial release # Revision 1.1.1 08/04/06 # Added copyright/license #----------------------------------------------------------------------------- # Note: For full performance measurements, it is assumed that the library # and this program have both been compiled with the -DANN_PERF flag. See # the Makefile in the ANN base directory for this flag. #----------------------------------------------------------------------------- #----------------------------------------------------------------------------- # Basic definitions # BASEDIR where include, src, lib, ... are # INCDIR include directory # LIBDIR library directory # BINDIR bin directory # LDFLAGS loader flags # ANNLIBS ANN library # OTHERLIBS other libraries #----------------------------------------------------------------------------- BASEDIR = .. INCDIR = $(BASEDIR)/include LIBDIR = $(BASEDIR)/lib BINDIR = $(BASEDIR)/bin LDFLAGS = -L$(LIBDIR) ANNLIBS = -lANN OTHERLIBS = -lm #----------------------------------------------------------------------------- # Some more definitions # ANNTEST name of test program #----------------------------------------------------------------------------- ANNTEST = ann_test HEADERS = rand.h TESTSOURCES = ann_test.cpp rand.cpp TESTOBJECTS = $(TESTSOURCES:.cpp=.o) #----------------------------------------------------------------------------- # Make the program #----------------------------------------------------------------------------- default: @echo "Specify a target configuration" targets: $(BINDIR)/$(ANNTEST) $(BINDIR)/$(ANNTEST): $(TESTOBJECTS) $(LIBDIR)/$(ANNLIB) $(C++) $(TESTOBJECTS) -o $(ANNTEST) $(LDFLAGS) $(ANNLIBS) $(OTHERLIBS) mv $(ANNTEST) $(BINDIR) #----------------------------------------------------------------------------- # configuration definitions #----------------------------------------------------------------------------- include ../Make-config #----------------------------------------------------------------------------- # Objects #----------------------------------------------------------------------------- ann_test.o: ann_test.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) ann_test.cpp rand.o: rand.cpp $(C++) -c -I$(INCDIR) $(CFLAGS) rand.cpp #----------------------------------------------------------------------------- # Cleaning #----------------------------------------------------------------------------- clean: -rm -f *.o *.out core realclean: clean ann-1.1.2+doc/test/test1-data.pts0000644000175000017500000000057111330212441017362 0ustar sylvestresylvestre-0.297462 0.176102 0.565538 -0.361496 0.909313 -0.182785 0.920712 0.478408 0.167682 0.0499836 0.305223 -0.0805835 0.114973 0.882453 0.742916 0.16376 0.0724605 -0.826775 0.690960 -0.559284 0.188485 -0.643934 0.749427 -0.942415 -0.970662 -0.223466 0.916110 0.879597 0.927417 -0.382593 -0.711327 0.278713 -0.519172 0.986146 0.135338 0.924588 -0.0837537 0.61687 0.0520465 0.896306 ann-1.1.2+doc/test/rand.cpp0000644000175000017500000005414011330212441016314 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: rand.cpp // Programmer: Sunil Arya and David Mount // Description: Routines for random point generation // Last modified: 08/04/06 (Version 1.1.1) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 0.2 03/26/98 // Changed random/srandom declarations for SGI's. // Revision 1.0 04/01/05 // annClusGauss centers distributed over [-1,1] rather than [0,1] // Added annClusOrthFlats distribution // Changed procedure names to avoid namespace conflicts // Added annClusFlats distribution // Added rand/srand option and fixed annRan0() initialization. // Revision 1.1.1 08/04/06 // Added planted distribution //---------------------------------------------------------------------- #include "rand.h" // random generator declarations using namespace std; // make std:: accessible //---------------------------------------------------------------------- // Globals //---------------------------------------------------------------------- int annIdum = 0; // used for random number generation //------------------------------------------------------------------------ // annRan0 - (safer) uniform random number generator // // The code given here is taken from "Numerical Recipes in C" by // William Press, Brian Flannery, Saul Teukolsky, and William // Vetterling. The task of the code is to do an additional randomizing // shuffle on the system-supplied random number generator to make it // safer to use. // // Returns a uniform deviate between 0.0 and 1.0 using the // system-supplied routine random() or rand(). Set the global // annIdum to any negative value to initialise or reinitialise // the sequence. //------------------------------------------------------------------------ double annRan0() { const int TAB_SIZE = 97; // table size: any large number int j; static double y, v[TAB_SIZE]; static int iff = 0; const double RAN_DIVISOR = double(ANN_RAND_MAX + 1UL); if (RAN_DIVISOR < 0) { cout << "RAN_DIVISOR " << RAN_DIVISOR << endl; exit(0); } //-------------------------------------------------------------------- // As a precaution against misuse, we will always initialize on the // first call, even if "annIdum" is not set negative. Determine // "maxran", the next integer after the largest representable value // of type int. We assume this is a factor of 2 smaller than the // corresponding value of type unsigned int. //-------------------------------------------------------------------- if (annIdum < 0 || iff == 0) { // initialize iff = 1; ANN_SRAND(annIdum); // (re)seed the generator annIdum = 1; for (j = 0; j < TAB_SIZE; j++) // exercise the system routine ANN_RAND(); // (values intentionally ignored) for (j = 0; j < TAB_SIZE; j++) // then save TAB_SIZE-1 values v[j] = ANN_RAND(); y = ANN_RAND(); // generate starting value } //-------------------------------------------------------------------- // This is where we start if not initializing. Use the previously // saved random number y to get an index j between 1 and TAB_SIZE-1. // Then use the corresponding v[j] for both the next j and as the // output number. //-------------------------------------------------------------------- j = int(TAB_SIZE * (y / RAN_DIVISOR)); y = v[j]; v[j] = ANN_RAND(); // refill the table entry return y / RAN_DIVISOR; } //------------------------------------------------------------------------ // annRanInt - generate a random integer from {0,1,...,n-1} // // If n == 0, then -1 is returned. //------------------------------------------------------------------------ static int annRanInt( int n) { int r = (int) (annRan0()*n); if (r == n) r--; // (in case annRan0() == 1 or n == 0) return r; } //------------------------------------------------------------------------ // annRanUnif - generate a random uniform in [lo,hi] //------------------------------------------------------------------------ static double annRanUnif( double lo, double hi) { return annRan0()*(hi-lo) + lo; } //------------------------------------------------------------------------ // annRanGauss - Gaussian random number generator // Returns a normally distributed deviate with zero mean and unit // variance, using annRan0() as the source of uniform deviates. //------------------------------------------------------------------------ static double annRanGauss() { static int iset=0; static double gset; if (iset == 0) { // we don't have a deviate handy double v1, v2; double r = 2.0; while (r >= 1.0) { //------------------------------------------------------------ // Pick two uniform numbers in the square extending from -1 to // +1 in each direction, see if they are in the circle of radius // 1. If not, try again //------------------------------------------------------------ v1 = annRanUnif(-1, 1); v2 = annRanUnif(-1, 1); r = v1 * v1 + v2 * v2; } double fac = sqrt(-2.0 * log(r) / r); //----------------------------------------------------------------- // Now make the Box-Muller transformation to get two normal // deviates. Return one and save the other for next time. //----------------------------------------------------------------- gset = v1 * fac; iset = 1; // set flag return v2 * fac; } else { // we have an extra deviate handy iset = 0; // so unset the flag return gset; // and return it } } //------------------------------------------------------------------------ // annRanLaplace - Laplacian random number generator // Returns a Laplacian distributed deviate with zero mean and // unit variance, using annRan0() as the source of uniform deviates. // // prob(x) = b/2 * exp(-b * |x|). // // b is chosen to be sqrt(2.0) so that the variance of the Laplacian // distribution [2/(b^2)] becomes 1. //------------------------------------------------------------------------ static double annRanLaplace() { const double b = 1.4142136; double laprand = -log(annRan0()) / b; double sign = annRan0(); if (sign < 0.5) laprand = -laprand; return(laprand); } //---------------------------------------------------------------------- // annUniformPts - Generate uniformly distributed points // A uniform distribution over [-1,1]. //---------------------------------------------------------------------- void annUniformPts( // uniform distribution ANNpointArray pa, // point array (modified) int n, // number of points int dim) // dimension { for (int i = 0; i < n; i++) { for (int d = 0; d < dim; d++) { pa[i][d] = (ANNcoord) (annRanUnif(-1,1)); } } } //---------------------------------------------------------------------- // annGaussPts - Generate Gaussian distributed points // A Gaussian distribution with zero mean and the given standard // deviation. //---------------------------------------------------------------------- void annGaussPts( // Gaussian distribution ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension double std_dev) // standard deviation { for (int i = 0; i < n; i++) { for (int d = 0; d < dim; d++) { pa[i][d] = (ANNcoord) (annRanGauss() * std_dev); } } } //---------------------------------------------------------------------- // annLaplacePts - Generate Laplacian distributed points // Generates a Laplacian distribution (zero mean and unit variance). //---------------------------------------------------------------------- void annLaplacePts( // Laplacian distribution ANNpointArray pa, // point array (modified) int n, // number of points int dim) // dimension { for (int i = 0; i < n; i++) { for (int d = 0; d < dim; d++) { pa[i][d] = (ANNcoord) annRanLaplace(); } } } //---------------------------------------------------------------------- // annCoGaussPts - Generate correlated Gaussian distributed points // Generates a Gauss-Markov distribution of zero mean and unit // variance. //---------------------------------------------------------------------- void annCoGaussPts( // correlated-Gaussian distribution ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension double correlation) // correlation { double std_dev_w = sqrt(1.0 - correlation * correlation); for (int i = 0; i < n; i++) { double previous = annRanGauss(); pa[i][0] = (ANNcoord) previous; for (int d = 1; d < dim; d++) { previous = correlation*previous + std_dev_w*annRanGauss(); pa[i][d] = (ANNcoord) previous; } } } //---------------------------------------------------------------------- // annCoLaplacePts - Generate correlated Laplacian distributed points // Generates a Laplacian-Markov distribution of zero mean and unit // variance. //---------------------------------------------------------------------- void annCoLaplacePts( // correlated-Laplacian distribution ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension double correlation) // correlation { double wn; double corr_sq = correlation * correlation; for (int i = 0; i < n; i++) { double previous = annRanLaplace(); pa[i][0] = (ANNcoord) previous; for (int d = 1; d < dim; d++) { double temp = annRan0(); if (temp < corr_sq) wn = 0.0; else wn = annRanLaplace(); previous = correlation * previous + wn; pa[i][d] = (ANNcoord) previous; } } } //---------------------------------------------------------------------- // annClusGaussPts - Generate clusters of Gaussian distributed points // Cluster centers are uniformly distributed over [-1,1], and the // standard deviation within each cluster is fixed. // // Note: Once cluster centers have been set, they are not changed, // unless new_clust = true. This is so that subsequent calls generate // points from the same distribution. It follows, of course, that any // attempt to change the dimension or number of clusters without // generating new clusters is asking for trouble. // // Note: Cluster centers are not generated by a call to uniformPts(). // Although this could be done, it has been omitted for // compatibility with annClusGaussPts() in the colored version, // rand_c.cc. //---------------------------------------------------------------------- void annClusGaussPts( // clustered-Gaussian distribution ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension int n_clus, // number of colors ANNbool new_clust, // generate new clusters. double std_dev) // standard deviation within clusters { static ANNpointArray clusters = NULL;// cluster storage if (clusters == NULL || new_clust) {// need new cluster centers if (clusters != NULL) // clusters already exist annDeallocPts(clusters); // get rid of them clusters = annAllocPts(n_clus, dim); // generate cluster center coords for (int i = 0; i < n_clus; i++) { for (int d = 0; d < dim; d++) { clusters[i][d] = (ANNcoord) annRanUnif(-1,1); } } } for (int i = 0; i < n; i++) { int c = annRanInt(n_clus); // generate cluster index for (int d = 0; d < dim; d++) { pa[i][d] = (ANNcoord) (std_dev*annRanGauss() + clusters[c][d]); } } } //---------------------------------------------------------------------- // annClusOrthFlats - points clustered along orthogonal flats // // This distribution consists of a collection points clustered // among a collection of axis-aligned low dimensional flats in // the hypercube [-1,1]^d. A set of n_clus orthogonal flats are // generated, each whose dimension is a random number between 1 // and max_dim. The points are evenly distributed among the clusters. // For each cluster, we generate points uniformly distributed along // the flat within the hypercube. // // This is done as follows. Each cluster is defined by a d-element // control vector whose components are either: // // CO_FLAG indicating that this component is to be generated // uniformly in [-1,1], // x a value other than CO_FLAG in the range [-1,1], // which indicates that this coordinate is to be // generated as x plus a Gaussian random deviation // with the given standard deviation. // // The number of zero components is the dimension of the flat, which // is a random integer in the range from 1 to max_dim. The points // are disributed between clusters in nearly equal sized groups. // // Note: Once cluster centers have been set, they are not changed, // unless new_clust = true. This is so that subsequent calls generate // points from the same distribution. It follows, of course, that any // attempt to change the dimension or number of clusters without // generating new clusters is asking for trouble. // // To make this a bad scenario at query time, query points should be // selected from a different distribution, e.g. uniform or Gaussian. // // We use a little programming trick to generate groups of roughly // equal size. If n is the total number of points, and n_clus is // the number of clusters, then the c-th cluster (0 <= c < n_clus) // is given floor((n+c)/n_clus) points. It can be shown that this // will exactly consume all n points. // // This procedure makes use of the utility procedure, genOrthFlat // which generates points in one orthogonal flat, according to // the given control vector. // //---------------------------------------------------------------------- const double CO_FLAG = 999; // special flag value static void genOrthFlat( // generate points on an orthog flat ANNpointArray pa, // point array int n, // number of points int dim, // dimension double *control, // control vector double std_dev) // standard deviation { for (int i = 0; i < n; i++) { // generate each point for (int d = 0; d < dim; d++) { // generate each coord if (control[d] == CO_FLAG) // dimension on flat pa[i][d] = (ANNcoord) annRanUnif(-1,1); else // dimension off flat pa[i][d] = (ANNcoord) (std_dev*annRanGauss() + control[d]); } } } void annClusOrthFlats( // clustered along orthogonal flats ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension int n_clus, // number of colors ANNbool new_clust, // generate new clusters. double std_dev, // standard deviation within clusters int max_dim) // maximum dimension of the flats { static ANNpointArray control = NULL; // control vectors if (control == NULL || new_clust) { // need new cluster centers if (control != NULL) { // clusters already exist annDeallocPts(control); // get rid of them } control = annAllocPts(n_clus, dim); for (int c = 0; c < n_clus; c++) { // generate clusters int n_dim = 1 + annRanInt(max_dim); // number of dimensions in flat for (int d = 0; d < dim; d++) { // generate side locations // prob. of picking next dim double Prob = ((double) n_dim)/((double) (dim-d)); if (annRan0() < Prob) { // add this one to flat control[c][d] = CO_FLAG; // flag this entry n_dim--; // one fewer dim to fill } else { // don't take this one control[c][d] = annRanUnif(-1,1);// random value in [-1,1] } } } } int offset = 0; // offset in pa array for (int c = 0; c < n_clus; c++) { // generate clusters int pick = (n+c)/n_clus; // number of points to pick // generate the points genOrthFlat(pa+offset, pick, dim, control[c], std_dev); offset += pick; // increment offset } } //---------------------------------------------------------------------- // annClusEllipsoids - points clustered around axis-aligned ellipsoids // // This distribution consists of a collection points clustered // among a collection of low dimensional ellipsoids whose axes // are alligned with the coordinate axes in the hypercube [-1,1]^d. // The objective is to model distributions in which the points are // distributed in lower dimensional subspaces, and within this // lower dimensional space the points are distributed with a // Gaussian distribution (with no correlation between the // dimensions). // // The distribution is given the number of clusters or "colors" // (n_clus), maximum number of dimensions (max_dim) of the lower // dimensional subspace, a "small" standard deviation // (std_dev_small), and a "large" standard deviation range // (std_dev_lo, std_dev_hi). // // The algorithm generates n_clus cluster centers uniformly from // the hypercube [-1,1]^d. For each cluster, it selects the // dimension of the subspace as a random number r between 1 and // max_dim. These are the dimensions of the ellipsoid. Then it // generates a d-element std dev vector whose entries are the // standard deviation for the coordinates of each cluster in the // distribution. Among the d-element control vector, r randomly // chosen values are chosen uniformly from the range [std_dev_lo, // std_dev_hi]. The remaining values are set to std_dev_small. // // Note that annClusGaussPts is a special case of this in which // max_dim = 0, and std_dev = std_dev_small. // // If the flag new_clust is set, then new cluster centers are // generated. // // This procedure makes use of the utility procedure genGauss // which generates points distributed according to a Gaussian // distribution. // //---------------------------------------------------------------------- static void genGauss( // generate points on a general Gaussian ANNpointArray pa, // point array int n, // number of points int dim, // dimension double *center, // center vector double *std_dev) // standard deviation vector { for (int i = 0; i < n; i++) { for (int d = 0; d < dim; d++) { pa[i][d] = (ANNcoord) (std_dev[d]*annRanGauss() + center[d]); } } } void annClusEllipsoids( // clustered around ellipsoids ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension int n_clus, // number of colors ANNbool new_clust, // generate new clusters. double std_dev_small, // small standard deviation double std_dev_lo, // low standard deviation for ellipses double std_dev_hi, // high standard deviation for ellipses int max_dim) // maximum dimension of the flats { static ANNpointArray centers = NULL; // cluster centers static ANNpointArray std_dev = NULL; // standard deviations if (centers == NULL || new_clust) { // need new cluster centers if (centers != NULL) // clusters already exist annDeallocPts(centers); // get rid of them if (std_dev != NULL) // std deviations already exist annDeallocPts(std_dev); // get rid of them centers = annAllocPts(n_clus, dim); // alloc new clusters and devs std_dev = annAllocPts(n_clus, dim); for (int i = 0; i < n_clus; i++) { // gen cluster center coords for (int d = 0; d < dim; d++) { centers[i][d] = (ANNcoord) annRanUnif(-1,1); } } for (int c = 0; c < n_clus; c++) { // generate cluster std dev int n_dim = 1 + annRanInt(max_dim); // number of dimensions in flat for (int d = 0; d < dim; d++) { // generate std dev's // prob. of picking next dim double Prob = ((double) n_dim)/((double) (dim-d)); if (annRan0() < Prob) { // add this one to ellipse // generate random std dev std_dev[c][d] = annRanUnif(std_dev_lo, std_dev_hi); n_dim--; // one fewer dim to fill } else { // don't take this one std_dev[c][d] = std_dev_small;// use small std dev } } } } int offset = 0; // next slot to fill for (int c = 0; c < n_clus; c++) { // generate clusters int pick = (n+c)/n_clus; // number of points to pick // generate the points genGauss(pa+offset, pick, dim, centers[c], std_dev[c]); offset += pick; // increment offset in array } } //---------------------------------------------------------------------- // annPlanted - Generates points from a "planted" distribution // In high dimensional spaces, interpoint distances tend to be // highly clustered around the mean value. Approximate nearest // neighbor searching makes little sense in this context, unless it // is the case that each query point is significantly closer to its // nearest neighbor than to other points. Thus, the query points // should be planted close to the data points. Given a source data // set, this procedure generates a set of query points having this // property. // // We are given a source data array and a standard deviation. We // generate points as follows. We select a random point from the // source data set, and we generate a Gaussian point centered about // this random point and perturbed by a normal distributed random // variable with mean zero and the given standard deviation along // each coordinate. // // Note that this essentially the same a clustered Gaussian // distribution, but where the cluster centers are given by the // source data set. //---------------------------------------------------------------------- void annPlanted( // planted nearest neighbors ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension ANNpointArray src, // source point array int n_src, // source size double std_dev) // standard deviation about source { for (int i = 0; i < n; i++) { int c = annRanInt(n_src); // generate source index for (int d = 0; d < dim; d++) { pa[i][d] = (ANNcoord) (std_dev*annRanGauss() + src[c][d]); } } } ann-1.1.2+doc/test/test1.save0000644000175000017500000000554411330212441016610 0ustar sylvestresylvestre------------------------------------------------------------ ann_test: Version 1.0 Copyright: David M. Mount and Sunil Arya. Latest Revision: Mar 1, 2005. ------------------------------------------------------------ validate = on (Warning: this may slow execution time.) stats = query_stats [Read Data Points: data_size = 20 file_name = test1-data.pts dim = 2 ] [Read Query Points: query_size = 10 file_name = test1-query.pts dim = 2 ] [Build ann-structure: split_rule = suggest shrink_rule = none data_size = 20 dim = 2 bucket_size = 1 process_time = 0 sec (Structure Statistics: n_nodes = 39 (opt = 40, best if < 400) n_leaves = 20 (0 contain no points) n_splits = 19 n_shrinks = 0 empty_leaves = 0 percent (best if < 50 percent) depth = 6 (opt = 4, best if < 17) avg_aspect_ratio = 1.48847 (best if < 20) ) ] (Computing true nearest neighbors for validation. This may take time.) [Run Queries: query_size = 10 dim = 2 search_method = standard epsilon = 0 near_neigh = 3 true_nn = 13 query_time = 0 sec/query (biased by perf measurements) (Performance stats: [ mean : stddev ]< min , max > leaf_nodes = [ 6.3 : 2.751 ]< 4 , 11 > splitting_nodes = [ 8.8 : 3.676 ]< 5 , 15 > shrinking_nodes = [ 0 : 0 ]< 0 , 0 > total_nodes = [ 15.1 : 6.35 ]< 9 , 26 > points_visited = [ 6.3 : 2.751 ]< 4 , 11 > coord_hits/pt = [ 0.57 : 0.2201 ]< 0.35 , 0.95 > floating_ops_(K) = [ 0.156 : 0.0563 ]< 0.101 , 0.254 > average_error = [ 0 : 0 ]< 0 , 0 > rank_error = [ 0 : 0 ]< 0 , 0 > ) ] [Run Queries: query_size = 10 dim = 2 search_method = priority epsilon = 0 near_neigh = 3 true_nn = 13 query_time = 0 sec/query (biased by perf measurements) (Performance stats: [ mean : stddev ]< min , max > leaf_nodes = [ 5.9 : 2.025 ]< 4 , 9 > splitting_nodes = [ 8.7 : 3.498 ]< 5 , 15 > shrinking_nodes = [ 0 : 0 ]< 0 , 0 > total_nodes = [ 14.6 : 5.42 ]< 9 , 24 > points_visited = [ 5.9 : 2.025 ]< 4 , 9 > 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0.302191 -0.024926 0.554097 -0.391123 0.543936 0.710791 -0.13657 -0.858949 -0.565543 -0.202202 0.904933 -0.522611 -0.700196 -0.0706605 0.68578 0.785019 -0.373929 0.320873 -0.22783 -0.983629 0.20534 0.0679298 0.054554 -0.285939 0.0105797 0.00241309 -0.961614 0.760555 -0.712269 0.18321 0.112195 -0.928513 -0.917439 0.447439 0.694376 0.0474544 -0.957016 0.415338 0.565741 -0.179495 0.15515 -0.130722 0.309835 0.391258 0.300341 0.782176 ann-1.1.2+doc/test/test2.save0000644000175000017500000001512311330212441016603 0ustar sylvestresylvestre------------------------------------------------------------ ann_test: Version 1.0 Copyright: David M. Mount and Sunil Arya. Latest Revision: Mar 1, 2005. ------------------------------------------------------------ validate = on (Warning: this may slow execution time.) stats = query_stats [Read Data Points: data_size = 5000 file_name = test2-data.pts dim = 8 ] [Read Query Points: query_size = 100 file_name = test2-query.pts dim = 8 ] [Build ann-structure: split_rule = suggest shrink_rule = none data_size = 5000 dim = 8 bucket_size = 1 process_time = 0.18 sec (Structure Statistics: n_nodes = 9999 (opt = 10000, best if < 100000) n_leaves = 5000 (0 contain no points) n_splits = 4999 n_shrinks = 0 empty_leaves = 0 percent (best if < 50 percent) depth = 17 (opt = 12, best if < 196) avg_aspect_ratio = 2.03396 (best if < 20) ) ] (Computing true nearest neighbors for validation. This may take time.) [Run Queries: query_size = 100 dim = 8 search_method = standard epsilon = 0 near_neigh = 3 true_nn = 13 query_time = 0.0008 sec/query (biased by perf measurements) (Performance stats: [ mean : stddev ]< min , max > leaf_nodes = [ 269.6 : 154.1 ]< 68 , 1046 > splitting_nodes = [ 448.2 : 259.2 ]< 100 , 1858 > shrinking_nodes = [ 0 : 0 ]< 0 , 0 > total_nodes = [ 717.8 : 412.6 ]< 168 , 2904 > points_visited = [ 269.6 : 154.1 ]< 68 , 1046 > coord_hits/pt = [ 0.1975 : 0.1075 ]< 0.0446 , 0.6974 > floating_ops_(K) = [ 8.492 : 4.716 ]< 1.939 , 32.61 > average_error = [ 0 : 0 ]< 0 , 0 > rank_error = [ 0 : 0 ]< 0 , 0 > ) ] [Run Queries: query_size = 100 dim = 8 search_method = priority epsilon = 0 near_neigh = 3 true_nn = 13 query_time = 0.0011 sec/query (biased by perf measurements) (Performance stats: [ mean : stddev ]< min , max > leaf_nodes = [ 237.7 : 131.6 ]< 68 , 801 > splitting_nodes = [ 408.1 : 227.7 ]< 100 , 1398 > shrinking_nodes = [ 0 : 0 ]< 0 , 0 > total_nodes = [ 645.8 : 358.5 ]< 168 , 2149 > points_visited = [ 237.7 : 131.6 ]< 68 , 801 > coord_hits/pt = [ 0.1679 : 0.08993 ]< 0.0472 , 0.5492 > floating_ops_(K) = [ 10.83 : 6.344 ]< 2.638 , 38.3 > average_error = [ 0 : 0 ]< 0 , 0 > rank_error = [ 0 : 0 ]< 0 , 0 > ) ] [Run Queries: query_size = 100 dim = 8 search_method = standard epsilon = 0.1 near_neigh = 3 true_nn = 13 query_time = 0.0006 sec/query (biased by perf measurements) (Performance stats: [ mean : stddev ]< min , max > leaf_nodes = [ 200.9 : 115.8 ]< 51 , 762 > splitting_nodes = [ 344.9 : 202.4 ]< 77 , 1407 > shrinking_nodes = [ 0 : 0 ]< 0 , 0 > total_nodes = [ 545.9 : 317.4 ]< 128 , 2169 > points_visited = [ 200.9 : 115.8 ]< 51 , 762 > coord_hits/pt = [ 0.1548 : 0.08517 ]< 0.0348 , 0.5494 > floating_ops_(K) = [ 6.606 : 3.703 ]< 1.513 , 25.14 > average_error = [ 0 : 0 ]< 0 , 0 > rank_error = [ 0 : 0 ]< 0 , 0 > ) ] [Run Queries: query_size = 100 dim = 8 search_method = priority epsilon = 0.1 near_neigh = 3 true_nn = 13 query_time = 0.0007 sec/query (biased by perf measurements) (Performance stats: [ mean : stddev ]< min , max > leaf_nodes = [ 176.1 : 101.1 ]< 49 , 629 > splitting_nodes = [ 314.3 : 186.9 ]< 77 , 1285 > shrinking_nodes = [ 0 : 0 ]< 0 , 0 > total_nodes = [ 490.4 : 286.6 ]< 128 , 1914 > points_visited = [ 176.1 : 101.1 ]< 49 , 629 > coord_hits/pt = [ 0.1309 : 0.07112 ]< 0.0374 , 0.4332 > floating_ops_(K) = [ 8.205 : 4.999 ]< 2.032 , 33.27 > average_error = [ 0 : 0 ]< 0 , 0 > rank_error = [ 0 : 0 ]< 0 , 0 > ) ] [Run Queries: query_size = 100 dim = 8 search_method = standard epsilon = 0.5 near_neigh = 3 true_nn = 13 query_time = 0.0002 sec/query (biased by perf measurements) (Performance stats: [ mean : stddev ]< min , max > leaf_nodes = [ 83.07 : 46.06 ]< 23 , 264 > splitting_nodes = [ 163.4 : 94.86 ]< 42 , 512 > shrinking_nodes = [ 0 : 0 ]< 0 , 0 > total_nodes = [ 246.5 : 140.2 ]< 67 , 776 > points_visited = [ 83.07 : 46.06 ]< 23 , 264 > coord_hits/pt = [ 0.0765 : 0.03992 ]< 0.0182 , 0.2192 > floating_ops_(K) = [ 3.224 : 1.734 ]< 0.891 , 9.572 > average_error = [ 0.0009039 : 0.009619 ]< 0 , 0.1516 > rank_error = [ 0 : 0 ]< 0 , 0 > ) ] [Run Queries: query_size = 100 dim = 8 search_method = priority epsilon = 0.5 near_neigh = 3 true_nn = 13 query_time = 0.0004 sec/query (biased by perf measurements) (Performance stats: [ mean : stddev ]< min , max > leaf_nodes = [ 69.72 : 38.29 ]< 21 , 246 > splitting_nodes = [ 146.8 : 81.69 ]< 40 , 475 > shrinking_nodes = [ 0 : 0 ]< 0 , 0 > total_nodes = [ 216.5 : 118.8 ]< 65 , 721 > points_visited = [ 69.72 : 38.29 ]< 21 , 246 > coord_hits/pt = [ 0.06206 : 0.03155 ]< 0.0182 , 0.194 > floating_ops_(K) = [ 3.608 : 1.989 ]< 1.126 , 12.28 > average_error = [ 0.001425 : 0.011 ]< 0 , 0.1516 > rank_error = [ 0 : 0 ]< 0 , 0 > ) ] ann-1.1.2+doc/test/rand.h0000644000175000017500000001204411330212441015756 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: rand.h // Programmer: Sunil Arya and David Mount // Description: Basic include file for random point generators // Last modified: 08/04/06 (Version 1.1.1) //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.0 04/01/05 // Added annClusOrthFlats distribution // Changed procedure names to avoid namespace conflicts // Added annClusFlats distribution // Revision 1.1.1 08/04/06 // Added planted distribution //---------------------------------------------------------------------- #ifndef rand_H #define rand_H //---------------------------------------------------------------------- // Basic includes //---------------------------------------------------------------------- #include // standard includes (rand/random) #include // math routines #include // basic ANN includes //---------------------------------------------------------------------- // Although random/srandom is a more reliable random number generator, // many systems do not have it. If it is not available, set the // preprocessor symbol ANN_NO_RANDOM, and this will substitute the use // of rand/srand for them. //---------------------------------------------------------------------- #ifdef ANN_NO_RANDOM // for systems not having random() #define ANN_RAND rand #define ANN_SRAND srand #define ANN_RAND_MAX RAND_MAX #else // otherwise use rand() #define ANN_RAND random #define ANN_SRAND srandom #define ANN_RAND_MAX 2147483647UL // 2**{31} - 1 // #define ANN_RAND_MAX 1073741824UL // 2**{30} #endif //---------------------------------------------------------------------- // Globals //---------------------------------------------------------------------- extern int annIdum; // random number seed //---------------------------------------------------------------------- // External entry points //---------------------------------------------------------------------- void annUniformPts( // uniform distribution ANNpointArray pa, // point array (modified) int n, // number of points int dim); // dimension void annGaussPts( // Gaussian distribution ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension double std_dev); // standard deviation void annCoGaussPts( // correlated-Gaussian distribution ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension double correlation); // correlation void annLaplacePts( // Laplacian distribution ANNpointArray pa, // point array (modified) int n, // number of points int dim); // dimension void annCoLaplacePts( // correlated-Laplacian distribution ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension double correlation); // correlation void annClusGaussPts( // clustered-Gaussian distribution ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension int n_clus, // number of colors (clusters) ANNbool new_clust, // generate new cluster centers double std_dev); // standard deviation within clusters void annClusOrthFlats( // clustered along orthogonal flats ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension int n_clus, // number of colors ANNbool new_clust, // generate new clusters. double std_dev, // standard deviation within clusters int max_dim); // maximum dimension of the flats void annClusEllipsoids( // clustered around ellipsoids ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension int n_clus, // number of colors ANNbool new_clust, // generate new clusters. double std_dev_small, // small standard deviation double std_dev_lo, // low standard deviation for ellipses double std_dev_hi, // high standard deviation for ellipses int max_dim); // maximum dimension of the flats void annPlanted( // planted nearest neighbors ANNpointArray pa, // point array (modified) int n, // number of points int dim, // dimension ANNpointArray src, // source point array int n_src, // source size double std_dev); // standard deviation about source #endif ann-1.1.2+doc/test/test2.in0000644000175000017500000000060311330212441016250 0ustar sylvestresylvestre validate on stats query_stats dim 8 data_size 5000 read_data_pts test2-data.pts query_size 100 read_query_pts test2-query.pts bucket_size 1 near_neigh 3 split_rule suggest shrink_rule none build_ann epsilon 0.0 run_queries standard run_queries priority epsilon 0.10 run_queries standard run_queries priority epsilon 0.50 run_queries standard run_queries priority ann-1.1.2+doc/test/test1.in0000644000175000017500000000041611330212441016251 0ustar sylvestresylvestre validate on stats query_stats dim 2 data_size 20 query_size 10 read_data_pts test1-data.pts read_query_pts test1-query.pts bucket_size 1 near_neigh 3 split_rule suggest shrink_rule none build_ann epsilon 0.0 run_queries standard run_queries priority ann-1.1.2+doc/Make-config0000644000175000017500000001211711330212441015746 0ustar sylvestresylvestre#----------------------------------------------------------------------- # Makefile variations depending on different configurations # # ANN: Approximate Nearest Neighbors # Version: 1.1 05/03/05 # # (This Make-config structure is based on the one used by Mesa by Brian # Paul. If you succeed in porting ANN to your favorite system, please # send email to mount@cs.umd.edu, and I'll try to include it in this # list.) # #---------------------------------------------------------------------- # The following configuration-dependent variables are passed to each # the Makefile in subdirectories: # # ANNLIB The name of the ANN library file (usually libANN.a) # C++ The C compiler (usually CC or g++) # MAKELIB The command and flags to make a library file (usually # "ar ...") # CFLAGS Flags to C++ compiler # RANLIB For "ranlib" = use ranlib, "true" = don't use ranlib #---------------------------------------------------------------------- # Revision 0.1 09/06/97 # Initial release # Revision 0.2 06/24/98 # Minor changes to fix compilation errors on SGI systems. # Revision 1.0 04/01/05 # Modifications for alpha with cxx # Removed CFLAGS2 options (just write your own) # Removed -DUSING... (Compilers are pretty consistent these days) # Added linux-g++ target # Revision 1.1 05/03/05 # Added macosx-g++ target #----------------------------------------------------------------------------- #----------------------------------------------------------------------------- # Compilation options (add these, as desired, to the CFLAGS variable # in the desired compilation target below). For example, # # "CFLAGS = -O3 -Wall -DANN_PERF" # # -g Debugging. # -O? Run-time optimization. # -Wall Be verbose about warnings. # # -DANN_PERF Enable performance evaluation. (This may slow execution # slightly.) # # -DANN_NO_LIMITS_H # Use this if limits.h or float.h does not exist on your # system. (Also see include/ANN/ANN.h for other changes # needed.) # # -DANN_NO_RANDOM # Use this option if srandom()/random() are not available # on your system. Pseudo-random number generation is used # in the utility program test/ann_test. The combination # srandom()/random() is considered the best pseudo-random # number generator, but is not available on all systems. # If they are not available on your system (for example, # Visual C++) then srand()/rand() will be used instead by # setting this parameter. # # -DWIN32 # This is used only for compilation under windows systems # (but instead of using this, use the various .vcproj # files in the MS_WIN32 directory). #----------------------------------------------------------------------------- # Linux using g++ linux-g++: $(MAKE) targets \ "ANNLIB = libANN.a" \ "C++ = g++" \ "CFLAGS = -O3" \ "MAKELIB = ar ruv" \ "RANLIB = true" # Mac OS X using g++ macosx-g++: $(MAKE) targets \ "ANNLIB = libANN.a" \ "C++ = g++" \ "CFLAGS = -O3" \ "MAKELIB = libtool -static -o " \ "RANLIB = true" # SunOS5 sunos5: $(MAKE) targets \ "ANNLIB = libANN.a" \ "C++ = CC" \ "CFLAGS = -O" \ "MAKELIB = ar ruv" \ "RANLIB = true" # SunOS5 with shared libraries sunos5-sl: $(MAKE) targets \ "ANNLIB = libANN.a" \ "C++ = CC" \ "CFLAGS = -Kpic -O" \ "MAKELIB = ld -G -o" \ "RANLIB = true" # SunOS5 with g++ sunos5-g++: $(MAKE) targets \ "ANNLIB = libANN.a" \ "C++ = g++" \ "CFLAGS = -O3" \ "MAKELIB = ar ruv" \ "RANLIB = true" # SunOS5 with g++ and shared libraries sunos5-g++-sl: $(MAKE) targets \ "ANNLIB = libANN.so" \ "C++ = g++" \ "CFLAGS = -fpic -O3" \ "MAKELIB = ld -G -o" \ "RANLIB = true" #----------------------------------------------------------------------- # Used for the author's testing and debugging only #----------------------------------------------------------------------- # debugging version for authors authors-debug: $(MAKE) targets \ "ANNLIB = libANN.a" \ "C++ = g++" \ "CFLAGS = -g -DANN_PERF -Wall" \ "MAKELIB = ar ruv" \ "RANLIB = true" # performance testing version for authors authors-perf: $(MAKE) targets \ "ANNLIB = libANN.a" \ "C++ = g++" \ "CFLAGS = -O3 -DANN_PERF -Wall" \ "MAKELIB = ar ruv" \ "RANLIB = true" #----------------------------------------------------------------------- # Some older ones that I have not tested with the latest version. #----------------------------------------------------------------------- sgi: $(MAKE) targets \ "ANNLIB = libANN.a" \ "C++ = CC -ansi" \ "CFLAGS = -O2" \ "MAKELIB = ar ruv" \ "RANLIB = true" # DEC Alpha with g++ alpha-g++: $(MAKE) targets \ "ANNLIB = libANN.a" \ "C++ = g++" \ "CFLAGS = -O3" \ "MAKELIB = ar ruv" \ "RANLIB = ranlib" # SunOS4 sunos4: $(MAKE) targets \ "ANNLIB = libANN.a" \ "C++ = CC" \ "CFLAGS = -O" \ "MAKELIB = ar ruv" \ "RANLIB = ranlib" # SunOS4 with g++ sunos4-g++: $(MAKE) targets \ "ANNLIB = libANN.a" \ "C++ = g++" \ "CFLAGS = -O3" \ "MAKELIB = ar ruv" \ "RANLIB = ranlib" # SunOS4 with g++ and shared libraries sunos4-g++-sl: $(MAKE) targets \ "ANNLIB = libANN.so" \ "C++ = g++" \ "CC = g++" \ "CFLAGS = -fPIC -O3" \ "MAKELIB = ld -assert pure-text -o" \ "RANLIB = true" ann-1.1.2+doc/Copyright.txt0000644000175000017500000000305711330212441016417 0ustar sylvestresylvestreANN: Approximate Nearest Neighbors Version: 1.1.2 Release Date: Jan 27, 2010 ---------------------------------------------------------------------------- Copyright (c) 1997-2010 University of Maryland and Sunil Arya and David Mount All Rights Reserved. This program is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser Public License for more details. A copy of the terms and conditions of the license can be found in License.txt or online at http://www.gnu.org/copyleft/lesser.html To obtain a copy, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. Disclaimer ---------- The University of Maryland and the authors make no representations about the suitability or fitness of this software for any purpose. It is provided "as is" without express or implied warranty. --------------------------------------------------------------------- Authors ------- David Mount Dept of Computer Science University of Maryland, College Park, MD 20742 USA mount@cs.umd.edu http://www.cs.umd.edu/~mount/ Sunil Arya Dept of Computer Science Hong University of Science and Technology Clearwater Bay, HONG KONG arya@cs.ust.hk http://www.cs.ust.hk/faculty/arya/ ann-1.1.2+doc/include/0000755000175000017500000000000011330212441015324 5ustar sylvestresylvestreann-1.1.2+doc/include/ANN/0000755000175000017500000000000011330212441015740 5ustar sylvestresylvestreann-1.1.2+doc/include/ANN/ANNperf.h0000644000175000017500000002001311330212441017376 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: ANNperf.h // Programmer: Sunil Arya and David Mount // Last modified: 03/04/98 (Release 0.1) // Description: Include file for ANN performance stats // // Some of the code for statistics gathering has been adapted // from the SmplStat.h package in the g++ library. //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.0 04/01/05 // Added ANN_ prefix to avoid name conflicts. //---------------------------------------------------------------------- #ifndef ANNperf_H #define ANNperf_H //---------------------------------------------------------------------- // basic includes //---------------------------------------------------------------------- #include // basic ANN includes //---------------------------------------------------------------------- // kd-tree stats object // This object is used for collecting information about a kd-tree // or bd-tree. //---------------------------------------------------------------------- class ANNkdStats { // stats on kd-tree public: int dim; // dimension of space int n_pts; // no. of points int bkt_size; // bucket size int n_lf; // no. of leaves (including trivial) int n_tl; // no. of trivial leaves (no points) int n_spl; // no. of splitting nodes int n_shr; // no. of shrinking nodes (for bd-trees) int depth; // depth of tree float sum_ar; // sum of leaf aspect ratios float avg_ar; // average leaf aspect ratio // // reset stats void reset(int d=0, int n=0, int bs=0) { dim = d; n_pts = n; bkt_size = bs; n_lf = n_tl = n_spl = n_shr = depth = 0; sum_ar = avg_ar = 0.0; } ANNkdStats() // basic constructor { reset(); } void merge(const ANNkdStats &st); // merge stats from child }; //---------------------------------------------------------------------- // ANNsampStat // A sample stat collects numeric (double) samples and returns some // simple statistics. Its main functions are: // // reset() Reset to no samples. // += x Include sample x. // samples() Return number of samples. // mean() Return mean of samples. // stdDev() Return standard deviation // min() Return minimum of samples. // max() Return maximum of samples. //---------------------------------------------------------------------- class DLL_API ANNsampStat { int n; // number of samples double sum; // sum double sum2; // sum of squares double minVal, maxVal; // min and max public : void reset() // reset everything { n = 0; sum = sum2 = 0; minVal = ANN_DBL_MAX; maxVal = -ANN_DBL_MAX; } ANNsampStat() { reset(); } // constructor void operator+=(double x) // add sample { n++; sum += x; sum2 += x*x; if (x < minVal) minVal = x; if (x > maxVal) maxVal = x; } int samples() { return n; } // number of samples double mean() { return sum/n; } // mean // standard deviation double stdDev() { return sqrt((sum2 - (sum*sum)/n)/(n-1));} double min() { return minVal; } // minimum double max() { return maxVal; } // maximum }; //---------------------------------------------------------------------- // Operation count updates //---------------------------------------------------------------------- #ifdef ANN_PERF #define ANN_FLOP(n) {ann_Nfloat_ops += (n);} #define ANN_LEAF(n) {ann_Nvisit_lfs += (n);} #define ANN_SPL(n) {ann_Nvisit_spl += (n);} #define ANN_SHR(n) {ann_Nvisit_shr += (n);} #define ANN_PTS(n) {ann_Nvisit_pts += (n);} #define ANN_COORD(n) {ann_Ncoord_hts += (n);} #else #define ANN_FLOP(n) #define ANN_LEAF(n) #define ANN_SPL(n) #define ANN_SHR(n) #define ANN_PTS(n) #define ANN_COORD(n) #endif //---------------------------------------------------------------------- // Performance statistics // The following data and routines are used for computing performance // statistics for nearest neighbor searching. Because these routines // can slow the code down, they can be activated and deactiviated by // defining the ANN_PERF variable, by compiling with the option: // -DANN_PERF //---------------------------------------------------------------------- //---------------------------------------------------------------------- // Global counters for performance measurement // // visit_lfs The number of leaf nodes visited in the // tree. // // visit_spl The number of splitting nodes visited in the // tree. // // visit_shr The number of shrinking nodes visited in the // tree. // // visit_pts The number of points visited in all the // leaf nodes visited. Equivalently, this // is the number of points for which distance // calculations are performed. // // coord_hts The number of times a coordinate of a // data point is accessed. This is generally // less than visit_pts*d if partial distance // calculation is used. This count is low // in the sense that if a coordinate is hit // many times in the same routine we may // count it only once. // // float_ops The number of floating point operations. // This includes all operations in the heap // as well as distance calculations to boxes. // // average_err The average error of each query (the // error of the reported point to the true // nearest neighbor). For k nearest neighbors // the error is computed k times. // // rank_err The rank error of each query (the difference // in the rank of the reported point and its // true rank). // // data_pts The number of data points. This is not // a counter, but used in stats computation. //---------------------------------------------------------------------- extern int ann_Ndata_pts; // number of data points extern int ann_Nvisit_lfs; // number of leaf nodes visited extern int ann_Nvisit_spl; // number of splitting nodes visited extern int ann_Nvisit_shr; // number of shrinking nodes visited extern int ann_Nvisit_pts; // visited points for one query extern int ann_Ncoord_hts; // coordinate hits for one query extern int ann_Nfloat_ops; // floating ops for one query extern ANNsampStat ann_visit_lfs; // stats on leaf nodes visits extern ANNsampStat ann_visit_spl; // stats on splitting nodes visits extern ANNsampStat ann_visit_shr; // stats on shrinking nodes visits extern ANNsampStat ann_visit_nds; // stats on total nodes visits extern ANNsampStat ann_visit_pts; // stats on points visited extern ANNsampStat ann_coord_hts; // stats on coordinate hits extern ANNsampStat ann_float_ops; // stats on floating ops //---------------------------------------------------------------------- // The following need to be part of the public interface, because // they are accessed outside the DLL in ann_test.cpp. //---------------------------------------------------------------------- DLL_API extern ANNsampStat ann_average_err; // average error DLL_API extern ANNsampStat ann_rank_err; // rank error //---------------------------------------------------------------------- // Declaration of externally accessible routines for statistics //---------------------------------------------------------------------- DLL_API void annResetStats(int data_size); // reset stats for a set of queries DLL_API void annResetCounts(); // reset counts for one queries DLL_API void annUpdateStats(); // update stats with current counts DLL_API void annPrintStats(ANNbool validate); // print statistics for a run #endif ann-1.1.2+doc/include/ANN/ANN.h0000644000175000017500000010375611330212441016541 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: ANN.h // Programmer: Sunil Arya and David Mount // Description: Basic include file for approximate nearest // neighbor searching. // Last modified: 01/27/10 (Version 1.1.2) //---------------------------------------------------------------------- // Copyright (c) 1997-2010 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.0 04/01/05 // Added copyright and revision information // Added ANNcoordPrec for coordinate precision. // Added methods theDim, nPoints, maxPoints, thePoints to ANNpointSet. // Cleaned up C++ structure for modern compilers // Revision 1.1 05/03/05 // Added fixed-radius k-NN searching // Revision 1.1.2 01/27/10 // Fixed minor compilation bugs for new versions of gcc //---------------------------------------------------------------------- //---------------------------------------------------------------------- // ANN - approximate nearest neighbor searching // ANN is a library for approximate nearest neighbor searching, // based on the use of standard and priority search in kd-trees // and balanced box-decomposition (bbd) trees. Here are some // references to the main algorithmic techniques used here: // // kd-trees: // Friedman, Bentley, and Finkel, ``An algorithm for finding // best matches in logarithmic expected time,'' ACM // Transactions on Mathematical Software, 3(3):209-226, 1977. // // Priority search in kd-trees: // Arya and Mount, ``Algorithms for fast vector quantization,'' // Proc. of DCC '93: Data Compression Conference, eds. J. A. // Storer and M. Cohn, IEEE Press, 1993, 381-390. // // Approximate nearest neighbor search and bbd-trees: // Arya, Mount, Netanyahu, Silverman, and Wu, ``An optimal // algorithm for approximate nearest neighbor searching,'' // 5th Ann. ACM-SIAM Symposium on Discrete Algorithms, // 1994, 573-582. //---------------------------------------------------------------------- #ifndef ANN_H #define ANN_H #ifdef WIN32 //---------------------------------------------------------------------- // For Microsoft Visual C++, externally accessible symbols must be // explicitly indicated with DLL_API, which is somewhat like "extern." // // The following ifdef block is the standard way of creating macros // which make exporting from a DLL simpler. All files within this DLL // are compiled with the DLL_EXPORTS preprocessor symbol defined on the // command line. In contrast, projects that use (or import) the DLL // objects do not define the DLL_EXPORTS symbol. This way any other // project whose source files include this file see DLL_API functions as // being imported from a DLL, wheras this DLL sees symbols defined with // this macro as being exported. //---------------------------------------------------------------------- #ifdef DLL_EXPORTS #define DLL_API __declspec(dllexport) #else #define DLL_API __declspec(dllimport) #endif //---------------------------------------------------------------------- // DLL_API is ignored for all other systems //---------------------------------------------------------------------- #else #define DLL_API #endif //---------------------------------------------------------------------- // basic includes //---------------------------------------------------------------------- #include // standard lib includes #include // math includes #include // I/O streams #include // C-style strings //---------------------------------------------------------------------- // Limits // There are a number of places where we use the maximum double value as // default initializers (and others may be used, depending on the // data/distance representation). These can usually be found in limits.h // (as LONG_MAX, INT_MAX) or in float.h (as DBL_MAX, FLT_MAX). // // Not all systems have these files. If you are using such a system, // you should set the preprocessor symbol ANN_NO_LIMITS_H when // compiling, and modify the statements below to generate the // appropriate value. For practical purposes, this does not need to be // the maximum double value. It is sufficient that it be at least as // large than the maximum squared distance between between any two // points. //---------------------------------------------------------------------- #ifdef ANN_NO_LIMITS_H // limits.h unavailable #include // replacement for limits.h const double ANN_DBL_MAX = MAXDOUBLE; // insert maximum double #else #include #include const double ANN_DBL_MAX = DBL_MAX; #endif #define ANNversion "1.1.2" // ANN version and information #define ANNversionCmt "" #define ANNcopyright "David M. Mount and Sunil Arya" #define ANNlatestRev "Jan 27, 2010" //---------------------------------------------------------------------- // ANNbool // This is a simple boolean type. Although ANSI C++ is supposed // to support the type bool, some compilers do not have it. //---------------------------------------------------------------------- enum ANNbool {ANNfalse = 0, ANNtrue = 1}; // ANN boolean type (non ANSI C++) //---------------------------------------------------------------------- // ANNcoord, ANNdist // ANNcoord and ANNdist are the types used for representing // point coordinates and distances. They can be modified by the // user, with some care. It is assumed that they are both numeric // types, and that ANNdist is generally of an equal or higher type // from ANNcoord. A variable of type ANNdist should be large // enough to store the sum of squared components of a variable // of type ANNcoord for the number of dimensions needed in the // application. For example, the following combinations are // legal: // // ANNcoord ANNdist // --------- ------------------------------- // short short, int, long, float, double // int int, long, float, double // long long, float, double // float float, double // double double // // It is the user's responsibility to make sure that overflow does // not occur in distance calculation. //---------------------------------------------------------------------- typedef double ANNcoord; // coordinate data type typedef double ANNdist; // distance data type //---------------------------------------------------------------------- // ANNidx // ANNidx is a point index. When the data structure is built, the // points are given as an array. Nearest neighbor results are // returned as an integer index into this array. To make it // clearer when this is happening, we define the integer type // ANNidx. Indexing starts from 0. // // For fixed-radius near neighbor searching, it is possible that // there are not k nearest neighbors within the search radius. To // indicate this, the algorithm returns ANN_NULL_IDX as its result. // It should be distinguishable from any valid array index. //---------------------------------------------------------------------- typedef int ANNidx; // point index const ANNidx ANN_NULL_IDX = -1; // a NULL point index //---------------------------------------------------------------------- // Infinite distance: // The code assumes that there is an "infinite distance" which it // uses to initialize distances before performing nearest neighbor // searches. It should be as larger or larger than any legitimate // nearest neighbor distance. // // On most systems, these should be found in the standard include // file or possibly . If you do not have these // file, some suggested values are listed below, assuming 64-bit // long, 32-bit int and 16-bit short. // // ANNdist ANN_DIST_INF Values (see or ) // ------- ------------ ------------------------------------ // double DBL_MAX 1.79769313486231570e+308 // float FLT_MAX 3.40282346638528860e+38 // long LONG_MAX 0x7fffffffffffffff // int INT_MAX 0x7fffffff // short SHRT_MAX 0x7fff //---------------------------------------------------------------------- const ANNdist ANN_DIST_INF = ANN_DBL_MAX; //---------------------------------------------------------------------- // Significant digits for tree dumps: // When floating point coordinates are used, the routine that dumps // a tree needs to know roughly how many significant digits there // are in a ANNcoord, so it can output points to full precision. // This is defined to be ANNcoordPrec. On most systems these // values can be found in the standard include files or // . For integer types, the value is essentially ignored. // // ANNcoord ANNcoordPrec Values (see or ) // -------- ------------ ------------------------------------ // double DBL_DIG 15 // float FLT_DIG 6 // long doesn't matter 19 // int doesn't matter 10 // short doesn't matter 5 //---------------------------------------------------------------------- #ifdef DBL_DIG // number of sig. bits in ANNcoord const int ANNcoordPrec = DBL_DIG; #else const int ANNcoordPrec = 15; // default precision #endif //---------------------------------------------------------------------- // Self match? // In some applications, the nearest neighbor of a point is not // allowed to be the point itself. This occurs, for example, when // computing all nearest neighbors in a set. By setting the // parameter ANN_ALLOW_SELF_MATCH to ANNfalse, the nearest neighbor // is the closest point whose distance from the query point is // strictly positive. //---------------------------------------------------------------------- const ANNbool ANN_ALLOW_SELF_MATCH = ANNtrue; //---------------------------------------------------------------------- // Norms and metrics: // ANN supports any Minkowski norm for defining distance. In // particular, for any p >= 1, the L_p Minkowski norm defines the // length of a d-vector (v0, v1, ..., v(d-1)) to be // // (|v0|^p + |v1|^p + ... + |v(d-1)|^p)^(1/p), // // (where ^ denotes exponentiation, and |.| denotes absolute // value). The distance between two points is defined to be the // norm of the vector joining them. Some common distance metrics // include // // Euclidean metric p = 2 // Manhattan metric p = 1 // Max metric p = infinity // // In the case of the max metric, the norm is computed by taking // the maxima of the absolute values of the components. ANN is // highly "coordinate-based" and does not support general distances // functions (e.g. those obeying just the triangle inequality). It // also does not support distance functions based on // inner-products. // // For the purpose of computing nearest neighbors, it is not // necessary to compute the final power (1/p). Thus the only // component that is used by the program is |v(i)|^p. // // ANN parameterizes the distance computation through the following // macros. (Macros are used rather than procedures for // efficiency.) Recall that the distance between two points is // given by the length of the vector joining them, and the length // or norm of a vector v is given by formula: // // |v| = ROOT(POW(v0) # POW(v1) # ... # POW(v(d-1))) // // where ROOT, POW are unary functions and # is an associative and // commutative binary operator mapping the following types: // // ** POW: ANNcoord --> ANNdist // ** #: ANNdist x ANNdist --> ANNdist // ** ROOT: ANNdist (>0) --> double // // For early termination in distance calculation (partial distance // calculation) we assume that POW and # together are monotonically // increasing on sequences of arguments, meaning that for all // v0..vk and y: // // POW(v0) #...# POW(vk) <= (POW(v0) #...# POW(vk)) # POW(y). // // Incremental Distance Calculation: // The program uses an optimized method of computing distances for // kd-trees and bd-trees, called incremental distance calculation. // It is used when distances are to be updated when only a single // coordinate of a point has been changed. In order to use this, // we assume that there is an incremental update function DIFF(x,y) // for #, such that if: // // s = x0 # ... # xi # ... # xk // // then if s' is equal to s but with xi replaced by y, that is, // // s' = x0 # ... # y # ... # xk // // then the length of s' can be computed by: // // |s'| = |s| # DIFF(xi,y). // // Thus, if # is + then DIFF(xi,y) is (yi-x). For the L_infinity // norm we make use of the fact that in the program this function // is only invoked when y > xi, and hence DIFF(xi,y)=y. // // Finally, for approximate nearest neighbor queries we assume // that POW and ROOT are related such that // // v*ROOT(x) = ROOT(POW(v)*x) // // Here are the values for the various Minkowski norms: // // L_p: p even: p odd: // ------------------------- ------------------------ // POW(v) = v^p POW(v) = |v|^p // ROOT(x) = x^(1/p) ROOT(x) = x^(1/p) // # = + # = + // DIFF(x,y) = y - x DIFF(x,y) = y - x // // L_inf: // POW(v) = |v| // ROOT(x) = x // # = max // DIFF(x,y) = y // // By default the Euclidean norm is assumed. To change the norm, // uncomment the appropriate set of macros below. //---------------------------------------------------------------------- //---------------------------------------------------------------------- // Use the following for the Euclidean norm //---------------------------------------------------------------------- #define ANN_POW(v) ((v)*(v)) #define ANN_ROOT(x) sqrt(x) #define ANN_SUM(x,y) ((x) + (y)) #define ANN_DIFF(x,y) ((y) - (x)) //---------------------------------------------------------------------- // Use the following for the L_1 (Manhattan) norm //---------------------------------------------------------------------- // #define ANN_POW(v) fabs(v) // #define ANN_ROOT(x) (x) // #define ANN_SUM(x,y) ((x) + (y)) // #define ANN_DIFF(x,y) ((y) - (x)) //---------------------------------------------------------------------- // Use the following for a general L_p norm //---------------------------------------------------------------------- // #define ANN_POW(v) pow(fabs(v),p) // #define ANN_ROOT(x) pow(fabs(x),1/p) // #define ANN_SUM(x,y) ((x) + (y)) // #define ANN_DIFF(x,y) ((y) - (x)) //---------------------------------------------------------------------- // Use the following for the L_infinity (Max) norm //---------------------------------------------------------------------- // #define ANN_POW(v) fabs(v) // #define ANN_ROOT(x) (x) // #define ANN_SUM(x,y) ((x) > (y) ? (x) : (y)) // #define ANN_DIFF(x,y) (y) //---------------------------------------------------------------------- // Array types // The following array types are of basic interest. A point is // just a dimensionless array of coordinates, a point array is a // dimensionless array of points. A distance array is a // dimensionless array of distances and an index array is a // dimensionless array of point indices. The latter two are used // when returning the results of k-nearest neighbor queries. //---------------------------------------------------------------------- typedef ANNcoord* ANNpoint; // a point typedef ANNpoint* ANNpointArray; // an array of points typedef ANNdist* ANNdistArray; // an array of distances typedef ANNidx* ANNidxArray; // an array of point indices //---------------------------------------------------------------------- // Basic point and array utilities: // The following procedures are useful supplements to ANN's nearest // neighbor capabilities. // // annDist(): // Computes the (squared) distance between a pair of points. // Note that this routine is not used internally by ANN for // computing distance calculations. For reasons of efficiency // this is done using incremental distance calculation. Thus, // this routine cannot be modified as a method of changing the // metric. // // Because points (somewhat like strings in C) are stored as // pointers. Consequently, creating and destroying copies of // points may require storage allocation. These procedures do // this. // // annAllocPt() and annDeallocPt(): // Allocate a deallocate storage for a single point, and // return a pointer to it. The argument to AllocPt() is // used to initialize all components. // // annAllocPts() and annDeallocPts(): // Allocate and deallocate an array of points as well a // place to store their coordinates, and initializes the // points to point to their respective coordinates. It // allocates point storage in a contiguous block large // enough to store all the points. It performs no // initialization. // // annCopyPt(): // Creates a copy of a given point, allocating space for // the new point. It returns a pointer to the newly // allocated copy. //---------------------------------------------------------------------- DLL_API ANNdist annDist( int dim, // dimension of space ANNpoint p, // points ANNpoint q); DLL_API ANNpoint annAllocPt( int dim, // dimension ANNcoord c = 0); // coordinate value (all equal) DLL_API ANNpointArray annAllocPts( int n, // number of points int dim); // dimension DLL_API void annDeallocPt( ANNpoint &p); // deallocate 1 point DLL_API void annDeallocPts( ANNpointArray &pa); // point array DLL_API ANNpoint annCopyPt( int dim, // dimension ANNpoint source); // point to copy //---------------------------------------------------------------------- //Overall structure: ANN supports a number of different data structures //for approximate and exact nearest neighbor searching. These are: // // ANNbruteForce A simple brute-force search structure. // ANNkd_tree A kd-tree tree search structure. ANNbd_tree // A bd-tree tree search structure (a kd-tree with shrink // capabilities). // // At a minimum, each of these data structures support k-nearest // neighbor queries. The nearest neighbor query, annkSearch, // returns an integer identifier and the distance to the nearest // neighbor(s) and annRangeSearch returns the nearest points that // lie within a given query ball. // // Each structure is built by invoking the appropriate constructor // and passing it (at a minimum) the array of points, the total // number of points and the dimension of the space. Each structure // is also assumed to support a destructor and member functions // that return basic information about the point set. // // Note that the array of points is not copied by the data // structure (for reasons of space efficiency), and it is assumed // to be constant throughout the lifetime of the search structure. // // The search algorithm, annkSearch, is given the query point (q), // and the desired number of nearest neighbors to report (k), and // the error bound (eps) (whose default value is 0, implying exact // nearest neighbors). It returns two arrays which are assumed to // contain at least k elements: one (nn_idx) contains the indices // (within the point array) of the nearest neighbors and the other // (dd) contains the squared distances to these nearest neighbors. // // The search algorithm, annkFRSearch, is a fixed-radius kNN // search. In addition to a query point, it is given a (squared) // radius bound. (This is done for consistency, because the search // returns distances as squared quantities.) It does two things. // First, it computes the k nearest neighbors within the radius // bound, and second, it returns the total number of points lying // within the radius bound. It is permitted to set k = 0, in which // case it effectively answers a range counting query. If the // error bound epsilon is positive, then the search is approximate // in the sense that it is free to ignore any point that lies // outside a ball of radius r/(1+epsilon), where r is the given // (unsquared) radius bound. // // The generic object from which all the search structures are // dervied is given below. It is a virtual object, and is useless // by itself. //---------------------------------------------------------------------- class DLL_API ANNpointSet { public: virtual ~ANNpointSet() {} // virtual distructor virtual void annkSearch( // approx k near neighbor search ANNpoint q, // query point int k, // number of near neighbors to return ANNidxArray nn_idx, // nearest neighbor array (modified) ANNdistArray dd, // dist to near neighbors (modified) double eps=0.0 // error bound ) = 0; // pure virtual (defined elsewhere) virtual int annkFRSearch( // approx fixed-radius kNN search ANNpoint q, // query point ANNdist sqRad, // squared radius int k = 0, // number of near neighbors to return ANNidxArray nn_idx = NULL, // nearest neighbor array (modified) ANNdistArray dd = NULL, // dist to near neighbors (modified) double eps=0.0 // error bound ) = 0; // pure virtual (defined elsewhere) virtual int theDim() = 0; // return dimension of space virtual int nPoints() = 0; // return number of points // return pointer to points virtual ANNpointArray thePoints() = 0; }; //---------------------------------------------------------------------- // Brute-force nearest neighbor search: // The brute-force search structure is very simple but inefficient. // It has been provided primarily for the sake of comparison with // and validation of the more complex search structures. // // Query processing is the same as described above, but the value // of epsilon is ignored, since all distance calculations are // performed exactly. // // WARNING: This data structure is very slow, and should not be // used unless the number of points is very small. // // Internal information: // --------------------- // This data structure bascially consists of the array of points // (each a pointer to an array of coordinates). The search is // performed by a simple linear scan of all the points. //---------------------------------------------------------------------- class DLL_API ANNbruteForce: public ANNpointSet { int dim; // dimension int n_pts; // number of points ANNpointArray pts; // point array public: ANNbruteForce( // constructor from point array ANNpointArray pa, // point array int n, // number of points int dd); // dimension ~ANNbruteForce(); // destructor void annkSearch( // approx k near neighbor search ANNpoint q, // query point int k, // number of near neighbors to return ANNidxArray nn_idx, // nearest neighbor array (modified) ANNdistArray dd, // dist to near neighbors (modified) double eps=0.0); // error bound int annkFRSearch( // approx fixed-radius kNN search ANNpoint q, // query point ANNdist sqRad, // squared radius int k = 0, // number of near neighbors to return ANNidxArray nn_idx = NULL, // nearest neighbor array (modified) ANNdistArray dd = NULL, // dist to near neighbors (modified) double eps=0.0); // error bound int theDim() // return dimension of space { return dim; } int nPoints() // return number of points { return n_pts; } ANNpointArray thePoints() // return pointer to points { return pts; } }; //---------------------------------------------------------------------- // kd- and bd-tree splitting and shrinking rules // kd-trees supports a collection of different splitting rules. // In addition to the standard kd-tree splitting rule proposed // by Friedman, Bentley, and Finkel, we have introduced a // number of other splitting rules, which seem to perform // as well or better (for the distributions we have tested). // // The splitting methods given below allow the user to tailor // the data structure to the particular data set. They are // are described in greater details in the kd_split.cc source // file. The method ANN_KD_SUGGEST is the method chosen (rather // subjectively) by the implementors as the one giving the // fastest performance, and is the default splitting method. // // As with splitting rules, there are a number of different // shrinking rules. The shrinking rule ANN_BD_NONE does no // shrinking (and hence produces a kd-tree tree). The rule // ANN_BD_SUGGEST uses the implementors favorite rule. //---------------------------------------------------------------------- enum ANNsplitRule { ANN_KD_STD = 0, // the optimized kd-splitting rule ANN_KD_MIDPT = 1, // midpoint split ANN_KD_FAIR = 2, // fair split ANN_KD_SL_MIDPT = 3, // sliding midpoint splitting method ANN_KD_SL_FAIR = 4, // sliding fair split method ANN_KD_SUGGEST = 5}; // the authors' suggestion for best const int ANN_N_SPLIT_RULES = 6; // number of split rules enum ANNshrinkRule { ANN_BD_NONE = 0, // no shrinking at all (just kd-tree) ANN_BD_SIMPLE = 1, // simple splitting ANN_BD_CENTROID = 2, // centroid splitting ANN_BD_SUGGEST = 3}; // the authors' suggested choice const int ANN_N_SHRINK_RULES = 4; // number of shrink rules //---------------------------------------------------------------------- // kd-tree: // The main search data structure supported by ANN is a kd-tree. // The main constructor is given a set of points and a choice of // splitting method to use in building the tree. // // Construction: // ------------- // The constructor is given the point array, number of points, // dimension, bucket size (default = 1), and the splitting rule // (default = ANN_KD_SUGGEST). The point array is not copied, and // is assumed to be kept constant throughout the lifetime of the // search structure. There is also a "load" constructor that // builds a tree from a file description that was created by the // Dump operation. // // Search: // ------- // There are two search methods: // // Standard search (annkSearch()): // Searches nodes in tree-traversal order, always visiting // the closer child first. // Priority search (annkPriSearch()): // Searches nodes in order of increasing distance of the // associated cell from the query point. For many // distributions the standard search seems to work just // fine, but priority search is safer for worst-case // performance. // // Printing: // --------- // There are two methods provided for printing the tree. Print() // is used to produce a "human-readable" display of the tree, with // indenation, which is handy for debugging. Dump() produces a // format that is suitable reading by another program. There is a // "load" constructor, which constructs a tree which is assumed to // have been saved by the Dump() procedure. // // Performance and Structure Statistics: // ------------------------------------- // The procedure getStats() collects statistics information on the // tree (its size, height, etc.) See ANNperf.h for information on // the stats structure it returns. // // Internal information: // --------------------- // The data structure consists of three major chunks of storage. // The first (implicit) storage are the points themselves (pts), // which have been provided by the users as an argument to the // constructor, or are allocated dynamically if the tree is built // using the load constructor). These should not be changed during // the lifetime of the search structure. It is the user's // responsibility to delete these after the tree is destroyed. // // The second is the tree itself (which is dynamically allocated in // the constructor) and is given as a pointer to its root node // (root). These nodes are automatically deallocated when the tree // is deleted. See the file src/kd_tree.h for further information // on the structure of the tree nodes. // // Each leaf of the tree does not contain a pointer directly to a // point, but rather contains a pointer to a "bucket", which is an // array consisting of point indices. The third major chunk of // storage is an array (pidx), which is a large array in which all // these bucket subarrays reside. (The reason for storing them // separately is the buckets are typically small, but of varying // sizes. This was done to avoid fragmentation.) This array is // also deallocated when the tree is deleted. // // In addition to this, the tree consists of a number of other // pieces of information which are used in searching and for // subsequent tree operations. These consist of the following: // // dim Dimension of space // n_pts Number of points currently in the tree // n_max Maximum number of points that are allowed // in the tree // bkt_size Maximum bucket size (no. of points per leaf) // bnd_box_lo Bounding box low point // bnd_box_hi Bounding box high point // splitRule Splitting method used // //---------------------------------------------------------------------- //---------------------------------------------------------------------- // Some types and objects used by kd-tree functions // See src/kd_tree.h and src/kd_tree.cpp for definitions //---------------------------------------------------------------------- class ANNkdStats; // stats on kd-tree class ANNkd_node; // generic node in a kd-tree typedef ANNkd_node* ANNkd_ptr; // pointer to a kd-tree node class DLL_API ANNkd_tree: public ANNpointSet { protected: int dim; // dimension of space int n_pts; // number of points in tree int bkt_size; // bucket size ANNpointArray pts; // the points ANNidxArray pidx; // point indices (to pts array) ANNkd_ptr root; // root of kd-tree ANNpoint bnd_box_lo; // bounding box low point ANNpoint bnd_box_hi; // bounding box high point void SkeletonTree( // construct skeleton tree int n, // number of points int dd, // dimension int bs, // bucket size ANNpointArray pa = NULL, // point array (optional) ANNidxArray pi = NULL); // point indices (optional) public: ANNkd_tree( // build skeleton tree int n = 0, // number of points int dd = 0, // dimension int bs = 1); // bucket size ANNkd_tree( // build from point array ANNpointArray pa, // point array int n, // number of points int dd, // dimension int bs = 1, // bucket size ANNsplitRule split = ANN_KD_SUGGEST); // splitting method ANNkd_tree( // build from dump file std::istream& in); // input stream for dump file ~ANNkd_tree(); // tree destructor void annkSearch( // approx k near neighbor search ANNpoint q, // query point int k, // number of near neighbors to return ANNidxArray nn_idx, // nearest neighbor array (modified) ANNdistArray dd, // dist to near neighbors (modified) double eps=0.0); // error bound void annkPriSearch( // priority k near neighbor search ANNpoint q, // query point int k, // number of near neighbors to return ANNidxArray nn_idx, // nearest neighbor array (modified) ANNdistArray dd, // dist to near neighbors (modified) double eps=0.0); // error bound int annkFRSearch( // approx fixed-radius kNN search ANNpoint q, // the query point ANNdist sqRad, // squared radius of query ball int k, // number of neighbors to return ANNidxArray nn_idx = NULL, // nearest neighbor array (modified) ANNdistArray dd = NULL, // dist to near neighbors (modified) double eps=0.0); // error bound int theDim() // return dimension of space { return dim; } int nPoints() // return number of points { return n_pts; } ANNpointArray thePoints() // return pointer to points { return pts; } virtual void Print( // print the tree (for debugging) ANNbool with_pts, // print points as well? std::ostream& out); // output stream virtual void Dump( // dump entire tree ANNbool with_pts, // print points as well? std::ostream& out); // output stream virtual void getStats( // compute tree statistics ANNkdStats& st); // the statistics (modified) }; //---------------------------------------------------------------------- // Box decomposition tree (bd-tree) // The bd-tree is inherited from a kd-tree. The main difference // in the bd-tree and the kd-tree is a new type of internal node // called a shrinking node (in the kd-tree there is only one type // of internal node, a splitting node). The shrinking node // makes it possible to generate balanced trees in which the // cells have bounded aspect ratio, by allowing the decomposition // to zoom in on regions of dense point concentration. Although // this is a nice idea in theory, few point distributions are so // densely clustered that this is really needed. //---------------------------------------------------------------------- class DLL_API ANNbd_tree: public ANNkd_tree { public: ANNbd_tree( // build skeleton tree int n, // number of points int dd, // dimension int bs = 1) // bucket size : ANNkd_tree(n, dd, bs) {} // build base kd-tree ANNbd_tree( // build from point array ANNpointArray pa, // point array int n, // number of points int dd, // dimension int bs = 1, // bucket size ANNsplitRule split = ANN_KD_SUGGEST, // splitting rule ANNshrinkRule shrink = ANN_BD_SUGGEST); // shrinking rule ANNbd_tree( // build from dump file std::istream& in); // input stream for dump file }; //---------------------------------------------------------------------- // Other functions // annMaxPtsVisit Sets a limit on the maximum number of points // to visit in the search. // annClose Can be called when all use of ANN is finished. // It clears up a minor memory leak. //---------------------------------------------------------------------- DLL_API void annMaxPtsVisit( // max. pts to visit in search int maxPts); // the limit DLL_API void annClose(); // called to end use of ANN #endif ann-1.1.2+doc/include/ANN/ANNx.h0000644000175000017500000001427011330212441016721 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: ANNx.h // Programmer: Sunil Arya and David Mount // Description: Internal include file for ANN // Last modified: 01/27/10 (Version 1.1.2) // // These declarations are of use in manipulating some of // the internal data objects appearing in ANN, but are not // needed for applications just using the nearest neighbor // search. // // Typical users of ANN should not need to access this file. //---------------------------------------------------------------------- // Copyright (c) 1997-2010 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.0 04/01/05 // Changed LO, HI, IN, OUT to ANN_LO, ANN_HI, etc. // Revision 1.1.2 01/27/10 // Fixed minor compilation bugs for new versions of gcc //---------------------------------------------------------------------- #ifndef ANNx_H #define ANNx_H #include // I/O manipulators #include // ANN includes //---------------------------------------------------------------------- // Global constants and types //---------------------------------------------------------------------- enum {ANN_LO=0, ANN_HI=1}; // splitting indices enum {ANN_IN=0, ANN_OUT=1}; // shrinking indices // what to do in case of error enum ANNerr {ANNwarn = 0, ANNabort = 1}; //---------------------------------------------------------------------- // Maximum number of points to visit // We have an option for terminating the search early if the // number of points visited exceeds some threshold. If the // threshold is 0 (its default) this means there is no limit // and the algorithm applies its normal termination condition. //---------------------------------------------------------------------- extern int ANNmaxPtsVisited; // maximum number of pts visited extern int ANNptsVisited; // number of pts visited in search //---------------------------------------------------------------------- // Global function declarations //---------------------------------------------------------------------- void annError( // ANN error routine const char* msg, // error message ANNerr level); // level of error void annPrintPt( // print a point ANNpoint pt, // the point int dim, // the dimension std::ostream &out); // output stream //---------------------------------------------------------------------- // Orthogonal (axis aligned) rectangle // Orthogonal rectangles are represented by two points, one // for the lower left corner (min coordinates) and the other // for the upper right corner (max coordinates). // // The constructor initializes from either a pair of coordinates, // pair of points, or another rectangle. Note that all constructors // allocate new point storage. The destructor deallocates this // storage. // // BEWARE: Orthogonal rectangles should be passed ONLY BY REFERENCE. // (C++'s default copy constructor will not allocate new point // storage, then on return the destructor free's storage, and then // you get into big trouble in the calling procedure.) //---------------------------------------------------------------------- class ANNorthRect { public: ANNpoint lo; // rectangle lower bounds ANNpoint hi; // rectangle upper bounds // ANNorthRect( // basic constructor int dd, // dimension of space ANNcoord l=0, // default is empty ANNcoord h=0) { lo = annAllocPt(dd, l); hi = annAllocPt(dd, h); } ANNorthRect( // (almost a) copy constructor int dd, // dimension const ANNorthRect &r) // rectangle to copy { lo = annCopyPt(dd, r.lo); hi = annCopyPt(dd, r.hi); } ANNorthRect( // construct from points int dd, // dimension ANNpoint l, // low point ANNpoint h) // hight point { lo = annCopyPt(dd, l); hi = annCopyPt(dd, h); } ~ANNorthRect() // destructor { annDeallocPt(lo); annDeallocPt(hi); } ANNbool inside(int dim, ANNpoint p);// is point p inside rectangle? }; void annAssignRect( // assign one rect to another int dim, // dimension (both must be same) ANNorthRect &dest, // destination (modified) const ANNorthRect &source); // source //---------------------------------------------------------------------- // Orthogonal (axis aligned) halfspace // An orthogonal halfspace is represented by an integer cutting // dimension cd, coordinate cutting value, cv, and side, sd, which is // either +1 or -1. Our convention is that point q lies in the (closed) // halfspace if (q[cd] - cv)*sd >= 0. //---------------------------------------------------------------------- class ANNorthHalfSpace { public: int cd; // cutting dimension ANNcoord cv; // cutting value int sd; // which side // ANNorthHalfSpace() // default constructor { cd = 0; cv = 0; sd = 0; } ANNorthHalfSpace( // basic constructor int cdd, // dimension of space ANNcoord cvv, // cutting value int sdd) // side { cd = cdd; cv = cvv; sd = sdd; } ANNbool in(ANNpoint q) const // is q inside halfspace? { return (ANNbool) ((q[cd] - cv)*sd >= 0); } ANNbool out(ANNpoint q) const // is q outside halfspace? { return (ANNbool) ((q[cd] - cv)*sd < 0); } ANNdist dist(ANNpoint q) const // (squared) distance from q { return (ANNdist) ANN_POW(q[cd] - cv); } void setLowerBound(int d, ANNpoint p)// set to lower bound at p[i] { cd = d; cv = p[d]; sd = +1; } void setUpperBound(int d, ANNpoint p)// set to upper bound at p[i] { cd = d; cv = p[d]; sd = -1; } void project(ANNpoint &q) // project q (modified) onto halfspace { if (out(q)) q[cd] = cv; } }; // array of halfspaces typedef ANNorthHalfSpace *ANNorthHSArray; #endif ann-1.1.2+doc/MS_Win32/0000755000175000017500000000000011330212441015202 5ustar sylvestresylvestreann-1.1.2+doc/MS_Win32/sample/0000755000175000017500000000000011330212441016463 5ustar sylvestresylvestreann-1.1.2+doc/MS_Win32/sample/sample.vcproj0000644000175000017500000001407011330212441021173 0ustar sylvestresylvestre ann-1.1.2+doc/MS_Win32/Ann.sln0000644000175000017500000000521411330212441016436 0ustar sylvestresylvestreMicrosoft Visual Studio Solution File, Format Version 10.00 # Visual Studio 2008 Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "dll", "dll\dll.vcproj", "{A7D00B21-CB9C-4BBB-8DEE-51025104F867}" EndProject Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "sample", "sample\sample.vcproj", "{C76F5A10-7A4A-4546-9414-296DB38BE825}" ProjectSection(ProjectDependencies) = postProject {A7D00B21-CB9C-4BBB-8DEE-51025104F867} = {A7D00B21-CB9C-4BBB-8DEE-51025104F867} EndProjectSection EndProject Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "test", "test\test.vcproj", "{6AC673C7-7B3F-4520-A761-647B212A4BEF}" ProjectSection(ProjectDependencies) = postProject {A7D00B21-CB9C-4BBB-8DEE-51025104F867} = {A7D00B21-CB9C-4BBB-8DEE-51025104F867} EndProjectSection EndProject Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "ann2fig", "ann2fig\ann2fig.vcproj", "{622DD7D8-0C0A-4303-9176-C9A8AF467E70}" ProjectSection(ProjectDependencies) = postProject {A7D00B21-CB9C-4BBB-8DEE-51025104F867} = {A7D00B21-CB9C-4BBB-8DEE-51025104F867} EndProjectSection EndProject Global GlobalSection(SolutionConfigurationPlatforms) = preSolution Debug|Win32 = Debug|Win32 Release|Win32 = Release|Win32 EndGlobalSection GlobalSection(ProjectConfigurationPlatforms) = postSolution {A7D00B21-CB9C-4BBB-8DEE-51025104F867}.Debug|Win32.ActiveCfg = Debug|Win32 {A7D00B21-CB9C-4BBB-8DEE-51025104F867}.Debug|Win32.Build.0 = Debug|Win32 {A7D00B21-CB9C-4BBB-8DEE-51025104F867}.Release|Win32.ActiveCfg = Release|Win32 {A7D00B21-CB9C-4BBB-8DEE-51025104F867}.Release|Win32.Build.0 = Release|Win32 {C76F5A10-7A4A-4546-9414-296DB38BE825}.Debug|Win32.ActiveCfg = Debug|Win32 {C76F5A10-7A4A-4546-9414-296DB38BE825}.Debug|Win32.Build.0 = Debug|Win32 {C76F5A10-7A4A-4546-9414-296DB38BE825}.Release|Win32.ActiveCfg = Release|Win32 {C76F5A10-7A4A-4546-9414-296DB38BE825}.Release|Win32.Build.0 = Release|Win32 {6AC673C7-7B3F-4520-A761-647B212A4BEF}.Debug|Win32.ActiveCfg = Debug|Win32 {6AC673C7-7B3F-4520-A761-647B212A4BEF}.Debug|Win32.Build.0 = Debug|Win32 {6AC673C7-7B3F-4520-A761-647B212A4BEF}.Release|Win32.ActiveCfg = Release|Win32 {6AC673C7-7B3F-4520-A761-647B212A4BEF}.Release|Win32.Build.0 = Release|Win32 {622DD7D8-0C0A-4303-9176-C9A8AF467E70}.Debug|Win32.ActiveCfg = Debug|Win32 {622DD7D8-0C0A-4303-9176-C9A8AF467E70}.Debug|Win32.Build.0 = Debug|Win32 {622DD7D8-0C0A-4303-9176-C9A8AF467E70}.Release|Win32.ActiveCfg = Release|Win32 {622DD7D8-0C0A-4303-9176-C9A8AF467E70}.Release|Win32.Build.0 = Release|Win32 EndGlobalSection GlobalSection(SolutionProperties) = preSolution HideSolutionNode = FALSE EndGlobalSection EndGlobal ann-1.1.2+doc/MS_Win32/Makefile0000644000175000017500000000434611330212441016651 0ustar sylvestresylvestre#----------------------------------------------------------------------------- # Makefile for Windows Versions. # # ANN: Approximate Nearest Neighbors # Version: 1.1.1 08/04/06 #----------------------------------------------------------------------------- # Copyright (c) 1997-2005 University of Maryland and Sunil Arya and # David Mount. All Rights Reserved. # # This software and related documentation is part of the Approximate # Nearest Neighbor Library (ANN). This software is provided under # the provisions of the Lesser GNU Public License (LGPL). See the # file ../ReadMe.txt for further information. # # The University of Maryland (U.M.) and the authors make no # representations about the suitability or fitness of this software for # any purpose. It is provided "as is" without express or implied # warranty. #----------------------------------------------------------------------------- # Revision 1.0 05/03/05 # Initial release # Revision 1.1.1 08/04/06 # Added copyright/license #----------------------------------------------------------------------------- #----------------------------------------------------------------------------- # This is not used for compiling the dll. It is just used for cleaning # things up for distribution. For compilcation, open the Ann.sln # solution file in Microsoft Windows Visual Studio.NET. #----------------------------------------------------------------------------- default: @echo "Enter one of the following:" @echo " make clean remove object files" @echo " make realclean remove library and executable files" @echo " " @echo "See file Makefile for other compilation options." #----------------------------------------------------------------------------- # Remove .o files and core files #----------------------------------------------------------------------------- clean: -rm -f -r ann2fig/Debug ann2fig/Release -rm -f -r dll/Debug dll/Release -rm -f -r sample/Debug sample/Release -rm -f -r test/Debug test/Release -rm -f Ann.ncb Ann.suo #----------------------------------------------------------------------------- # Remove everthing that can be remade #----------------------------------------------------------------------------- realclean: clean -rm -f bin/* ann-1.1.2+doc/MS_Win32/dll/0000755000175000017500000000000011330212441015755 5ustar sylvestresylvestreann-1.1.2+doc/MS_Win32/dll/dll.vcproj0000644000175000017500000003403611330212441017763 0ustar sylvestresylvestre ann-1.1.2+doc/MS_Win32/test/0000755000175000017500000000000011330212441016161 5ustar sylvestresylvestreann-1.1.2+doc/MS_Win32/test/test.vcproj0000644000175000017500000001530311330212441020367 0ustar sylvestresylvestre ann-1.1.2+doc/MS_Win32/bin/0000755000175000017500000000000011330212441015752 5ustar sylvestresylvestreann-1.1.2+doc/MS_Win32/ann2fig/0000755000175000017500000000000011330212441016526 5ustar sylvestresylvestreann-1.1.2+doc/MS_Win32/ann2fig/ann2fig.vcproj0000644000175000017500000001040411330212441021276 0ustar sylvestresylvestre ann-1.1.2+doc/ReadMe.txt0000644000175000017500000000476011330212622015607 0ustar sylvestresylvestreANN: Approximate Nearest Neighbors Version: 1.1.2 Release date: Jan 27, 2010 ---------------------------------------------------------------------------- Copyright (c) 1997-2010 University of Maryland and Sunil Arya and David Mount. All Rights Reserved. See Copyright.txt and License.txt for complete information on terms and conditions of use and distribution of this software. ---------------------------------------------------------------------------- Authors ------- David Mount Dept of Computer Science University of Maryland, College Park, MD 20742 USA mount@cs.umd.edu http://www.cs.umd.edu/~mount/ Sunil Arya Dept of Computer Science Hong University of Science and Technology Clearwater Bay, HONG KONG arya@cs.ust.hk http://www.cs.ust.hk/faculty/arya/ Introduction ------------ ANN is a library written in the C++ programming language to support both exact and approximate nearest neighbor searching in spaces of various dimensions. It was implemented by David M. Mount of the University of Maryland, and Sunil Arya of the Hong Kong University of Science and Technology. ANN (pronounced like the name ``Ann'') stands for Approximate Nearest Neighbors. ANN is also a testbed containing programs and procedures for generating data sets, collecting and analyzing statistics on the performance of nearest neighbor algorithms and data structures, and visualizing the geometric structure of these data structures. The ANN source code and documentation is available from the following web page: http://www.cs.umd.edu/~mount/ANN For more information on ANN and its use, see the ``ANN Programming Manual,'' which is provided with the software distribution. ---------------------------------------------------------------------------- History Version 0.1 03/04/98 Preliminary release Version 0.2 06/24/98 Changes for SGI compiler. Version 1.0 04/01/05 Fixed a number of small bugs Added dump/load operations Added annClose to eliminate minor memory leak Improved compatibility with current C++ compilers Added compilation for Microsoft Visual Studio.NET Added compilation for Linux 2.x Version 1.1 05/03/05 Added make target for Mac OS X Added fixed-radius range searching and counting Added instructions on compiling/using ANN on Windows platforms Fixed minor output bug in ann2fig Version 1.1.1 08/04/06 Added "planted" distribution Updated old source comments for GNU LPL. Version 1.1.2 01/27/10 Fixed minor compilation bugs for new versions of gcc ann-1.1.2+doc/doc/0000755000175000017500000000000011644667627014502 5ustar sylvestresylvestreann-1.1.2+doc/doc/ann.bib0000644000175000017500000002556010220271373015716 0ustar sylvestresylvestre@inproceedings{AMN94 , author = "S. Arya and D. M. Mount and N. Netanyahu and R. Silverman and A. Y. Wu" , title = "An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions" , booktitle = "Proc. 5th ACM-SIAM Sympos. Discrete Algorithms" , year = 1994 , pages = "573--582" } @article{AMN98 , author = "S. Arya and D. M. Mount and N. S. Netanyahu and R. Silverman and A. Wu" , title = "An Optimal Algorithm for Approximate Nearest Neighbor Searching" , journal = "J. ACM" , volume = 45 , year = 1998 , pages = "891--923" } @inproceedings{AMN95 , author = "S. Arya and D. M. Mount and O. Narayan" , title = "Accounting for boundary effects in nearest neighbor searching" , booktitle = "Proc. 11th Annu. ACM Sympos. Comput. Geom." , year = 1995 , pages = "336--344" } @inproceedings{ArM93 , author = "S. Arya and D. M. Mount" , title = "Approximate Nearest Neighbor Queries in Fixed Dimensions" , booktitle = "Proc. 4th ACM-SIAM Sympos. Discrete Algorithms" , year = 1993 , pages = "271--280" , update = "93.05 smid" } @inproceedings{ArM93b , author = "S. Arya and D. M. 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Edelsbrunner" , title = "Algorithms in Combinatorial Geometry" , series = "EATCS Monographs on Theoretical Computer Science" , volume = "10" , publisher = "Springer-Verlag" , address = "Heidelberg, West Germany" , year = 1987 , keywords = "design of algorithms, discrete geometry, book" , update = "93.09 erickson" } @article{FBF77 , author = "J. H. Friedman and J. L. Bentley and R. A. Finkel" , title = "An algorithm for finding best matches in logarithmic expected time" , journal = "ACM Transactions on Mathematical Software" , year = 1977 , volume = "3" , number = "3" , pages = "209--226" } @inproceedings{GaR93 , author = "I. Galperin and R. L. Rivest" , title = "Scapegoat trees" , booktitle = "Proc. 4th ACM-SIAM Sympos. Discrete Algorithms" , year = 1993 , pages = "165--174" } @inproceedings{GRS93 , author = "M. Golin and R. Raman and C. Schwarz and M. Smid" , title = "Randomized Data Structures for the Dynamic Closest-Pair Problem" , booktitle = "Proc. 4th ACM-SIAM Sympos. Discrete Algorithms" , year = 1993 , pages = "301--310" , update = "93.05 smid" } @inproceedings{Kle97 , author = "J. Kleinberg" , title = "Two Algorithms for Nearest-Neighbor Search in High Dimension" , booktitle = "Proc. 29th Annu. ACM Sympos. Theory Comput." , nickname = "STOC 97" , year = 1997 , pages = "599--608" , update = "97.07 agarwal" } @inproceedings{LeS92 , author = "H.-P. Lenhof and M. Smid" , title = "Enumerating the $k$ closest pairs optimally" , booktitle = "Proc. 33rd Ann. IEEE Sympos. Found. Comput. Sci." , year = 1992 , pages = "380--386" } @inproceedings{MMS94 , author = "J. S. B. Mitchell and D. M. Mount and S. Suri" , title = "Query-sensitive ray shooting" , booktitle = "Proc. 10th Annu. ACM Sympos. Comput. Geom." , year = 1994 , pages = "359--368" } @inproceedings{MNS95 , author = "D. M. Mount and N. Netanyahu and R. Silverman and A. Y. Wu" , title = "Chromatic Nearest Neighbor Searching: {A} Query Sensitive Approach" , booktitle = "Proc. 7th Canad. Conf. Comput. Geom." , year = 1995 , pages = "261--266" } @inproceedings{MiV92 , author = "S. A. Mitchell and S. A. Vavasis" , title = "Quality mesh generation in three dimensions" , booktitle = "Proc. 8th Annu. ACM Sympos. Comput. Geom." , year = 1992 , pages = "212--221" , succeeds = "mv-qmgtd-92t" } @inproceedings{OhS83 , author = "Y. Ohsawa and M. Sakauchi" , title = "The {BD}-tree: {A} new ${N}$-dimensional data structure with highly efficient dynamic characteristics" , booktitle = "IFIP Conf." , address = "Paris" , year = 1983 , pages = "539--544" } @book{Ope93 , author = "OpenGL Architecture Review Board" , title = "OpenGL Programming Guide" , publisher = "Addison-Wesley" , address = "Reading, MA" , year = 1993 } @inproceedings{Ove96 , author = "M. H. Overmars" , title = "Designing the Computational Geometry Algorithms Library CGAL" , booktitle = "Proc. 1st ACM Workshop on Appl. Comput. Geom." , site = "Philadelphia, PA, USA" , month = may , year = 1996 , pages = "113--119" , update = "97.11 held" } @book{PrS85 , author = "F. P. Preparata and M. I. Shamos" , title = "Computational Geometry: An Introduction" , publisher = "Springer-Verlag" , address = "New York, NY" , year = 1985 , keywords = "book" , oldlabel = "geom-727" } @inproceedings{Riv74 , author = "R. L. Rivest" , title = "{On the optimality of Elias's algorithm for performing best-match searches}" , booktitle = "Information Processing" , year = 1974 , publisher = "North Holland Publishing Company" , pages = "678--681" } @article{Sal89 , author = "J. Salowe" , title = "{$L_{\infty}$} interdistance selection by parametric search" , journal = "Inform. Process. Lett." , volume = "30" , year = 1989 , pages = "9--14" , oldlabel = "geom-2539" } @inproceedings{Sal91 , author = "J. S. Salowe" , title = "Shallow interdistance selection and interdistance enumeration" , booktitle = "Proc. 2nd Workshop Algorithms Data Struct." , series = "Lecture Notes in Computer Science" , volume = "519" , publisher = "Springer-Verlag" , year = 1991 , pages = "117--128" , keywords = "proximity, distance" , oldlabel = "geom-2615" } @article{Sal92 , author = "J. S. Salowe" , title = "Enumerating interdistances in space" , journal = "Internat. J. Comput. Geom. Appl." , volume = "2" , year = 1992 , pages = "49--59" , keywords = "distance, fixed-radius near neighbors, parametric search, selec tion" } @book{Sam90 , author = "H. Samet" , title = "The Design and Analysis of Spatial Data Structures" , publisher = "Addison Wesley" , address = "Reading, MA" , year = 1990 } @article{SlT83 , author = "D. D. Sleator and R. E. Tarjan" , title = "A data structure for dynamic trees" , journal = "J. Comput. Syst. Sci." , year = 1983 , volume = "26" , pages = "362--391" } @article{SoM87 , author = "M. R. Soleymani and S. D. Morgera" , title = "An efficient nearest neighbor search method" , journal = "IEEE Transactions on Communications" , year = 1987 , volume = "35" , number = "6" , pages = "677--679" } @article{Spr91 , author = "R. L. Sproull" , title = "Refinements to nearest-neighbor searching" , journal = "Algorithmica" , year = 1991 , volume = "6" , pages = "579--589" } @article{SSS92 , author = "C. Schwarz and M. Smid and J. Snoeyink" , title = "An optimal algorithm for the on-line closest-pair problem" , journal = "Algorithmica" , volume = "12" , year = 1994 , pages = "18--29" } @article{Tou80 , author = "G. T. Toussaint" , title = "The relative neighborhood graph of a finite planar set" , journal = "Pattern Recognition" , year = 1980 , volume = "12" , number = "4" , pages = "261--268" } @article{Vai89 , author = "P. M. Vaidya" , title = "An {$O(n \log n)$} algorithm for the all-nearest-neighbors problem" , journal = "Discrete Comput. Geom." , volume = "4" , year = 1989 , pages = "101--115" , oldlabel = "geom-1733.2" , succeeds = "v-oannp-86" } @article{Wil64 , author = "J. W. J. Williams" , title = "Algorithm 232 (heapsort)" , journal = "Communications of the ACM" , volume = "7" , year = 1964 , pages = "347--348" } @inproceedings{YaY85 , author = "A. C. Yao and F. F. Yao" , title = "A general approach to $d$-dimensional geometric queries" , booktitle = "Proc. 17th Ann. ACM Sympos. Theory Comput." , year = 1985 , pages = "163--168" } ann-1.1.2+doc/doc/Makefile0000644000175000017500000000533111161453316016122 0ustar sylvestresylvestre#----------------------------------------------------------------------------- # Makefile for ANN User's Manual # # ANN: Approximate Nearest Neighbors # Version: 1.1.1 08/04/06 #----------------------------------------------------------------------------- # Copyright (c) 1997-2005 University of Maryland and Sunil Arya and # David Mount. All Rights Reserved. # # This software and related documentation is part of the Approximate # Nearest Neighbor Library (ANN). This software is provided under # the provisions of the Lesser GNU Public License (LGPL). See the # file ../ReadMe.txt for further information. # # The University of Maryland (U.M.) and the authors make no # representations about the suitability or fitness of this software for # any purpose. It is provided "as is" without express or implied # warranty. #----------------------------------------------------------------------------- # Revision 0.1 03/04/98 # Initial release # Revision 1.1.1 08/04/06 # Added copyright/license #----------------------------------------------------------------------------- #----------------------------------------------------------------------------- # Basic definitions # BASEDIR where include, src, lib, ... are #----------------------------------------------------------------------------- BASEDIR = .. #----------------------------------------------------------------------------- # Some more definitions # ANNMAN name of user's manual # FIGURES list of included figures #----------------------------------------------------------------------------- ANNMAN = ANNmanual FIGURES = Figs/ann.eps Figs/kd-tree.eps #----------------------------------------------------------------------------- # Make the program #----------------------------------------------------------------------------- default: ps ps: $(ANNMAN).ps pdf: $(ANNMAN).pdf $(ANNMAN).pdf: $(ANNMAN).dvi dvipdf $(ANNMAN).dvi %.eps: %.fig fig2dev -L eps $< $@ $(ANNMAN).ps: $(ANNMAN).dvi dvips $(ANNMAN).dvi $(ANNMAN).dvi: $(ANNMAN).tex $(ANNMAN).bbl $(FIGURES) latex $(ANNMAN).tex latex $(ANNMAN).tex $(ANNMAN).bbl: $(ANNMAN).tex $(FIGURES) latex $(ANNMAN).tex bibtex $(ANNMAN) #----------------------------------------------------------------------------- # configuration definitions #----------------------------------------------------------------------------- include ../Make-config #----------------------------------------------------------------------------- # Cleaning #----------------------------------------------------------------------------- clean: -rm -f core *.aux *.dvi *.log *.blg *.bbl *.toc $(FIGURES); realclean: clean -rm -f $(ANNMAN).ps # (The following is intentionally omitted, beacuse it is part of # the distribution.) # -rm -f $(ANNMAN).pdf ann-1.1.2+doc/doc/ANNmanual.tex0000644000175000017500000035331011330216231017010 0ustar sylvestresylvestre%---------------------------------------------------------------------- % File: ANNmanual.tex % By: David Mount % Last modified: 05/03/05 % Description: User manual for ANN %---------------------------------------------------------------------- % Copyright (c) 1997-2005 University of Maryland and Sunil Arya and % David Mount. All Rights Reserved. % % This software and related documentation is part of the Approximate % Nearest Neighbor Library (ANN). This software is provided under % the provisions of the Lesser GNU Public License (LGPL). See the % file ../ReadMe.txt for further information. % % The University of Maryland (U.M.) and the authors make no % representations about the suitability or fitness of this software for % any purpose. It is provided "as is" without express or implied % warranty. %---------------------------------------------------------------------- % History: % Revision 0.1 03/04/98 % Initial release % Revision 1.0 04/01/05 % Added comments to ann_sample code % Added clus_orth_flats distribution % Added clus_ellipsoids distribution % Changed name of standard kd-tree split rule from "standard" to "kd" % Added ANN logo to title page. % Added description of ANNcoordPrec. % Added description of thePoints, nPoints, and theDim. % Added description of load constructor. % Updated description of ANN_BD_CENTROID. % Changed dump file suffix in ann2fig from ".ann" to ".dmp". % Revision 1.1 05/03/05 % Added instructions for Microsoft compilations. % Added annkFRSearch information %---------------------------------------------------------------------- \documentclass[11pt]{article} % plain manuscript (11pt) \usepackage{fullpage} \usepackage{amsmath} % AMS math \usepackage{amssymb} % special AMS math symbols \usepackage{graphicx} \usepackage{url} %----------------------------------------------------------------------- % % Math shortcuts - floor, ceiling, ... % %----------------------------------------------------------------------- \newcommand\floor[1]{\left\lfloor #1\right\rfloor} \newcommand\ceil[1]{\left\lceil #1\right\rceil} \newcommand\ang[1]{\langle #1\rangle} %----------------------------------------------------------------------- % Tighter list environments %----------------------------------------------------------------------- \newenvironment{enumerate*}% % Tighter enumerated list {\begin{enumerate}% \setlength{\itemsep}{-0.5ex}% \setlength{\parsep}{0pt}}% {\end{enumerate}} \newenvironment{itemize*}% % Tighter itemized list {\begin{itemize}% \setlength{\itemsep}{-0.5ex}% \setlength{\parsep}{0pt}}% {\end{itemize}} \newenvironment{description*}% % Tighter decsription list {\begin{description}% \setlength{\itemsep}{-0.5ex}% \setlength{\parsep}{0pt}}% {\end{description}} %----------------------------------------------------------------------- % % Typing shortcuts % %----------------------------------------------------------------------- \newcommand{\ANN}[0]{\textsf{ANN}} \newcommand{\ANNversion}[0]{1.1} \newcommand{\ANNyear}[0]{2010} \newcommand{\anntest}[0]{\textsf{ann\_test}} \newcommand{\annsample}[0]{\textsf{ann\_sample}} \newcommand{\annfig}[0]{\textsf{ann2fig}} \newcommand{\dist}[0]{{\rm dist}} \newcommand{\ROOT}[0]{\textit{root}} \newcommand{\POW}[0]{\textit{pow}} \newcommand{\DIFF}[0]{\ominus} \newcommand{\SUM}[0]{\oplus} \newcommand{\STRING}[0]{$\ang{\textit{string}\/}$} \newcommand{\FILE}[0]{$\ang{\textit{file}\/}$} \newcommand{\INT}[0]{$\ang{\textit{int}\/}$} \newcommand{\FLOAT}[0]{$\ang{\textit{float}\/}$} \newcommand{\RE}{\mathbb{R}} % real space \newcommand{\BSL}{\hbox{$\backslash$}} \begin{document} \bibliographystyle{alpha} \pagenumbering{roman} \setcounter{page}{0} \title{ANN Programming Manual} \author{David M. Mount\thanks{Email: \textsf{mount@cs.umd.edu}. The support of the National Science Foundation under grants CCR--9712379 and CCR-0098151 is gratefully acknowledged.}\\ Department of Computer Science and \\ Institute for Advanced Computer Studies \\ University of Maryland, College Park, Maryland. } \date{{\ANN}, Version {\ANNversion}\\ Copyright, {\ANNyear} David M. Mount \\ ~ \\ \centerline{\includegraphics[height=2.0in]{Figs/annlogo.eps}} } \maketitle \thispagestyle{empty} \newpage \tableofcontents \newpage \pagenumbering{arabic} \setcounter{page}{1} %---------------------------------------------------------------------- \section{Introduction} %---------------------------------------------------------------------- %---------------------------------------------------------------------- \subsection{What is {\ANN}?} %---------------------------------------------------------------------- {\ANN} is a library written in the C++ programming language to support both exact and approximate nearest neighbor searching in spaces of various dimensions. It was implemented by David M. Mount of the University of Maryland and Sunil Arya of the Hong Kong University of Science and Technology. {\ANN} (pronounced like the name ``Ann'') stands for the \emph{Approximate Nearest Neighbor} library. {\ANN} is also a testbed containing programs and procedures for generating data sets, collecting and analyzing statistics on the performance of nearest neighbor algorithms and data structures, and visualizing the geometric structure of these data structures. In the \emph{nearest neighbor problem} a set $P$ of data points in $d$-dimensional space is given. These points are preprocessed into a data structure, so that given any query point $q$, the nearest (or generally $k$ nearest) points of $P$ to $q$ can be reported efficiently. {\ANN} is designed for data sets that are small enough that the search structure can be stored in main memory (in contrast to approaches from databases that assume that the data resides in secondary storage). Points are assumed to be represented as coordinate vectors of reals (or integers). The distance between two points can be defined in many ways. {\ANN} assumes that distances are measured using any class of distance functions called \emph{Minkowski metrics}. These include the well known Euclidean distance, Manhattan distance, and max distance. Answering nearest neighbor queries efficiently, especially in higher dimensions, seems to be very difficult problem. It is always possible to answer any query by a simple brute-force process of computing the distances between the query point and each of the data points, but this may be too slow for many applications that require that a large number of queries be answered on the same data set. Instead the approach is to preprocess a set of data points into a data structure from which nearest neighbor queries are then answered. There are a number of data structures that have been proposed for solving this problem. See, for example, \cite{AMN98,Ben90,Cla97,Kle97,PrS85,Spr91}, for more information on this problem. One difficulty with exact nearest neighbor searching is that for virtually all methods other than brute-force search, the running time or space grows exponentially as a function of dimension. Consequently these methods are often not significantly better than brute-force search, except in fairly small dimensions. However, it has been shown by Arya and Mount \cite{ArM93} and Arya, et al.~\cite{AMN98} that if the user is willing to tolerate a small amount of error in the search (returning a point that may not be the nearest neighbor, but is not significantly further away from the query point than the true nearest neighbor) then it is possible to achieve significant improvements in running time. {\ANN} is a system for answering nearest neighbor queries both \emph{exactly} and \emph{approximately}. This manual describes how to download and install {\ANN}, how to use the library, how to change its configuration for different distance functions and data representations, and finally how to use its utility programs for testing and visualizing the data structure. %---------------------------------------------------------------------- \subsection{Downloading and Using {\ANN}} %---------------------------------------------------------------------- The current version of {\ANN} is version {\ANNversion}. The {\ANN} source code and documentation is available from the {\ANN} web page: \begin{center} \url{http://www.cs.umd.edu/~mount/ANN} \end{center} The unbundled software consists of the following major files and directories. % \begin{description*} \item[\hbox{\sf ReadMe.txt:}] General description of the library. \item[\hbox{\sf Copyright.txt:}] Copyright information. \item[\hbox{\sf License.txt:}] Conditions of use for the library. \item[\hbox{\sf include:}] Include files for compiling programs that use the library. \item[\hbox{\sf src:}] The source files for the library. \item[\hbox{\sf sample:}] A small sample program, which illustrates how to input a point set, build a search structure for the set, and answer nearest neighbor queries. (See Section~\ref{annsample.sec}.) \item[\hbox{\sf test:}] A program that provides a simple script input for building search trees and comparing their performance on point sets that are either read from an input file or generated according to some probability distribution. (See Section~\ref{anntest.sec}.) \item[\hbox{\sf ann2fig:}] A program that generates a visual representation (in fig format) of the tree's spatial decomposition. (See Section~\ref{ann2fig.sec}.) \item[\hbox{\sf lib:}] Where the compiled library is stored. \item[\hbox{\sf bin:}] Where the compiled executables are stored. \item[\hbox{\sf doc:}] This documentation. \item[\hbox{\sf MS\_Win32:}] Solution and project files for compilation under Microsoft Visual Studio~.NET. \end{description*} %---------------------------------------------------------------------- \subsection{Compiling {\ANN}} %---------------------------------------------------------------------- {\ANN} requires an ANSI standard C++ compiler. It has been compiled successfully on Unix and Linux systems including Sun Workstations running SunOS 5.X (Solaris), Linux Red Hat 2.X, and on DEC Alphas running Digital Unix v4.X, on SGIs running IRIX 6.X. Makefiles for all these systems. It has also been compiled under Microsoft Windows XP (under Visual Studio~.NET). \subsubsection{Compiling on Unix/Linux Systems} After downloading the sources, change to the {\ANN} root directory (from which directories such as \textsf{bin}, \textsf{doc}, and \textsf{include} branch off) and enter the command ``\textsf{make}''. This will provide a list of platforms and options under which to compile {\ANN}. If you do not see your particular configuration on this list, then you might try modifying the file \textsf{Make-config} for your particular system. The authors welcome any additions to the list of supported platforms. There are some additional compilation options that can be enabled or disabled. These are described in Section~\ref{compileopt.sec}. To recompile the library, enter the command ``\textsf{make realclean}'' to delete the library and utility programs, and then reenter the make command for compilation. \subsubsection{Compiling on Microsoft Windows Systems} To compile under Visual C++ running within Microsoft Visual Studio~.NET, go to the directory \textsf{MS\_Win32}. Open the solution file \textsf{Ann.sln}, select the ``Release'' configuration, and select ``Build $\rightarrow$ Build Solution.'' After compilation, the file \textsf{ANN.lib} is stored in the directory \textsf{MS\_Win32{\BSL}dll{\BSL}Release}. The file \textsf{ANN.dll} file and executables of the utility programs are stored in the directory \textsf{bin} (relative to the {\ANN} root directory). These two files, along with the files in the directory \textsf{include/ANN} are needed for compiling applications that use {\ANN}. \subsubsection{Precompiled Files for Microsoft Windows} For Microsoft Windows users that do not need to modify the software, a bundle containing all the files you need to use {\ANN} has been provided. This contains the include files in \textsf{include/ANN} along with \textsf{ANN.lib} and \textsf{ANN.dll}. It can be downloaded directly from \url{http://www.cs.umd.edu/~mount/ANN}. In order to use these with an application it is necessary to copy each of these files to appropriate directories for the compiler and linker to locate them, and then to set the appropriate compiler, linker, and path settings so the system can locate all these files. You should consult your local system documentation for this information. An example of how to do this for the sample program is given in Section~\ref{compilesample.sec}. %---------------------------------------------------------------------- \subsection{Compiling Applications that Use the Library} %---------------------------------------------------------------------- In order to use {\ANN} in a C++ program, the program must include the header file for {\ANN}, which contains the declarations for the {\ANN} objects and procedures. This is done with the following statement in the C++ source code. {\small \begin{verbatim} #include \end{verbatim} } This assumes that the {\ANN} include directory is already on the compiler's search path for include files. On most Unix/Linux-based C++ compilers, this is done by setting the ``-I'' (capital letter ``i'') option on the compilation command line to point to the include directory in the {\ANN} base directory. Then the program is linked with the {\ANN} library. On Unix/Linux-based systems this is done with the ``\textsf{-l}'' (lower-case letter ``$\ell$'') option, assuming that the library search path has been set to include the {\ANN} library directory. The library search path can be set with the ``\textsf{-L}'' option. For example, on my Unix system, the following command line could be used to compile the program \textsf{my\_program.cpp} using the {\ANN} library and the GNU C++ compiler. Let \textsf{ann} denote the path to root {\ANN} directory. {\small \begin{verbatim} g++ my_program.cpp -Iann/include -Lann/lib -lANN \end{verbatim} } Some additional information on compiling applications that use {\ANN} on Microsoft Windows systems can be found in Section~\ref{compilesample.sec}. %---------------------------------------------------------------------- \newpage \section{The {\ANN} Library}\label{annlib.sec} %---------------------------------------------------------------------- {\ANN} is a library of C++ objects and procedures that supports approximate nearest neighbor searching. In \emph{nearest neighbor searching}, we are given a set of data points $S$ in real $d$-dimensional space, $\RE^d$, and are to build a data structure such that, given any query point $q \in \RE^d$, the nearest data point to $q$ can be found efficiently. In general, we are given $k \ge 1$, and are asked to return the $k$-nearest neighbors to $q$ in $S$. In \emph{approximate nearest neighbor searching}, an error bound $\epsilon \ge 0$ is also given. The search algorithm returns $k$ distinct points of $S$, such that for $1 \le i \le k$, the ratio between the distance to the $i$th reported point and the true $i$th nearest neighbor is at most $1+\epsilon$. \ANN's features include the following. \begin{itemize} \item It supports $k$-nearest neighbor searching, by specifying $k$ with the query. \item It supports both exact and approximate nearest neighbor searching, by specifying an approximation factor $\epsilon \ge 0$ with the query. \item It supports any Minkowski distance metric, including the $L_1$ (Manhattan), $L_2$ (Euclidean), and $L_{\infty}$ (Max) metrics. \item Preprocessing time and space are both linear in the number of points $n$ and the dimension $d$, and are independent of $\epsilon$. Thus the data structure requires storage that is only moderately larger than the underlying data set. \end{itemize} {\ANN} was written as a testbed for a class of nearest neighbor searching algorithms, particularly those based on orthogonal decompositions of space. These include kd-trees \cite{Ben90,FBF77}, and box-decomposition trees \cite{AMN98}. These will be described in Section~\ref{structs.sec}. The library supports a number of different methods for building these search structures. It also supports two methods for searching these structures: standard tree-ordered search \cite{ArM93b} and priority search \cite{AMN98}. These will be described in Section~\ref{search.sec}. In addition to the library there are two programs provided for testing and evaluating the performance of various search methods. The first, called {\anntest}, provides a primitive script language that allows the user to generate data sets and query sets, either by reading from a file or randomly through the use of a number of built-in point distributions. Any of a number of nearest neighbor search structures can be built, and queries can be run through this structure. This program outputs a number of performance statistics, including the average execution time, number of nodes visited in the data structure, and the average error made in the case of approximate nearest neighbors. An operation is provided to have the data structure dumped to a file and to load the data structure from a dumped file. The second program, called {\annfig}, takes the dumped data structure and generates an illustration of the data structure, which is output to a file in a simple graphics format. When the dimension is higher than two, this program can output any planar 2-dimensional ``slice'' of the data structure. An example is shown in Figure~\ref{ann.fig}. The output of {\annfig} is the same format used by the Unix program xfig. Through the Unix program \textsf{fig2dev}, it is possible to convert this format to a number of other picture formats, including encapsulated postscript. \begin{figure}[htbp] \centerline{\includegraphics[height=2.0in]{Figs/ann.eps}} \caption{Sample output of {\annfig} for a kd-tree and a box-decomposition tree.} \label{ann.fig} \end{figure} %---------------------------------------------------------------------- \subsection{Using {\ANN}}\label{using.sec} %---------------------------------------------------------------------- This section discusses how to use {\ANN} for answering nearest neighbors in its default configuration, namely computing the nearest neighbor using Euclidean distance for points whose coordinates are of type \textsf{double}. Later in Section~\ref{custom.sec} we discuss how to customize {\ANN} for different coordinate types and different norms. \subsubsection{Coordinates, Points, Distances, and Indices}\label{point.sec} Each point in $d$-dimensional space is assumed to be expressed as a $d$-vector of coordinates \[ p = (p_0, p_1, \ldots, p_{d-1}). \] (Indices start from 0, as is C++'s convention.) A coordinate is of type \textsf{ANNcoord}. By default, \textsf{ANNcoord} is defined to be of type \textsf{double}, but it is possible to modify the {\ANN} include files to change this and other {\ANN} types, as described in Section~\ref{point2.sec}. {\ANN} defines the distance between two points to be their Euclidean distance, that is \[ \dist(p,q) = \left(\sum_{0 \le i < d} (p_i-q_i)^2 \right)^{1/2}. \] (Section~\ref{norm.sec} explains how to modify {\ANN} for other Minkowski norms.) For the purposes of comparing distances, it is not necessary to compute the final square root in the above expression. {\ANN} actually computes \emph{squared distances} rather than true Euclidean distances. A squared distance is defined to be of type \textsf{ANNdist}. It is defined to be \textsf{double} by default (but can be changed). By using squared distances rather than true Euclidean distances, {\ANN} not only saves on the time of computing square roots, but has the advantage that integer types can be used instead to accurately represent distances when integer type coordinates are used. (It worth emphasizing that, even though {\ANN} represents distances internally as squared distances, when it computes $\epsilon$-approximate nearest neighbors, the approximation is relative to the true, not squared, distance.) The most basic object manipulated by {\ANN} is a \emph{point}, which is defined in C++ to be a dimensionless array of coordinates, or more simply a pointer to a coordinate.% % \footnote{It is natural to wonder why {\ANN} does not define a special point class, which might store additional information about points. This would then necessitate that the library be templated about the point type. Since compiler support for templating was rather weak in the mid-90's when {\ANN} was first implemented designed, it was decided instead to decouple the user's point object from the {\ANN} point type. In this way we allow the user to define a point object in any way desired. The user then interfaces with {\ANN} by simply providing a pointer to the point's coordinates. In many cases, this may just be a field in the user's own point class.} % Thus we define \textsf{ANNpoint} to be {\small \begin{verbatim} typedef ANNcoord* ANNpoint; // a point \end{verbatim} } It is the user's responsibility to allocate and deallocate storage for points. Each point must have at least as many components allocated as the dimension of the space. Any extra components are ignored. Since {\ANN} operates on arrays of points and distances, we also define dimensionless arrays of these two objects: % {\small \begin{verbatim} typedef ANNpoint* ANNpointArray; // an array of points typedef ANNdist* ANNdistArray; // an array of squared distances \end{verbatim} } We will see later that a set of data points is presented to {\ANN} as an \textsf{ANNpointArray}. {\ANN} returns the results of a nearest neighbor query as an integer index into this array. To make it clear when we are doing so, {\ANN} defines the type \textsf{ANNidx} to be a psuedonym for \textsf{int}. The result of a $k$-nearest neighbor query is returned as a pointer to an array of indices, which is of type \textsf{ANNidxArray}, defined as follows. % {\small \begin{verbatim} typedef ANNidx* ANNidxArray; // an array of point indices \end{verbatim} } Finally, {\ANN} provides a boolean type called \textsf{ANNbool}. (Although ANSI C++ provides a type \textsf{bool}, this is not supported in some of the older compilers.) Its values are \textsf{ANNfalse} and \textsf{ANNtrue}. \subsubsection{Nearest Neighbor Search Structure}\label{struct.sec} The principal structure that {\ANN} uses for performing nearest neighbor searches is called an \textsf{ANNpointSet}. This is an abstract object which supports two search operations, \textsf{annkSearch()}, which computes the approximate $k$ nearest neighbors of a query point, and \textsf{annKFRSearch()}, which performs a combination of a fixed-radius approximate $k$ nearest neighbor search and a range search (see the description below). {\ANN} provides three concrete instantiations of an \textsf{ANNpointSet}: \textsf{ANNbruteForce}, \textsf{ANNkd\_tree}, and \textsf{ANNbd\_tree}. The first of these stores the points as an array, and implements a simple brute-force search for nearest neighbors. It is provided primarily for the use of the implementors to validate the correctness of the more sophisticated search structures, and should not be used for actual nearest neighbor queries. Among the other two, we will first introduce only the more basic one, the \textsf{ANNkd\_tree}, and leave the \textsf{ANNbd\_tree} to be discussed in Section~\ref{struct2.sec}. The \textsf{ANNkd\_tree} supports the following operations. \begin{description} \item[Constructor:] This builds a kd-tree from a set of $n$ data points in dimension $d$, stored in a point array $pa$. The procedure allocates the necessary storage for the data structure. It is assumed that there is at least one data point ($n \ge 1$) and that the dimension is strictly positive ($d \ge 1$). Warning: This procedure does virtually no error checking, and if these assumptions are violated or if storage cannot be allocated, then the most likely result will be that the program aborts. A (simplified) prototype is given below. (See Section~\ref{struct2.sec} for more complete information.) The order in which the points appear in the points array is significant, because nearest neighbors are returned by their index in this array. Following C++ conventions, the items are indexed from 0 to $n-1$. {\small \begin{verbatim} ANNkd_tree::ANNkd_tree( ANNpointArray pa, // data point array int n, // number of points int d); // dimension \end{verbatim} } To conserve space, the tree does not actually store the data points, but rather stores pointers to the array $pa$. For this reason the contents of $pa$ should be unchanged throughout the lifetime of the data structure. \item[$k$-Nearest Neighbor Search:] This member function is given a query point $q$, a nonnegative integer $k$, an array of point indices, \textit{nn\_idx}, and an array of distances, \textit{dists}. Both arrays are assumed to contain at least $k$ elements. The procedure computes the $k$ nearest neighbors to $q$ in the point set, and stores the indices of the nearest neighbors (relative to the point array \textit{pa} given in the constructor). The nearest neighbor is stored in $\textit{nn\_idx}[0]$, the second nearest in $\textit{nn\_idx}[1]$, and so on. The \emph{squared} distances to the corresponding points are stored in the array \textit{dists}. Optionally, a real value $\epsilon \ge 0$ may be supplied. If so, then the $i$th nearest neighbor is a $(1+\epsilon)$ approximation to the true $i$th nearest neighbor. That is, the true (not squared) distance to this point may exceed the true distance to the real $i$th nearest neighbor of $q$ by a factor of $(1+\epsilon)$. If $\epsilon$ is omitted then nearest neighbors are computed exactly. {\ANN} supports two different methods for searching the kd-tree. Here we present the simpler one, which is the more efficient for small values of $\epsilon$. Another searching algorithm, called priority search, is presented later in Section~\ref{prsearch.sec}. {\small \begin{verbatim} virtual void ANNkd_tree::annkSearch( ANNpoint q, // query point int k, // number of near neighbors to find ANNidxArray nn_idx, // nearest neighbor array (modified) ANNdistArray dists, // dist to near neighbors (modified) double eps=0.0); // error bound \end{verbatim} } \item[Fixed-radius $k$-Nearest Neighbor Search:] This member function is a modification of the above procedure, which searches for up to $k$ nearest neighbors, but confines the search to a fixed radius bound. It is given a query point $q$, a (squared) radius bound \textit{sqRad}, a nonnegative integer $k$. Optionally, it is given an array of point indices, \textit{nn\_idx}, an array of distances, \textit{dists}. If provided, both arrays are assumed to contain at least $k$ elements. This procedure performs two different types of search. First, if $k$ is positive and the two arrays \textit{nn\_idx} and \textit{dists} are provided, then among the points whose squared distance from $q$ is at most \textit{sqRad}, it finds the $k$ closest of these to $q$. If the number of points within the squared radius bound is some value $k'< k$, then only the first $k'$ entries of these arrays have meaningful entries. The other entries of \textit{nn\_idx} contain the special value \textit{ANN\_NULL\_IDX} and the other entries of \textit{dists} contain the special value \textit{ANN\_DIST\_INF} (which are defined in \textsf{ANN.h}). This is called a fixed-radius search, because it ignores all the points that lie outside of the radius bound. It is not however, a true fixed-radius search, because it computes only the closest $k$ points that lie within the radius bound. Thus, if the value of $k$ is less than the total number of points $k'$ in the radius bound, the farthest $k'-k$ points within the radius will not be reported. (This limitation is because {\ANN} allocates all its arrays statically.) It is easy, however, to determine whether any points were missed. The procedure returns a count of the total number of points that lie within the radius bound. (This feature is always enabled, even if $k = 0$.) In order to produce a true fixed-radius search, first set $k=0$ and run the procedure in order to obtain the number $k'$ of points that lie within the radius bound. Then, allocate index and distance arrays of size $k'$ each, and repeat the fixed-radius search by setting $k=k'$ and passing in these two arrays. Optionally, a real value $\epsilon \ge 0$ may be supplied. If so, the squared radius bound is treated as an approximate quantity in the following sense. Assuming that we are using Euclidean distances, let $r = \sqrt{\textit{sqRad}}$ be the true radius bound. Every data point whose distance from $q$ is less than $r/(1+\epsilon)$ will be considered, and any point whose distance from $q$ is greater than $r$ will not be considered. The remaining points either may or may not be considered (at the discretion of the search algorithm). Among the points that are considered, the $i$th elements of \textit{nn\_idx} and \textit{dists} contain the $i$th closest point to $q$, and the procedure returns a count of all the points under consideration. Here is the prototype of the fixed-radius search procedure. {\small \begin{verbatim} virtual int ANNkd_tree::annkFRSearch( ANNpoint q, // query point ANNdist sqRad, // squared radius int k = 0, // number of near neighbors to return ANNidxArray nn_idx = NULL, // nearest neighbor array (modified) ANNdistArray dd = NULL, // dist to near neighbors (modified) double eps = 0.0); // error bound \end{verbatim} } Unlike \textsf{annkSearch()}, there is no priority search version of of \textsf{annkFRSearch()}. Because it visits all the points in the search radius one by one, the search procedure is rather inefficient if the number of points in the radius bound is large. \item[Other Information:] There are three functions provided for extracting information from a search structure. These are particularly useful if the structure has been loaded from a file (through the load constructor). The function \textsf{theDim()} returns the dimension of the space, \textsf{nPoints()} returns the number of points in the structure, and \textsf{thePoints()} returns a pointer to the array of data points. {\small \begin{verbatim} virtual int ANNkd_tree::theDim(); // return the dimension of space virtual int ANNkd_tree::nPoints(); // return the number of points // return a pointer to points virtual ANNpointArray ANNkd_tree::thePoints(); \end{verbatim} } \item[Destructor:] The destructor deallocates the search structure. (It does not deallocate the points.) {\small \begin{verbatim} ANNkd_tree::~ANNkd_tree(); \end{verbatim} } \item[Closing {\ANN}:] The library allocates a small amount of storage, which is shared by all search structures built during the program's lifetime. Because the data is shared, it is not deallocated, even when the all the individual structures are deleted. To avoid the resulting (minor) memory leak, the following function can be called after all search structures have been destroyed. (It is not a member function of the structure.) {\small \begin{verbatim} void annClose(); \end{verbatim} } \end{description} \subsubsection{Point Utility Procedures}\label{util.sec} As mentioned earlier \textsf{ANNpoint}, is of type \textsf{ANNcoord*}, a pointer to a dimensionless array of coordinates (see Section~\ref{point.sec}). An \textsf{ANNpointArray} is a dimensionless array of such points, that is, of type \textsf{ANNpoint*}. Since a point type does not record its own dimension, all procedures that operate on points must be supplied the dimension. {\ANN} provides a few utility procedures to aid in performing some useful operations on points. \begin{description} \item[annDist:] This returns the squared distance between two points $p$ and $q$ in dimension $d$. For reasons of efficiency, {\ANN} does not use this procedure for most of its distance computations. {\small \begin{verbatim} ANNdist annDist( int dim, // dimension of space ANNpoint p, ANNpoint q); \end{verbatim} } \item[annAllocPt:] This allocates storage for a point $p$ in dimension $d$. That is, it allocates an array of size $d$ whose elements are of type \textsf{ANNcoord}. In addition to the dimension, it can also be passed a coordinate value (0 by default), which it uses to initialize all coordinates of the point. This procedure returns a pointer to the allocated point, and \textsf{NULL} if storage cannot be allocated for any reason. {\small \begin{verbatim} ANNpoint annAllocPt( int dim, // dimension of the space ANNcoord c = 0); // initial coordinate value \end{verbatim} } \item[annDeallocPt:] Deallocates storage for a point $p$ as allocated by \textsf{annAllocPt}. As a side effect (for safety) it assigns $p$ the value \textsf{NULL}. {\small \begin{verbatim} void annDeallocPt( ANNpoint& p); // (set to NULL on return) \end{verbatim} } \item[annAllocPts:] This is used to allocate an array of points. It first allocates an array of $n$ pointers to points (each element is of type \textsf{ANNpoint}), and for each element it allocates storage for $d$ coordinates, and stores a pointer to this storage in the element. It returns a pointer to this array of pointers. It performs no initialization of the coordinate values. {\small \begin{verbatim} ANNpointArray annAllocPts( int n, // number of points int dim); // dimension \end{verbatim} } \item[annDeallocPts:] This deallocates the storage allocated by {\tt annAllocPts}. This procedure should only be applied to arrays of points allocated by \textsf{annAllocPts}. As a side effect (for safety) it assigns $pa$ the value \textsf{NULL}. {\small \begin{verbatim} void annDeallocPts( ANNpointArray& pa); // (set to NULL on return) \end{verbatim} } \item[annCopyPt:] This makes a copy of a point by first allocating storage for a new point and then copying the contents of the source point to the new point. A pointer to the newly allocated point is returned. {\small \begin{verbatim} ANNpoint annCopyPt( int dim, // dimension ANNpoint source); // point to copy \end{verbatim} } \end{description} \subsubsection{A Sample Program} \label{annsample.sec} In this section we present is a sample program demonstrating the basic elements of {\ANN}. The program inputs command line arguments such as the dimension $d$, the number of nearest neighbors $k$, the error bound $\epsilon$, and the file names containing the query and data point. The program allocates storage for data points, one query point, and results, consisting of the nearest neighbor indices and the distances. The program inputs the data points and builds a kd-tree search structure for these points. Then it reads query points, and for each computes $k$ approximate nearest neighbors with error bound $\epsilon$, and outputs the results. The presentation below shows only the most relevant elements of the program. The complete source can be found in \textsf{sample/ann\_sample.cpp}. (All file names are given relative to the {\ANN} root directory.) To simplify the presentation, the procedures \textsf{getArgs()} and {\tt readPt()} have been omitted. The first reads command line arguments and initializes the global parameters. The second reads a single point from an input stream, and returns false if the end of file is encountered. {\small \begin{verbatim} #include // C standard library #include // file I/O #include // ANN declarations using namespace std; // make std:: accessible void getArgs(int argc, char **argv) { ... } // get command-line arguments bool readPt(istream& in, ANNpoint p) { ... } // read point (false on EOF) // // Global variables, initialized in getArgs // int k = 1; // number of nearest neighbors int dim = 2; // dimension double eps = 0; // error bound int maxPts = 1000; // maximum number of data points istream* dataIn = NULL; // input for data points istream* queryIn = NULL; // input for query points int main(int argc, char **argv) { int nPts; // actual number of data points ANNpointArray dataPts; // data points ANNpoint queryPt; // query point ANNidxArray nnIdx; // near neighbor indices ANNdistArray dists; // near neighbor distances ANNkd_tree* kdTree; // search structure getArgs(argc, argv); // read command-line arguments queryPt = annAllocPt(dim); // allocate query point dataPts = annAllocPts(maxPts, dim); // allocate data points nnIdx = new ANNidx[k]; // allocate near neigh indices dists = new ANNdist[k]; // allocate near neighbor dists nPts = 0; // read data points while (nPts < maxPts && readPt(*dataIn, dataPts[nPts])) nPts++; kdTree = new ANNkd_tree( // build search structure dataPts, // the data points nPts, // number of points dim); // dimension of space while (readPt(*queryIn, queryPt)) { // read query points kdTree->annkSearch( // search queryPt, // query point k, // number of near neighbors nnIdx, // nearest neighbors (returned) dists, // distance (returned) eps); // error bound cout << "NN: Index Distance\n"; for (int i = 0; i < k; i++) { // print summary dists[i] = sqrt(dists[i]); // unsquare distance cout << i << " " << nnIdx[i] << " " << dists[i] << "\n"; } } delete [] nnIdx; // clean things up delete [] dists; delete kdTree; annClose(); // done with ANN return EXIT_SUCCESS; } \end{verbatim} } \subsubsection{Compiling Sample Applications that use {\ANN}} \label{compilesample.sec} The sample program is typical in structure to applications that use {\ANN}. If you are on a Unix/Linux system, the sample program is automatically compiled when you the file \textsf{sample/Makefile} can be used to compile the program (perhaps with minor modifications needed, depending on your system). Assuming that {\ANN} has already been compiled, the GNU g++ compiler is used, and \textsf{ann} denotes the path to root {\ANN} directory, the sample program can be compiled using: {\small \begin{verbatim} g++ ann_sample.cpp -o ann_sample -Iann/include -Lann/lib -lANN \end{verbatim} } If you are working on a typical Microsoft Windows system with Microsoft Visual Studio~.NET, here are some hints as to how to compile the sample program. The procedure is basically the same for any other C++ application that uses {\ANN}. (Please note that I am not an experienced Windows programmer, so please consult your system documentation if this does not work for you.) If you have downloaded the entire {\ANN} distribution, you can certainly compile the sample program by opening the project file \textsf{MS\_Win32{\BSL}sample{\BSL}sample.vcproj}. This assumes that that you have the full {\ANN} distribution and have already compiled the {\ANN} library. It is possible to compile an application that uses {\ANN} with just the following three elements, which are available from the ``Precompiled files for for users of Microsoft Windows 2000'' link on the {\ANN} web page. % \begin{description*} \item[Include files:] The directory \textsf{ANN} containing the three {\ANN} include files, \textsf{ANN.h}, \textsf{ANNx.h}, and \textsf{ANNperf.h}, \item[Library file:] \textsf{ANN.lib}, \item[dll file:] \textsf{ANN.dll}. \end{description*} Let us now illustrate how to compile the sample program from scratch. First, you will need to download the ANN full distribution, and make a copy of the file \textsf{sample{\BSL}ann\_sample.cpp}. \begin{description*} \item[Copy Files:] First, copy all the above files to a location that suits your preferences. For the sake of illustration, we will make the following assumptions in the subsequent presentation, but you may use whatever directories you like (in fact, they can all just be the same directory). % \begin{description*} \item[Source file:] Copy the file \textsf{ann\_sample.cpp} to a directory containing your project source files, say, \textsf{C:{\BSL}My Sources}. \item[Include files:] Copy the contents of the directory \textsf{ANN}, which contains the three {\ANN} include files, to a directory where your include files are stored, say, \textsf{C:{\BSL}My Includes}. (Alternatively, you can store this in the default directory where the linker looks for standard libraries, something like \textsf{C:{\BSL}Program Files{\BSL}Microsoft Visual Studio~.NET 2003{\BSL}Vc7{\BSL}include}.) \item[Lib file:] Copy the file \textsf{ANN.lib} to a directory where your library files are stored, say, \textsf{C:{\BSL}My Libs}. (Alternatively, you can store this in the default directory where the linker looks for standard libraries, something like, \textsf{C:{\BSL}Program Files{\BSL}Microsoft Visual Studio~.NET 2003{\BSL}Vc7{\BSL}lib}.) \item[DLL file:] Copy the file \textsf{ANN.dll} to a directory where your DLL files are stored, say, \textsf{C:{\BSL}My DLLS}. (Alternatively, you can store this in the system directory on your path environment variable, say, \textsf{C:{\BSL}WINDOWS{\BSL}system32}.) \end{description*} \item[Create a New Project:] Open Visual Studio~.NET and select the command ``New Project.'' Select the appropriate project type. For {\annsample}, this will be ``WIN32 Console Project.'' Enter the desired project name (say, ``{\annsample}'') and enter the path name of the directory where you would like the project files to be stored. (This may just be the same directory that contains \textsf{ann\_sample.cpp} sources.) \item[Add the Source:] Select the menu option ``Project'' $\rightarrow$ ``Add Existing Item'' and use the browser window to select your copy of the file \textsf{ann\_sample.cpp}. \item[Location of the include files:] In the ``Solution Explorer'' window, find the entry for your project name (say, ``{\annsample}'') and right click and select ``Properties.'' From the resulting pop-up window select ``C/C++'' $\rightarrow$ ``General.'' Locate the field named ``Additional Include Directories'' and enter the full path name of the directory into which you copied the directory \textsf{ANN}, say, ``\textsf{C:{\BSL}My Includes}''. (If you chose to copy this directory to the default include directory, this is not necessary.) \item[Location of the Library:] In the ``Solution Explorer'' window, window, find the entry for your project name (say, ``{\annsample}'') and right click and select ``Properties.'' From the resulting pop-up window select ``Linker'' $\rightarrow$ ``General.'' Locate the field named ``Additional Library Directories'' and enter the full path name of the directory where you stored \textsf{ANN.lib}, say, ``\textsf{C:{\BSL}My Libs}''. (If you chose to copy this file to the default library directory, this is not necessary.) \item[Location of the DLL:] The system searches the directories whose names appear in the \emph{Path} environment variable for the locations of DLL files. If you have chosen to store \textsf{ANN.dll} in your \textsf{WINDOWS{\BSL}system32} directory, then you not need to do anything more, since this will be searched. If you stored the file in a different directory, then you need to add this name to your Path variable. To do this, first open the Control Panel and select ``System'' (under ``Performance and Maintenance''). Click on the ``Advanced'' tab and select ``Environment Variables''. Find the variable ``PATH'' or ``Path'' (either under ``System variables'' or ``User variables''). If it does not exist, then add it and enter in it the full path name of the directory where you stored the file \textsf{ANN.dll}, for example ``\textsf{C:{\BSL}My Libs}''. If it already exists, click the variable name to highlight it, and then click the ``Edit'' button. At the end of this string append a semicolon (``;'') followed by the above path name. \item[Compile your program:] To compile the program return to Visual Studio~.NET and select the menu command ``Build'' $\rightarrow$ ``Build Solution.'' (It should not produce any error messages, but if it complains about not being able to find \textsf{ANN.h} then recheck the above step about include files. If it complains about not being able to find \textsf{ANN.lib} then recheck the above step about the library file.) \end{description*} At this point you should be able to execute the program. To do this, open a Command Prompt window, and go to the directory containing the executable file \textsf{ann\_sample.exe}. Then enter \textsf{ann\_sample}. It should print the program's usage message. (If it complains that \textsf{ANN.dll} could not be found, recheck the above step about DLL files.) This is not very interesting. If you copy the files \textsf{sample{\BSL}data.pts} and \textsf{sample{\BSL}query.pts} from the full {\ANN} distribution into this directory, then the sample program can be run using the command: \begin{verbatim} ann_sample -df data.pts -qf query.pts \end{verbatim} %---------------------------------------------------------------------- \subsection{Configuring {\ANN}}\label{custom.sec} %---------------------------------------------------------------------- In this section we describe a number of methods for configuring {\ANN}. These include dealing with different distance measures, altering the types of coordinates, and dealing with the issue of whether a point can be its own nearest neighbor. It was felt that these features are typically set once for any given application, and that it would significantly complicate the library to allow support all possible combinations of settings. For this reason, these changes are made by altering {\ANN}'s main header file \textsf{include/ANN/ANN.h}. Once set, they cannot be changed without recompiling the entire library. \subsubsection{Norms and Distances}\label{norm.sec} {\ANN} computes the distance between two points $p$ and $q$ as the length of the vector difference \[ p-q = (p_0 - q_0, p_1 - q_1, \ldots, p_{d-1}-q_{d-1}). \] {\ANN}'s internal structure is oriented towards this type of distance, and it does not support, nor can it be easily modified, to handle other types of similarity measures, e.g., the cosine similarity measure, which based on the inner products of two vectors. {\ANN} employs a simple (but not elegant) method for computing vector lengths, which allows all the Minkowski norms. Given a vector $v$, and positive integer $k$, define the \emph{Minkowski $L_k$ norm} to be \[ \|v\|_k = \left( \sum_{0 \le i < d} |v_i|^k \right)^{1/k}. \] The familiar Euclidean norm is just the $L_2$ norm, and is {\ANN}'s default. The Manhattan norm is the $L_1$ distance. The max norm is the limiting case as $k$ tends to infinity \[ \|v\|_{\infty} = \max_{0 \le i < d} | v_i |. \] As mentioned earlier, for the purposes of comparing the relative sizes of distances, it is not necessary to compute the final power of $1/k$, and so {\ANN} does not do so. With some abuse of notation, we refer to the resulting quantity as the \emph{squared norm} (even though squaring is only applicable to the Euclidean norm). In general, {\ANN} assumes that the distance between points $p$ and $q$ is computed as the length of the difference vector $v = p - q$, by the following formula: \[ \|v\| = \ROOT(\POW(v_0) \SUM \POW(v_1) \SUM \cdots \SUM \POW(v_{d-1})), \] where $\ROOT()$, $\POW()$ are unary functions and $\SUM$ is any associative and commutative binary operator. For example, in the default case of the Euclidean norm, $\POW(x) = x^2$, $x \SUM y = x + y$ and $\ROOT(x) = \sqrt{x}$. It is assumed that $\POW()$ takes an argument of type \textsf{ANNcoord} and returns an \textsf{ANNdist}. The operator $\SUM$ works on objects of type \textsf{ANNdist}, and $\ROOT()$ takes an argument of type \textsf{ANNdist} and returns an object of type \textsf{double}. {\ANN} does not compute the $\ROOT()$ function. There is one more wrinkle in modifying distance computations. To speed-up the internal distance computations in nearest neighbor searching in high dimensional space, {\ANN} uses a technique called \emph{incremental distance calculation} \cite{ArM93b}. In incremental distance calculation, we are given two vectors $u$ and $v$, which differ only in one known coordinate, $i$, such that $|u_i| < |v_i|$. Further, suppose we already know $\|u\|$. We can compute $\|v\|$ in any Minkowski norm with only an additional constant number of computations (independent of the dimension). For this, we need a binary operator $\DIFF$, which behaves like an inverse for the $\SUM$ operator. Then \[ \|v\| = \|u\| \SUM (\POW(u_i) \DIFF \POW(v_i)). \] When $\SUM$ is addition, then we define $\DIFF$ to be subtraction. In the case of the $L_{\infty}$ norm, where $\SUM$ is $\max$, there is no inverse for $\SUM$. But we can exploit the facts that for this metric, $\POW$ is absolute value, and $|u_i| \le |v_i|$ and define $x \DIFF y = y$, to achieve the desired result. The main header file, \textsf{include/ANN/ANN.h}, contains a set of macros which control the computation of norms. They are \textsf{ANN\_POW}, \textsf{ANN\_SUM} (for $\SUM$), \textsf{ANN\_ROOT}, and \textsf{ANN\_DIFF} (for $\DIFF$). The following table shows the values of these functions and corresponding macros for the Minkowski norms. \begin{figure}[htbp] \begin{center} \begin{tabular}{||l|l||l|l|l|l||} \hline\hline Function & Macro & $L_1$ & $L_2$ & $L_p$ & $L_{\infty}$\\ \hline $\POW(x)$ & \textsf{ANN\_POW(x)} & $|x|$ & $x^2$ & $|x|^p$& $|x|$ \\ $x \SUM y$ & \textsf{ANN\_SUM(x,y)} & $x+y$ & $x+y$ & $x+y$ & $\max(x, y)$\\ $\ROOT(x)$ & \textsf{ANN\_ROOT(x)} & $x$ & $\sqrt{x}$& $x^{1/p}$& $x$ \\ $x \DIFF y$ & \textsf{ANN\_DIFF(x,y)}& $y-x$ & $y-x$ & $y-x$ & $y$ \\ \hline\hline \end{tabular} \end{center} \end{figure} To change the norm, make the appropriate changes in the header file, and recompile the library. \subsubsection{More on Points, Cordinates, and Distances}\label{point2.sec} One of the basic issues in providing a general purpose library for nearest neighbor searching is that of providing a method for defining the types used for point coordinates and distances. One way to do this would be through the use of templates in C++ (as is done in CGAL \cite{Ove96}) or by replicating all of the basic procedures (as is done in OpenGL \cite{Ope93}). In {\ANN} we took the simpler, but less flexible approach of making this a configuration parameter. As a consequence, {\ANN} can support any combination of coordinates and distances, but only one for any given compilation of the library. There are two data types defined in the file \textsf{include/ANN/ANN.h} which are used to define these types. These are the data type for point coordinates, \textsf{ANNcoord}, and the type for squared distances, \textsf{ANNdist}. Their default values are: {\small \begin{verbatim} typedef double ANNcoord; // coordinate data type typedef double ANNdist; // distance data type \end{verbatim} } In general, \textsf{ANNcoord} may be set to any signed numeric type: \textsf{char}, \textsf{short}, \textsf{int}, \textsf{long}, \textsf{float}, \textsf{double}. (The reason for requiring that coordinates be signed is that the program computes differences of numbers of unknown relative magnitudes.) The type \textsf{ANNdist} may be set to the desired type to hold squared distances. Observe that \textsf{ANNdist} should generally be of an equal or stronger type than \textsf{ANNcoord}. That is, if \textsf{ANNcoord} is set to \textsf{int}, then \textsf{ANNdist} should be either \textsf{int}, \textsf{long}, \textsf{float}, or \textsf{double}. {\ANN} does not check for overflows in squared distance computations. {\ANN} assumes that there are two constant values defined in \textsf{include/ANN/ANN.h}. These are \textsf{ANN\_DBL\_MAX}, which stores the maximum possible double value and \textsf{ANN\_DIST\_INF}, which stores the maximum possible (squared) distance value. On most systems, \textsf{ANN\_DBL\_MAX} is assigned to \textsf{DBL\_MAX}, which is defined in one of the C++ standard include files $\ang{\textsf{limits.h}}$ or $\ang{\textsf{float.h}}$.% % \footnote{Some older systems do not have these include files. If so, the library should be compiled with the option \textsf{-DANN\_NO\_LIMITS\_H}, and an appropriate substitute should be provided in \textsf{include/ANN/ANN.h}.} % The value of \textsf{ANN\_DIST\_INF} depends on the definition of \textsf{ANNdist}. For example, if \textsf{ANNdist} is \textsf{double}, then \textsf{ANN\_DIST\_INF} can be set to \textsf{ANN\_DBL\_MAX}. If it is \textsf{long}, then the maximum long value (e.g., \textsf{LONG\_MAX}) can be used. The routine that dumps a tree needs to know roughly how many significant digits there are in a \textsf{ANNcoord}, so it can output points to full precision. This is defined as \textsf{ANNcoordPrec}. Its value needs only be set of \textsf{ANNcoord} is a floating-point type. All of these entities are defined in \textsf{include/ANN/ANN.h}. \subsubsection{Self Matches} In some applications of nearest neighbor searching, the nearest neighbor of a point is not allowed to be the point itself. That is, the nearest neighbor is defined to be the point of strictly positive distance that is closest to the query point. This occurs, for example, when computing the nearest neighbor from each point in a set to a different point in the same set. By setting the parameter \textsf{ANN\_ALLOW\_SELF\_MATCH} in the file \textsf{include/ANN/ANN.h} to \textsf{ANNfalse} and then recompiling the package, the nearest neighbor must be of strictly positive distance from the query point. By default this parameter is set to \textsf{ANNtrue}, allowing self matches. %---------------------------------------------------------------------- \subsection{Modifying the Search Structure}\label{struct2.sec} %---------------------------------------------------------------------- One of the goals of {\ANN} is to provide a testbed for various data structures for approximate and exact nearest neighbor searching. {\ANN} provides a number of search structures, all within a common framework. For optimum performance and speed, it is sometimes advantageous to modify the search structure, depending on the nature of the data point or query point distributions. Before describing these changes, it is important to understand a bit of how the basic data structures operate. \subsubsection{{\ANN} Data Structures}\label{structs.sec} The two main data structures that {\ANN} supports are \emph{kd-trees} \cite{Ben90,FBF77} and \emph{box-decomposition trees} (or bd-trees for short) \cite{AMN98}. Let us discuss each in greater detail. The kd-tree data structure is based on a recursive subdivision of space into disjoint hyperrectangular regions called \emph{cells}. (See Fig.~\ref{kd-tree.fig}.) Each node of the tree is associated with such region $B$, called a \emph{box}, and is associated with a set of data points that lie within this box. The root node of the tree is associated with a bounding box that contains all the data points. Consider an arbitrary node in the tree. As long as the number of data points associated with this node is greater than a small quantity, called the \emph{bucket size}, the box is split into two boxes by an axis-orthogonal hyperplane that intersects this box. There are a number of different \emph{splitting rules}, which determine how this hyperplane is selected. We will discuss these in detail later. \begin{figure}[htbp] \centerline{\includegraphics[height=1.5in]{Figs/kd-tree.eps}} \caption{A kd-tree of bucket-size one and the corresponding spatial decomposition.} \label{kd-tree.fig} \end{figure} These two boxes are the cells associated with the two children of this node. The data points lying in the original box are split between these two children, depending on which side of the splitting hyperplane they lie. Points lying on the hyperplane itself may be associated with either child (according to the dictates of the splitting rule). When the number of points that are associated with the current box falls below the bucket size, then the resulting node is declared a \emph{leaf node}, and these points are stored with the node. The problem with the splitting operation used in kd-trees is that, when points are highly clustered, it may either take many splits to partition these points or the splits may result is highly elongated boxes (which can be problematic when searching is performed). {\ANN} supports the bd-tree data structure to provide greater robustness for highly clustered data sets. The bd-tree is a variant of the data structure described in \cite{AMN98}. It differs from the kd-tree mainly in that, in addition to the splitting operation, there is a more general decomposition operation called \emph{shrinking}. As above, consider a node whose associate box $B$ contains more points than the bucket size. A \emph{shrinking rule} is then invoked. This rule may opt to simply defer and perform a split according to the prevailing splitting rule. Otherwise, it selects an axis-aligned box $B'$ lying within $B$. The points lying inside $B'$ are associated with one child and the points lying outside $B'$ are associated with the other child. As before, points lying on the boundary of $B'$ may be associated with either child. Thus, in addition to the data points themselves, a kd-tree is specified by two additional parameters, the bucket size and a splitting rule. A box-decomposition tree is defined by these two parameters as well, and an additional parameter, the shrinking rule. {\ANN} provides a number of different splitting rules and shrinking rules. It also provides reasonable default values for these parameters. The (almost) complete prototypes for the constructors for kd-trees and bd-trees are given below. Refer back to Section~\ref{struct.sec} for definitions of the data point array $pa$, number of points $n$, and dimension $d$. The types \textsf{ANNsplitRule} and \textsf{ANNshrinkRule} are splitting rules and shrinking rules. They are described in later sections. {\small \begin{verbatim} enum ANNsplitRule { // splitting rules for kd-trees ANN_KD_STD, // standard kd-splitting rule ANN_KD_MIDPT, // midpoint split ANN_KD_FAIR, // fair-split ANN_KD_SL_MIDPT, // sliding midpoint split ANN_KD_SL_FAIR, // sliding fair-split ANN_KD_SUGGEST}; // the authors' suggestion for best enum ANNshrinkRule { // shrinking rules for bd-trees ANN_BD_NONE, // no shrinking at all (just kd-tree) ANN_BD_SIMPLE, // simple splitting ANN_BD_CENTROID, // centroid splitting ANN_BD_SUGGEST}; // the authors' suggested choice ANNkd_tree( // build a kd-tree from a point array ANNpointArray pa, // point array int n, // number of points int d, // dimension int bs = 1, // bucket size ANNsplitRule split = ANN_KD_SUGGEST); // splitting rule ANNbd_tree( // build a bd-tree from a point array ANNpointArray pa, // point array int n, // number of points int d, // dimension int bs = 1, // bucket size ANNsplitRule split = ANN_KD_SUGGEST, // splitting rule ANNshrinkRule shrink = ANN_BD_SUGGEST); // shrinking rule \end{verbatim} } % There are additional arguments which may be passed to the constructors % when subsequent point insertion is desired. These are described in % Section~\ref{insert.sec}. \subsubsection{Internal Tree Structure}\label{intern.sec} Before discussing the various splitting and shrinking rules, we digress to discuss the internal structure of these two trees. This material is not needed for using the data structures, but it provides some background for understanding how the search algorithms work. The root structure for both kd- and bd-trees contains the same information. It contains global information such as the number of points $n$, the dimension of the space $d$, and the bucket size, $b$. It does not store the points, but rather maintains a pointer to the array $pa$ of data points given in the constructor. It allocates an $n$-element array $\it pidx$ of point indices. It also stores a bounding hyperrectangle that contains all the data points, and a pointer to the root of the kd- or bd-tree. A leaf node in either type of tree stores the number of points that are associated with this node (which ranges from 0 up to the bucket size) and an array of point indices. This point index array is actually a subarray of \textit{pidx}. A splitting node in a kd-tree contains the following information. First, it stores the integer \emph{cutting dimension} (from 0 to $d-1$) indicating the coordinate axis that is orthogonal to the cutting hyperplane. Second it stores the \emph{cutting value} where this plane intersects this axis. It also contains the two pointers to the left and right children (containing points lying to the low and high side of the cutting plane, respectively). The search algorithm uses a technique called \emph{incremental distance computation} \cite{ArM93b} for speeding up the computation of distances between the query point and the associated cells of nodes of the tree. In order to implement incremental distance computation, it also stores two associated pieces of information with the cell. Consider the two hyperplanes bounding the cell that are parallel to the cutting plane. It stores the values at which these two hyperplanes intersect the cutting dimension's axis. Leaf and splitting nodes in a bd-tree contain exactly the same information as in the kd-tree. The only difference is that the tree may also contain shrinking nodes. A shrinking node consists of a set of at most $2d$ orthogonal halfspaces. Each orthogonal halfspace is represented by storing a cutting dimension, a cutting value (which together define an orthogonal hyperplane), and an integer $-1$ or $+1$, which indicates to which side (negative or positive, respectively) of this plane the halfspace lies. The node contains the number of orthogonal halfspaces bounding the inner box, and an array of these halfspaces. (The reason for not storing all $2d$ bounding halfspaces is that in high dimensional applications, the shrinking node may only involve a relatively small number of halfspaces.) \subsubsection{Splitting Rules for kd-trees}\label{splitrule.sec} This section describes the various splitting rules for kd-trees that are supported by {\ANN}. Let $S$ denote the current subset of data points to be stored in the tree, let $n$ denote the number of points in $S$, let $C$ denote the current cell. Let $R(C)$ denote the bounding rectangle for the current cell. The points of $S$ are all contained in $R(C)$. Let $R(S)$ denote the bounding rectangle for $S$. This rectangle is contained within (and may be equal to) $R(C)$. Initially, $S$ is the set of all data points, and $C$ is the root of the kd-tree, and $R(C)$ is the enclosing bounding rectangle for $S$. Define the \emph{aspect ratio} of a rectangle to be the ratio between its longest and shortest side lengths. Given a dimension, define the \emph{point spread} of $S$ along this dimension to be the difference between the largest and smallest coordinate for this dimension. This is equivalent to the longest side of $R(S)$. Given a set of numbers $A$, a \emph{median partition} of the $n$ numbers is a partition of $A$ into two subsets, one with $\floor{n/2}$ elements whose values are no greater than the median of $A$, and the other with $\ceil{n/2}$ elements whose values are no less than the median of $A$. \begin{description} \item[\hbox{\sf ANN\_KD\_STD:}] This is called the \emph{standard kd-tree splitting rule}. The splitting dimension is the dimension of the maximum spread of $S$. The splitting point is the median of the coordinates of $S$ along this dimension. A median partition of the points $S$ is then performed. This rule guarantees that the final tree has height $\ceil{\log_2 n}$, and size $O(n)$, but the resulting cells may have arbitrarily high aspect ratio. \item[\hbox{\sf ANN\_KD\_MIDPT:}] This is a simple splitting rule, which guarantees that cells have bounded aspect ratio, and is called the \emph{midpoint splitting rule}. It simply cuts the current cell through its midpoint orthogonal to its longest side. It can be seen as a binary variant of a quad tree, since with every $d$ levels of the tree, a hypercube of side length $x$ is partitioned into equal hypercubes of side length $x/2$ each. If there are ties, it selects the dimension with the maximum point spread. This rule can produce \emph{trivial splits}, meaning that all of the points of $S$ lie to one side of the splitting plane. As a result, the depth of and size of the resulting tree can be arbitrarily large, and both may even exceed $n$ if the points are highly clustered. \item[\hbox{\sf ANN\_KD\_SL\_MIDPT:}] This is a simple modification of the midpoint splitting rule, called the \emph{sliding-midpoint rule}. It first attempts to perform a midpoint split, by the same method described above. If points of $S$ lie on both sides of the splitting plane then the algorithm acts exactly as it would for the midpoint split. However, if a trivial split were to result, then it attempts to avoid this by ``sliding'' the splitting plane toward the points until it encounters the first data point. More formally, if the split is performed orthogonal to the $i$th coordinate, and all the points of $S$ have $i$-coordinates that are larger than that of the splitting plane, then the splitting plane is translated so that its $i$th coordinate equals the minimum $i$th coordinate among all the points of $S$. Let this point be $p_1$. Then the points are partitioned with $p_1$ in one part of the partition, and all the other points of $S$ in the other part. A symmetrical rule is applied if the points all have $i$th coordinates smaller than the splitting plane. This rule cannot result in any trivial splits, implying that the tree has maximum depth $n$ and size $O(n)$. It is possible to generate a cell $C$ of very high aspect ratio, but it can be shown that if it does, then $C$ is necessarily adjacent to a sibling cell $C'$ that is fat along the same dimension that $C$ is skinny. It turns out that cells of high aspect ratio are not problematic for nearest neighbor searching if this occurs. \item[\hbox{\sf ANN\_KD\_FAIR:}] This is a compromise between the standard kd-tree splitting rule (which always splits data points at their median) and the midpoint splitting rule (which always splits a box through its center. It is called the \emph{fair-split rule}. The goal of this rule is to achieve as nicely balanced a partition as possible, provided that the aspect ratio bound is never violated. A constant \textsf{FS\_ASPECT\_RATIO = 3} is defined in the source file \textsf{src/kd\_split.cpp}. Given a cell, it first determines the sides of this cell that can be split in some way so that the ratio of the longest to shortest side does not exceed \textsf{FS\_ASPECT\_RATIO} are identified. Among these sides, it selects the one in which the points have the largest spread. It then splits the points in the most even manner possible, subject to maintaining the bound on the ratio of the resulting cells. To determine that the aspect ratio will be preserved, we determine the longest side (other than this side), and determine how narrowly we can cut this side, without causing the aspect ratio bound to be exceeded. This procedure is more robust than either the kd-tree splitting rule or the pure midpoint splitting rule when data points are highly clustered. However, like the midpoint splitting rule, if points are highly clustered, it may generate a large number of trivial splits, and may generate trees whose size exceeds $O(n)$. \item[\hbox{\sf ANN\_KD\_SL\_FAIR:}] This rule is called \emph{sliding fair-split}. It is a splitting rule that is designed to combine the strengths of both fair-split with sliding midpoint split. Sliding fair-split is based on the theory that there are two types of splits that are good: balanced splits that produce fat boxes, and unbalanced splits provided the cell with fewer points is fat. This splitting rule operates by first computing the longest side of the current bounding box. Then it asks which sides could be split and still satisfy the aspect ratio bound with respect to this side. Among these, it selects the side with the largest spread (just as fair-split would). It then considers the most extreme cuts that would be allowed by the aspect ratio bound. This is done by dividing the longest side of the box by the aspect ratio bound. If the median cut lies between these extreme cuts, then we use the median cut. If not, then consider the extreme cut that is closer to the median. If all the points lie to one side of this cut, then we slide the cut until it hits the first point. This may violate the aspect ratio bound, but will never generate empty cells. However the sibling of every such skinny cell is fat, as with sliding midpoint split. \item[\hbox{\sf ANN\_KD\_SUGGEST:}] This is the default splitting rule. It is set to the splitting rule which, in the authors' opinion, performs best with typical data sets. It is currently set to \textsf{ANN\_KD\_SL\_MIDPT}, the sliding midpoint rule. \end{description} \subsubsection{Shrinking Rules for bd-trees}\label{shrinkrule.sec} This section describes the various shrinking rules for bd-trees that are supported by {\ANN}. Let $S$, $C$, and $n$, be the same as defined in the previous section and let $d$ denote the dimension {\ANN} first attempts to perform shrinking. Each of shrinking rules have the option of electing to not shrink. If this is the case, then processing is passed to the current splitting rule instead. \begin{description} \item[\hbox{\sf ANN\_BD\_NONE:}] When this rule is selected, no shrinking is performed at all, only splitting. A bd-tree generated with this shrinking rule is identical to a kd-tree. \item[\hbox{\sf ANN\_BD\_SIMPLE:}] This is called a \emph{simple shrink}. It depends on two constants: \textsf{BD\_GAP\_THRESH} whose value is $0.5$, and \textsf{BD\_CT\_THRESH} whose value is 2. It first computes the tight bounding box of the points, and computes the $2d$ \emph{gaps}, that is, the distances between each side of the tight enclosing rectangle for the data points $R(S)$ and the corresponding side of the cell's bounding rectangle $R(C)$. If at least \textsf{BD\_CT\_THRESH} of the gaps are larger than the length the longest side of $R(S)$ times \textsf{BD\_GAP\_THRESH}, then it shrinks all sides whose gaps are at least this large. After the shrink has been performed, all of the points of $S$ lie in the inner box of the shrink, and the outer box contains no points. If none of the gaps is large enough, then no shrinking is performed, and splitting is performed instead. \item[\hbox{\sf ANN\_BD\_CENTROID:}] This rule is called a \emph{centroid shrink}. Its operation depends on two constants: \textsf{BD\_MAX\_SPLIT\_FAC} and \textsf{BD\_FRACTION}, both of whose value are $0.5$. It repeatedly applies the current splitting rule (without actually generating new cells in the tree). In each case we see which half of the partition contains the larger number of points, and we repeat the splitting on this part. This is repeated until the number of points falls below a fraction of \textsf{BD\_FRACTION} of the original size of $S$. If it takes more than \textsf{dim*BD\_MAX\_SPLIT\_FAC} splits for this to happen, then we shrink to the final inner box. All the other points of $S$ are placed in the outer box. Otherwise, shrinking is not performed, and splitting is performed instead. \item[\hbox{\sf ANN\_BD\_SUGGEST:}] This is the default shrinking rule. It is set to the shrinking rule which, in the authors' opinion, performs best in most circumstances. It is currently set to \textsf{ANN\_BD\_SIMPLE}. \end{description} %---------------------------------------------------------------------- \subsection{Search Algorithms}\label{search.sec} %---------------------------------------------------------------------- {\ANN} supports two different methods for searching both kd- and bd-trees. The first is called \emph{standard search}. It is the simpler of the two methods, and visits cells in order based on the hierarchical structure of the search tree. The second method, called \emph{priority search}, visits cells in increasing order of distance from the query point, and hence, should converge more rapidly on the true nearest neighbor. However, priority search requires the use of a heap, and so has a somewhat higher overhead. When the error bound is small, standard search seems to be slightly faster. When larger error bounds are used, or when early termination is used (described in Section~\ref{term.sec} below) then priority search seems to be superior. \subsubsection{Standard Search}\label{stdsearch.sec} Standard search is an adaptation of the search algorithm described by Friedman, Bentley, and Finkel \cite{FBF77}, but for approximate nearest neighbor searching. The algorithm operates recursively. When first encountering a node of the kd-tree the algorithm first visits the child that is closest to the query point. On return, if the box containing the other child lies within $1/(1+\epsilon)$ times the distance to the closest point seen so far, then the other child is visited recursively. The distance between a box and the query point is computed exactly (not approximated), using incremental distance updates, as described by Arya and Mount \cite{ArM93b}. The search is similar for bd-trees. For shrinking nodes we compute the distances to the inner box and the outer box and recurse on the closer. In case of a tie, we favor the inner box. The prototype is given below. The argument $q$ is the query point, $k$ is the number of nearest neighbors, to return \textit{nn\_idx} is an array of at least $k$ point indices, and $\it dists$ is an array of at least $k$ elements of type \textsf{ANNdist}, and $\it eps$ is the (optional) error bound in nearest neighbor searching. If $\it eps$ is omitted or zero, then the $k$ nearest neighbors are computed exactly. The $k$ (approximate) nearest neighbor squared distances are stored in the elements of $\it dists$, and the indices of the nearest neighbors are returned in the elements of $\it nn\_idx$. An error results if $k$ exceeds the number of data points. The next two sections describe the search algorithms in greater detail. {\small \begin{verbatim} virtual void annkSearch( // standard search ANNpoint q, // query point int k, // number of near neighbors to return ANNidxArray nn_idx, // nearest neighbor array (returned) ANNdistArray dists, // dists to near neighbors (returned) double eps=0.0); // error bound \end{verbatim} } \subsubsection{Priority Search}\label{prsearch.sec} Priority search is described by Arya and Mount \cite{ArM93}. The cell of the kd-tree containing the query point is located, and cells are visited in increasing order of distance from the query point. This is done as follows. Whenever we arrive at a nonleaf node, we compute the distances from the query point to the cells of the two children. We enqueue the further child on a priority queue, sorted by distance, and then visit the closer child recursively. On arriving at a leaf node, we compute the distances to the points stored in this node, and continue by dequeing the next item from the priority queue. The search stops either when the priority queue is empty (meaning that the entire tree has been searched) or when the distance to the nearest cell on the priority queue exceeds the distance to the nearest point seen by a factor of more than $1/(1+\epsilon)$. The search is similar for bd-trees. For shrinking nodes we compute the distances to the inner box and to the outer box. We visit the closer one and enqueue the further, breaking ties in favor of the inner box. (Note that this differs slightly from the description in \cite{AMN98}. There the cell of the outer child is the set theoretic difference between the inner box and the outer box, implying a more complex distance computation.) The prototype for both trees is essentially the same as that of the standard search, described above. A priority-search variant of \textsf{annkSearch()} is provided, and the prototype is given below. There is no priority-search variant of the fixed-radius search, \textsf{annkFRSearch()}. {\small \begin{verbatim} virtual void annkPriSearch( // priority search ANNpoint q, // query point int k, // number of near neighbors to return ANNidxArray nn_idx, // nearest neighbor array (returned) ANNdistArray dists, // dists to near neighbors (returned) double eps=0.0); // error bound \end{verbatim} } \subsubsection{Early Termination Option}\label{term.sec} In situations where response time is critical, the search algorithm (either standard or priority search) can be forced to terminate prior to the normal termination conditions described earlier. This is done by invoking the function \textsf{annMaxPtsVisit()}. The single integer argument is the maximum number of points that the search algorithm will visit before terminating. The algorithm maintains a count of the number of points visited, and tests this quantity before visiting each leaf node. Since the test is only made prior to visiting each leaf, it may visit some additional points depending on the bucket size. The bound remains in effect until it is changed by a subsequent call to this function. To disable early termination, call the function with the argument 0. This is not a member function, but a free-standing procedure, which sets a global variable. Thus, if there are two search structures to which queries are being performed, and different maximum point values are desired for each, then it would be necessary to call this function prior to switching between the structures. {\small \begin{verbatim} void annMaxPtsVisit( int maxPts); \end{verbatim} } If this bound is set, the neraest neighbor search procedures may terminate before all of the $k$ nearest neighbors have been encountered. Therefore, this function should be invoked with care. %---------------------------------------------------------------------- \subsection{Search Tree Utility Functions}\label{utilproc.sec} %---------------------------------------------------------------------- {\ANN} provides a number of utility member functions for gathering statistics on kd-trees and bd-trees, printing the tree in a format suitable for reading, and dumping the tree for the purpose of reading it by another program. Since they are member functions, they are invoked in essentially the same way as is the \textsf{annkSearch} procedure. \subsubsection{Printing the Search Structure}\label{print.sec} The procedure Print is used to print the contents of a kd- or bd-tree in a format that is suitable for reading. This is provided primarily for debugging purposes. This procedure prints the nodes of the tree according to a right-to-left inorder traversal. That is, for an internal node it first prints the high (or outer) child, then the node itself, then the low (or inner) child. (This is done this way because by tilting the output clockwise, the traversal appears to be left to right.) For each leaf, it prints the number of points associated with the leaf, and for each point it outputs the index of the point. For each splitting node, it outputs the cutting dimension ($cd$), the cutting value ($cv$), the low bound ($\it lbnd$), and the high bound ($\it hbnd$) for the node. For shrinking nodes it prints the set of bounding halfspaces, two per line. For each bounding halfspace it prints the cutting dimension, the cutting value, and indicates whether the inner box lies on the greater or lesser side of the cutting value. The level of the node in the tree is indicated by its indentation in the output. If the boolean \textit{with\_pts} argument is true, then the data coordinates points are printed before the tree, otherwise they are not printed. The other argument is the output stream to which the output is sent. {\small \begin{verbatim} void Print( // print the tree (for debugging) ANNbool with_pts, // print points as well? ostream& out); // output stream \end{verbatim} } \subsubsection{Saving and Restoring the Search Structure on a File}\label{dump.sec} The member function \textsf{Dump()} copies a kd- or bd-tree and the associated points to a stream. (It is currently not provided from the brute-force data structure.) The tree is printed in preorder, first printing each node, then the low (or inner) child, followed by the high (or outer child). This output format is not intended for human reading, but instead for saving the data structure for the purposes of loading it later, or for consumption by another program (such as {\annfig}), for analysis of the tree. As with Print, the first argument indicates whether the points are to be printed, and the second argument is the output stream to which the output is sent. {\small \begin{verbatim} void Dump( // dump entire tree ANNbool with_pts, // print points as well? ostream& out); // output stream \end{verbatim} } To restore a saved structure, there is a constructor, which is given an input stream, which is assumed to have been created through the \textsf{Dump()} function, and creates a search structure from the contents of this file. It is assumed that the file was saved with the points printed. {\small \begin{verbatim} ANNkd_tree( // build structure from a dump file istream& in); // input stream for dump file \end{verbatim} } For example, to save the current structure \textsf{the\_tree} to ostream \textsf{foo} and then load a new structure from istream \textsf{bar} the following could be used. {\small \begin{verbatim} ANNkd_tree* the_tree = new ANNkd_tree(...); the_tree->Dump(ANNtrue, foo); // save the current tree contents delete the_tree; // deallocate (to prevent memory leaks) // ... (sometime later) the_tree = new ANNkd_tree(bar); // restore a copy of the old tree \end{verbatim} } The dump output format consists of the following elements. All entries on a line are separated by white space. \begin{description} \item[Header:] A line containing \textsf{\#ANN} followed the version number for {\ANN}. \item[Points:] If the parameter \textit{with\_pts} is true, then this section is printed. It starts with a line beginning with the word \textsf{points}, followed by the dimension of the space $d$, and the number of points $n$. This is then followed by $n$ lines, each containing the integer index of the point, followed by the $d$ coordinates of the point. One issue for floating point data is the desired output precision. This is stored in the variable \textsf{ANNcoordPrec} in the file \textsf{include/ANN/ANN.h}. \item[Tree Structure:] The tree structure describes the tree contents. It begins with a single header entry followed by a series of entries, one for each node of the tree, given according to a preorder traversal of the tree, as described above. There is no distinction made between kd-trees and bd-trees, except that kd-trees have no shrinking nodes. \begin{description} \item[Header:] This starts with a line containing the word \textsf{tree}, followed by the dimension $d$, the number of points $n$, and the bucket size $b$. This is followed by 2 lines, giving the lower endpoint and upper endpoint of the bounding box of the tree's root cell. \item[Leaf node:] The starts with the word \textsf{leaf} followed by the number of points $m$ stored in this leaf (from 0 to $b$), followed by the $m$ integer indices of these points. \item[Splitting node:] Starts with the word \textsf{split} followed by the cutting dimension, cutting value, lower bound and upper bound for the node. \item[Shrinking node:] Starts with the word \textsf{shrink} followed by the number of bounding sides $m$, followed by $m$ lines, each containing a cutting dimension, cutting value, and the side indicator ($1$ or $-1$), for this bounding side. \end{description} \end{description} \subsubsection{Gathering Statistics on Tree Structure} The procedure getStats computes statistics on the shape and properties of the search tree. These are returned in the structure \textsf{ANNkdStats}. This is something of a misnomer, because the stats apply to both kd-trees and bd-trees. This structure is returned (as the argument) to the following procedure. {\small \begin{verbatim} void getStats( // compute tree statistics ANNkdStats& st); // the statistics (returned) \end{verbatim} } The statistics structure contains the following public members, which are all set by the call to \textsf{getStats}. The total number of leaves is stored in \textsf{n\_lf}. In order to save space, {\ANN} distinguishes between leaves that do and do not contain points. Leaves that contain no points are called \emph{trivial leaves}, and are counted in \textsf{n\_tl}. (Because some splitting rules may generate a large number of trivial leaves, {\ANN} saves space by storing just one \emph{canonical} trivial leaf cell, and each trivial leaf generated by the algorithm is implemented by a single pointer to this canonical cell.) Internal nodes are of two types, splitting nodes and shrinking nodes. The former is counted in \textsf{n\_spl} and the latter in \textsf{n\_shr}. Since kd-trees do not perform shrinking, the value of \textsf{n\_shr} is nonzero only for bd-trees. The maximum depth of the tree is stored in \textsf{depth}. The \emph{aspect ratio} of a leaf cell is the ratio between the lengths of its longest and shortest sides. There is theoretical evidence that nearest neighbor searching is most efficient when the aspect ratio is relatively small (say, less than 20). The average aspect ratio of all the leaf cells is stored in \textsf{avg\_ar}. {\small \begin{verbatim} class ANNkdStats { // stats on kd-tree public: int dim; // dimension of space int n_pts; // number of points int bkt_size; // bucket size int n_lf; // number of leaves int n_tl; // number of trivial leaves int n_spl; // number of splitting nodes int n_shr; // number of shrinking nodes (bd-trees only) int depth; // depth of tree float avg_ar; // average leaf aspect ratio } \end{verbatim} } %---------------------------------------------------------------------- \subsection{Compile-Time Options}\label{compileopt.sec} %---------------------------------------------------------------------- {\ANN} contains a number of options that are activated when the program is compiled. These are activated or deactivated by adding these parameters to the ``\textsf{CFLAGS}'' variable in the file \textsf{Make-config}, before compiling the library. For example: \begin{verbatim} "CFLAGS = -O3 -Wall -DANN_PERF" \end{verbatim} Some of these options are described below (see \textsf{Make-config} for others). By default, none of these are active, except the ``-O'' for optimization. \begin{description*} \item[\hbox{\sf -O:}] (or ``\textsf{-O3}'') Produce code optimized for execution speed. \item[\hbox{\sf -DANN\_PERF:}] This causes code to be compiled that performs additional performance measurements on the efficiency of the structure (e.g., the average CPU time per query). Setting this option can slow execution by around 10\%. \item[\hbox{\sf -DANN\_NO\_LIMITS\_H:}] Use this if your system does not have either of the include files $\ang{\textsf{limits.h}}$ or $\ang{\textsf{float.h}}$, which are needed for the definition of system-dependent quantities like \textsf{DBL\_MAX}. (Also see \textsf{include/ANN/ANN.h} for other changes that may be needed.) \item[\hbox{\sf -DANN\_NO\_RANDOM:}] Use this if your system does not support the built-in pseudo-random number generators \textsf{srandom()} or \textsf{random()}. Pseudo-random number generation is used in the utility program \textsf{test/ann\_test}. (It is not required if you just want to compile the {\ANN} library.) Virtually all C++ systems provide a simple pseudo-random number in the form of two build-in functions \textsf{srand()} and \textsf{rand()}. However, these functions are inferior to the less widely available functions \textsf{srandom()} and \textsf{random()}. By setting this option, the program will use functions \textsf{srand()} and \textsf{rand()} instead. This is needed on most Microsoft Visual C++ systems. \end{description*} %---------------------------------------------------------------------- \newpage \section{Utility Programs} %---------------------------------------------------------------------- As mentioned earlier, {\ANN} is not just a library for nearest neighbor searching, but it is also provides a testbed for nearest neighbor data structures and algorithms. There are two utility programs provided with {\ANN} for the purpose of evaluating and visualizing search structures (under various splitting and shrinking rules) for a number of different data distributions. These are {\anntest} and {\annfig}, described in the following sections. If you are just interested in the {\ANN} library, you do not need to compile these two programs. %---------------------------------------------------------------------- \subsection{\anntest: A Test and Evaluation Program}\label{anntest.sec} %---------------------------------------------------------------------- The program {\anntest} provides a simple script language for setting up experiments involving {\ANN}. It allows the user to generate data and query sets of various sizes, dimensions, and distributions, to build kd- and bd-trees of various types, and then run queries and outputting various performance statistics. The program reads commands from the standard input and writes its results to the standard output. The input consists of a sequence of \emph{directives}, each consisting of a directive name, followed by list of 0 or more arguments (depending on the directive). Arguments and directives are separated by white space (blank, tab, and newline). String arguments are not quoted, and consist of a sequence of nonwhite characters. The character ``\#'' denotes a comment. The following characters up to the end of line are ignored. Comments may only be inserted between directives (not within the argument list of a directive). Directives are of two general types: \emph{operations}, which cause some action to be performed and \emph{parameter settings}, which set the values of various parameters that affect later operations. As each line of the input file is read, the appropriate operation is performed or the appropriate parameter value is set. For example, to build a kd-tree with a certain splitting rule, first set the parameter that controls the splitting rule, and then invoke the operation for building the tree. A number of the operations (particularly those involving data generation) involve generation of pseudo-random numbers. The pseudo-random number generator can be controlled by an integer \emph{seed} parameter. Once the seed is set, the subsequent sequence of pseudo-random numbers is completely determined. For example, to generate identical but pseudo-random data point sets and query point sets, first set the seed to some desired value, issue the operation to generate the data points, then reset the seed to this same value, and then issue the operation to generate the query points. The following section lists the basic operations (directives that perform actions), and the remaining sections describe various parameters that affect how these operations are performed. Arguments and their type are indicated with angled brackets. For example \STRING\ means that the argument is a character string. String and filename arguments consist of a sequence of characters with no embedded whitespaces (blank, tab, or newline). No quoting is needed (nor is it allowed). Currently there is no facility for placing comments within the script file. \subsubsection{Operations} \begin{description} \item[\hbox{\sf output\_label \STRING:}] Prints the string to the output file. \item[\hbox{\sf gen\_data\_pts:}] Generates a set of pseudo-random data points. The number of points is determined by the \textsf{data\_size} parameter, the number of coordinates is determined by the \textsf{dim} parameter, and the point distribution is determined by the \textsf{distribution} parameter. Data points generated by an earlier call to this operation or the \textsf{read\_data\_pts} operation are discarded. Relevant parameters: \textsf{data\_size}, \textsf{dim}, \textsf{std\_dev}, \textsf{corr\_coef}, \textsf{colors}, \textsf{seed}, and \textsf{distribution}. \item[\hbox{\sf gen\_query\_pts:}] Same as \textsf{gen\_data\_pts} but for the current query point set. Relevant parameters: \textsf{data\_size}, \textsf{dim}, \textsf{std\_dev}, \textsf{corr\_coef}, \textsf{colors}, \textsf{seed}, and \textsf{distribution}. \item[\hbox{\sf read\_data\_pts \FILE:}] Reads a set of data points from the given file. Each point consists of a sequence of \textsf{dim} numbers (of type \textsf{ANNcoord}) separated by whitespace (blank, newline, or tab). It is assumed that the file contains no more points than given by the \textsf{data\_size} parameter, otherwise only this many points of the data set are input. Relevant parameters: \textsf{data\_size}, \textsf{dim}. \item[\hbox{\sf read\_query\_pts \FILE:}] Same as \textsf{read\_data\_pts} but for the current query point set. The parameter \textsf{query\_size} indicates the maximum number of points. Relevant parameters: \textsf{query\_size}, \textsf{dim}. \item[\hbox{\sf build\_ann:}] Builds either a kd-tree or bd-tree for the current data point set according to current splitting rule (see the \textsf{split\_rule} parameter) and shrinking rule (see \textsf{shrink\_rule}). If the shrinking rule is ``none'' then a kd-tree results, and otherwise a bd-tree results. Relevant parameters: \textsf{split\_rule}, \textsf{shrink\_rule}. \item[\hbox{\sf run\_queries \STRING:}] Apply nearest neighbor searching to the current query point set using the current approximate nearest neighbor structure (resulting from \textsf{build\_ann}, for the current number of nearest neighbors (see \textsf{near\_neigh}), and the current error bound (see \textsf{epsilon}), and with the search strategy specified in the argument. Possible strategies are: \begin{description} \item[\hbox{\sf standard:}] Standard search. (See Section~\ref{stdsearch.sec}.) \item[\hbox{\sf priority:}] Priority search. (See Section~\ref{prsearch.sec}.) \end{description} Relevant parameters: \textsf{epsilon}, \textsf{near\_neigh}, \textsf{max\_pts\_visit}. \item[\hbox{\sf dump \FILE:}] Dump the current search structure to the specified file. See Section~\ref{dump.sec}. If the dump file is to be read by the {\annfig} program, then the file name should end with the suffix ``.dmp''. \item[\hbox{\sf load \FILE:}] Loads a tree from a data file that was created by the dump operation. Any existing tree structure and data point storage will be deallocated. \end{description} \subsubsection{Options Affecting Tree Structure:} \begin{description} \item[\hbox{\sf split\_rule \STRING:}] Type of splitting rule to use in building a kd-tree or bd-tree. Choices are as follows. See Section~\ref{splitrule.sec} for further information. \begin{description} \item[\hbox{\sf standard:}] Perform standard optimized kd-tree splitting. \item[\hbox{\sf midpt:}] Perform midpoint splitting. \item[\hbox{\sf fair:}] Perform fair-split splitting. \item[\hbox{\sf sl\_midpt:}] Perform sliding midpoint splitting. \item[\hbox{\sf sl\_fair:}] Perform sliding fair-split splitting. \item[\hbox{\sf suggest:}] Perform the authors' suggested choice for the best splitting rule. (Currently \textsf{sl\_midpt}.) \end{description} Default: \textsf{suggest}. \item[\hbox{\sf shrink\_rule \STRING:}] Specifies the type of shrinking rule to use in building a bd-tree data structure. If \textsf{none} is specified, then no shrinking is performed and the result is a kd-tree. Choices are as follows. See Section~\ref{shrinkrule.sec} for further information. \begin{description} \item[\hbox{\sf none:}] Perform no shrinking. \item[\hbox{\sf simple:}] Perform simple shrinking. \item[\hbox{\sf centroid:}] Perform centroid shrinking. \item[\hbox{\sf suggest:}] Perform the authors' suggested choice for best. (Currently \textsf{none}.) \end{description} Default: \textsf{none}. \item[\hbox{\sf bucket\_size \INT:}] Bucket size, that is, the maximum number of points stored in each leaf node of the search tree. Bucket sizes larger than 1 are recommended for the ``midpt'' splitting rule when the dimension is 3 or higher. It is also recommended when performance evaluation shows that there are a large number of trivial leaf cells. Default: 1. \end{description} \subsubsection{Options Affecting Data and Query Point Generation} The test program generates points according to the following probability distributions. \begin{description} \item[\hbox{\sf uniform:}] Each coordinate is chosen uniformly from the interval $[-1,1]$. \item[\hbox{\sf gauss:}] Each coordinate is chosen from the Gaussian distribution with the current standard deviation (see \textsf{std\_dev}) and mean 0. \item[\hbox{\sf clus\_gauss:}] Some number of cluster centers (set by the parameter \textsf{colors} below) are chosen from the above uniform distribution. Then each point is generated by selecting a random cluster center, and generating a point with a Gaussian distribution with the current standard deviation (see \textsf{std\_dev}) centered about this cluster center. Note that once the cluster centers have been set, they are not changed for the remainder of the execution of the program. This is done so that subsequent calls to generate points from a clustered distribution will be generated under the same distribution. \item[\hbox{\sf laplace:}] Each coordinate is chosen from the Laplacian distribution with zero mean and the standard deviation one. \item[Correlated distributions:] The following two distributions have been chosen to model data from applications in speech processing. These two point distributions were formed by grouping the output of autoregressive sources into vectors of length $d$. It uses the following recurrence to generate successive outputs: \[ X_i = \rho X_{i-1} + W_i, \] where $W_n$ is a sequence of zero-mean, independent, identically distributed random variables. The recurrence depends on three parameters, the choice of $X_1$, the choice of $W_i$, and the value of the correlation coefficient, $\rho$. For both of the distributions below, $\rho$, is set to the current value of the parameter \textsf{corr\_coef}. The values of $X_1$ and $W_i$ are defined below. The first component $X_1$ is selected from the corresponding uncorrelated distribution (either Gaussian or Laplacian) and the remaining components are generated by the above equation. $W_n$ is chosen by marginal density of $X_n$ is normal with the current standard deviation. \begin{description} \item[\hbox{\sf co\_gauss:}] Both $X_1$ and $W_i$ are chosen from the Gaussian distribution with the current standard deviation (see \textsf{std\_dev}) and mean 0. \item[\hbox{\sf co\_laplace:}] Both $X_1$ and $W_i$ are chosen from the Laplacian distribution zero mean and the standard deviation one. \end{description} \item[\hbox{\sf clus\_orth\_flats:}] This distribution consists of a set points clustered among a collection of lower dimensional flats (hyperplanes) within the hypercube $[-1,1]^d$. A set of \textsf{color} orthogonal flats are generated each of whose dimension is a random integer between 1 and \textsf{max\_clus\_dim}. The points are evenly distributed among the clusters. For each cluster, we generate points uniformly distributed along the flat within the hypercube, and with a Gaussian error with standard deviation \textsf{std\_dev} added. (See parameters \textsf{color}, \textsf{std\_dev}, and \textsf{max\_clus\_dim} below.) \item[\hbox{\sf clus\_ellipsoids:}] This distribution consists of a set points clustered among a collection of lower dimensional ellipsoids. A set of \textsf{color} clusters are generated each of which is centered about a point chosen uniformly from $[-1,1]^d$. Each cluster has a dimension, which is selected randomly from 1 to \textsf{max\_clus\_dim}. For each of the unselected coordinates, the coordinate is centered around the cluster center with a Gaussian error with a standard deviation \textsf{std\_dev} (which is presumably small). Otherwise, for the selected coordinates, a standard deviation for this coordinate and cluster is generated uniformly in the range $[\textsf{std\_dev\_lo}, \textsf{std\_dev\_hi}]$. The points are evenly distributed among the clusters. (See parameters \textsf{color}, \textsf{std\_dev}, \textsf{std\_dev}, \textsf{std\_dev}, and \textsf{max\_clus\_dim} below.) \item[\hbox{\sf planted:}] In high dimensional spaces, interpoint distances tend to be highly clustered around the mean value. Approximate nearest neighbor searching makes little sense in this context, unless it is the case that each query point is significantly closer to its nearest neighbor than to other points. Thus, the query points should be planted close to the data points. Given a source data set, this procedure generates a set of query points having this property. A source data array and a standard deviation are given. A random point is generated as follows. We select a random point from the source data set, and we generate a Gaussian point centered about this random point and perturbed by a normal distributed random variable with mean zero and the given standard deviation along each coordinate. (Note that this essentially the same a clustered Gaussian distribution, but where the cluster centers are given by the source data set.) \end{description} \noindent Here are the parameters that affect point generation and representation. \begin{description} \item[\hbox{\sf dim \INT:}] The dimension of the space. (Warning: Once set, if this value is changed then new data points and query points should be generated.) Default: 2. \item[\hbox{\sf seed \INT:}] Set the seed for future pseudo-random number generation. Default: 0. \item[\hbox{\sf data\_size \INT:}] The number of data points. When reading data points from a file, this indicates the maximum number of points for purposes of storage allocation. Default: 100. \item[\hbox{\sf query\_size \INT:}] The number of query points. When reading query data points from a file, this indicates the maximum number of points for purposes of storage allocation. Default: 100. \item[\hbox{\sf std\_dev \FLOAT:}] The standard deviation (used in \textsf{gauss}, \textsf{clus\_gauss}, and \textsf{clus\_orth\_flats} distributions). For the \textsf{clus\_ellipsoids} distribution it is the small distribution for the unselected dimensions. Default: 1. \item[\hbox{\sf std\_dev\_lo \FLOAT:}] (and \textsf{std\_dev\_hi}) are the standard deviations for the selected dimensions in the \textsf{clus\_ellipsoids} distribution. Default: 1. \item[\hbox{\sf corr\_coef \FLOAT:}] The correlation coefficient (used in \textsf{co\_gauss} and \textsf{co\_lapace} distributions). Default: 0.05. \item[\hbox{\sf colors \INT:}] The number of color classes (clusters) (used in the \textsf{clus\_gauss} and \textsf{clus\_orth\_flats} distributions). Default: 5. \item[\hbox{\sf max\_clus\_dim \INT:}] Maximum number of dimensions in each flat of the \textsf{clus\_orth\_flats} and \textsf{clus\_ellipsoids} distributions. Default: 1. \item[\hbox{\sf distribution \STRING:}] The type of point distribution. These can be selected from the list given above. Default: \textsf{uniform}. \end{description} \subsubsection{Options Affecting Nearest Neighbor Searching} \begin{description} \item[\hbox{\sf epsilon \FLOAT:}] The relative error bound for approximate nearest neighbor searching. Default: 0. \item[\hbox{\sf near\_neigh \INT:}] The number of nearest neighbors to report. This must not exceed the number of data points, or an error will result. Default: 1. \item[\hbox{\sf max\_pts\_visit \INT:}] The maximum number of points to visit before terminating. If set to zero, then the search runs until its natural termination condition is satisfied. Default: 0 (use the natural termination condition). \item[\hbox{\sf radius\_bound \FLOAT:}] Sets an upper bound on the nearest neighbor search radius. If the bound is positive, then fixed-radius nearest neighbor searching is performed, and the count of the number of points in the range is returned. If the bound is zero, then standard search is used. This can only be used with standard, not priority, search. Default = 0 (uses standard search.) \end{description} \subsubsection{Options Affecting the Amount of Output} The program has a various levels of output ``verbosity.'' At the lowest level (\textsf{silent}) no output is generated, and at the highest level (\textsf{show\_struct}) the contents of the tree, all results, and statistics are printed. The output levels grow monotonically, so that each subsequent level prints all the information from the previous levels. \begin{description} \item[\hbox{\sf stats \STRING:}] The parameter value may be any of the following. \begin{description} \item[\hbox{\sf silent:}] No output is generated. \item[\hbox{\sf exec\_time:}] Prints the execution time in CPU seconds for queries. \item[\hbox{\sf prep\_stats:}] Prints preprocessing statistics for the tree structure and time to construct are printed after the \textsf{build\_ann} operation has been performed. This includes the CPU time to build the structure, the depth of the search tree and the number of various types of nodes in the tree. \item[\hbox{\sf query\_stats:}] Prints statistics about the query processing after the \textsf{run\_queries} operation has been performed. These are described in greater detail below. \item[\hbox{\sf query\_res:}] Prints the results of the queries, that is, the indices of the $k$ nearest neighbors as reported by the algorithm after \textsf{run\_queries} has been performed. \item[\hbox{\sf show\_pts:}] This causes data points (or query points) to be printed after operations like \textsf{gen\_data\_pts} and \textsf{read\_data\_pts} have been performed. \item[\hbox{\sf show\_struct:}] This causes the contents of the search tree to be printed after the operation \textsf{build\_ann} has been performed. \end{description} \end{description} \subsubsection{Options Affecting the Validation} One of the interesting aspects of approximate nearest neighbor searching is that the program typically produces average approximation errors that are much smaller (often by a factor of 10) than allowed by the error parameter \textsf{eps}. This program can be used to measure the \emph{average error} over a set of queries. This is done by first running the queries using the approximation algorithm and saving the results, and then running the queries using exact nearest neighbor searching (which is done by the brute-force data structure). The average error for a single reported nearest neighbor at distance $x$, is computed by first finding the distance $x^*$ to the corresponding true nearest neighbor. If $x=x^*=0$ then the error is defined to be 0, and otherwise it is $(x - x^*)/x^*$. These errors are computed for all query points and over all $k$ nearest neighbors for each query point. As part of the validation process, the program checks that no error exceeds \textsf{eps}, and issues an error message if this is violated. The second type of error is called the \emph{rank error}. Define the rank of the data point as the number of data points that are at least as close as this point is to the query point. Thus the nearest neighbor has rank 1 (assuming no other points are of equal distance). To compute the rank error of each result, we compute its rank $r$ among the true nearest neighbors that were computed. (If it is further from all the true nearest, then $r$ is $\textsf{true\_nn}+1$.) If this point is reported as the $j$-th nearest neighbor (where the closest point is $j=1$) then the rank error for this point is $\max(0, j-r)$. The rank error is computed for all query points and all the $k$ nearest neighbors for each query point. \begin{description} \item[\hbox{\sf validate \STRING:}] This enables validation. This is used for debugging and error analysis (described further below). When validation is enabled, some number of exact nearest neighbors (as indicated by the parameter \textsf{true\_near\_neigh}) are computed by a simple brute force algorithm, and average errors and rank errors are computed. Because the brute-force algorithm is used, the validation process can take a very long time, especially for large data sets in high dimensional spaces. Valid arguments are: either \textsf{on} or \textsf{off}. Default: \textsf{off}. \item[\hbox{\sf true\_near\_neigh \INT:}] This parameter indicates the number of true nearest neighbors to compute for the validation process. This information is used in computing rank errors and average errors. Its value should be at least as high as the value of \textsf{near\_neighbor}. The default value of this parameter is 10 more than the value of \textsf{near\_neigh}, the number of nearest neighbors for each query. \end{description} Here is an annotated example of an input to the {\anntest} program. The comments to the right are not part of the file. The parameters have been indented to distinguish them from operations. {\small \begin{verbatim} output_label test-run-0 # output a label for this run validate on # enable validation dim 16 # points in dimension 16 stats query_stats # output performance statistics for queries seed 121212 # pseudo-random number seed data_size 1000 distribution uniform gen_data_pts # generate 1000 uniform data points in dim 16 query_size 100 colors 10 std_dev 0.05 distribution clus_gauss gen_query_pts # generate 100 query points in 10 clusters bucket_size 2 split_rule fair shrink_rule none build_ann # build a kd-tree with fair-split and bucket size 2 epsilon 0.1 near_neigh 5 max_pts_visit 100 # stop search if more than 100 points seen true_near_neigh 20 # compute 20 nearest neighbors when validating run_queries standard # run queries; 5 near neighbors, allowing 10% error data_size 500 read_data_pts data.in # read up to 500 points from file data.in split_rule sl_midpt shrink_rule simple build_ann # build bd-tree; sliding midpoint and simple shrink epsilon 0 run_queries priority # run the same queries; with no allowable error \end{verbatim} } %---------------------------------------------------------------------- \subsection{\annfig: Visualization Tool}\label{ann2fig.sec} %---------------------------------------------------------------------- The program {\annfig} inputs an {\ANN} dump file, as generated by the \textsf{dump} operation of the {\anntest} program, and (optionally) the coordinates of the data points, and generates a 2-dimensional display of the geometric structure of the search tree. The output form is called \emph{fig format}, e.g., as used by the \textsf{xfig} program (Ver 3.1). The resulting fig file may then be displayed using xfig, or converted to any of a number of other formats using the Unix program \textsf{fig2dev}. An example is shown in Fig.~\ref{ann.fig} in Section~\ref{annlib.sec}. If the points are in dimension 2, then the entire tree is displayed. If the dimension is larger than 2 then the user has the option of selecting any orthogonal 2-dimensional ``slice'' to be displayed. A slice is an axis-aligned 2-dimensional plane in $d$-dimensional space. We assume that dimensions are numbered from 0 to $d-1$. The slice is specified giving the two \emph{plane dimensions} that correspond to the $x$- and $y$-dimensions of the final output, and then giving the values at which this plane cuts each of the remaining coordinate axes, called \emph{slicing values}. There are two ways to specify the slicing values. The first is by giving a real \emph{default slicing value}, $z$, which means that the slicing plane cuts all the coordinate axes (other than the plane dimensions) at the value $z$. The other is by specifying a set of \emph{slicing pairs} each consisting of a dimension $i$, $0 \le i < d$, and value $z$, which means that the plane cuts the $i$th coordinate axis at value $z$. For example, given a 4-dimensional space, with coordinates 0 through 3, the 2-dimensional plane $x_2 = 0.5$, $x_3 = -2.4$, could be specified by the slicing pairs $(2,0.5)$ and $(3,-2.4)$. Given the slicing plane, a leaf cell is either disjoint from the slicing plane or it intersects the slicing plane in a rectangle. In the former case, the leaf cell is not displayed. In the latter case the rectangle of intersection is drawn, and all data points lying within the cell are projected orthogonally onto the slicing plane and then drawn as small circles. The input to {\annfig} is a dump file as generated by the \textsf{dump} operation. It is assumed that the file name ends with the suffix ``.dmp''. The command-line arguments to {\annfig} (given below) specify the plane dimensions and the default slicing value and any slicing pairs. The plane dimensions are specified by the \textsf{-dx} and \textsf{-dy} command-line options. By default, the plane dimensions are 0 and 1 for the $x$- and $y$- display dimensions, respectively. The default slicing value is specified by the \textsf{-sv} options. Its default value is 0. Each slicing pair is specified by the \textsf{-sl} option, which is followed by two numbers, the slicing dimension and the slicing value. There may be any number of slicing pairs specified by repeating the \textsf{-sl} option. Other than the plane dimensions, if slicing pairs are not specified for a dimension, then the default slicing value is used instead. The figure is bounded by the intersection of the bounding box of the kd- or bd-tree with the slicing plane. The size and placement of this bounding box in the final figure is controlled by specifying the $x$- and $y$-offsets of the box (through the \textsf{-x} and \textsf{-y} relative to the upper left corner of the figure (in inches), and the length of the longer side of the box (through the \textsf{sz} option). The box is translated and scaled to match this offset and longest side length before drawing. By default the offsets are each 1 inch, and the size is 5 inches. There are also command-line arguments to specify the number of fig units per inch (the \textsf{-upi} option), and the radius of the circles used for drawing points (the \textsf{-ps} option, given in fig units). The default units per inch value is 1200, and the default point size value is 10 fig units. Here is a summary of the command line arguments. Square brackets are used to represent optional arguments, the asterisk ($*$) means that the argument may be repeated zero or more times. The file name is given without the ``.dmp'' suffix, and the output is written to a file with the same name, but with the suffix ``.fig''. \begin{obeylines} ~ \qquad \textsf{ann2fig} ~[\textsf{-upi} \textit{scale}] ~[\textsf{-x} \textit{xoffset}] ~[\textsf{-y} \textit{yoffset}] ~[\textsf{-sz} \textit{size}] ~[\textsf{-dx} $\it dim_x$] ~[\textsf{-dy} $\it dim\_y$] \qquad\qquad [\textsf{-sl} \textit{dim value}]$^*$ ~[\textsf{-ps} \textit{pointsize}] ~\textit{file} \end{obeylines} \newpage \bibliography{ann} \end{document} ann-1.1.2+doc/doc/Copyright.txt0000644000175000017500000000305610464722022017173 0ustar sylvestresylvestreANN: Approximate Nearest Neighbors Version: 1.1.1 Release Date: Aug 4, 2006 ---------------------------------------------------------------------------- Copyright (c) 1997-2005 University of Maryland and Sunil Arya and David Mount All Rights Reserved. This program is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser Public License for more details. A copy of the terms and conditions of the license can be found in License.txt or online at http://www.gnu.org/copyleft/lesser.html To obtain a copy, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. Disclaimer ---------- The University of Maryland and the authors make no representations about the suitability or fitness of this software for any purpose. It is provided "as is" without express or implied warranty. --------------------------------------------------------------------- Authors ------- David Mount Dept of Computer Science University of Maryland, College Park, MD 20742 USA mount@cs.umd.edu http://www.cs.umd.edu/~mount/ Sunil Arya Dept of Computer Science Hong University of Science and Technology Clearwater Bay, HONG KONG arya@cs.ust.hk http://www.cs.ust.hk/faculty/arya/ ann-1.1.2+doc/doc/Figs/0000755000175000017500000000000011157657105015357 5ustar sylvestresylvestreann-1.1.2+doc/doc/Figs/ann.eps0000644000175000017500000045420410217651222016643 0ustar sylvestresylvestre%!PS-Adobe-2.0 EPSF-2.0 %%Title: ann.fig %%Creator: fig2dev Version 3.1 Patchlevel 2 %%CreationDate: Tue Sep 9 16:43:40 1997 %%For: mount@polygon.cs.umd.edu (Dave &,AVW 3209,4052704,3018900017) %Magnification: 1.00 %%Orientation: Portrait %%BoundingBox: 0 0 461 196 %%Pages: 0 %%BeginSetup %%IncludeFeature: *PageSize Letter %%EndSetup %%EndComments /$F2psDict 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DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2712 4245 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2755 4274 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2566 4168 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2574 4162 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2639 4159 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2661 4155 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2642 4140 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2630 4116 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2638 4108 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2609 4011 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2644 4054 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2651 4079 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2646 4049 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2649 4008 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2706 4106 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2739 4148 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2717 4105 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2802 4218 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2811 4209 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2947 4390 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2847 4089 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2850 4117 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2880 4104 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2824 4029 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2804 3998 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2814 4022 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2820 4003 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2837 4077 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2864 3991 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2971 4087 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2952 4082 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2587 3980 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2606 3964 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2597 3954 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2598 3904 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2598 3934 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2615 3954 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2642 3953 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2641 3893 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2664 3922 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2590 3854 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2603 3836 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2664 3817 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2609 3806 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2709 3953 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2737 3964 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2668 3886 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2677 3861 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2709 3872 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2701 3809 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2744 3826 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2611 3734 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2652 3781 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2614 3698 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2557 3612 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2706 3784 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2670 3748 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2729 3764 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2775 3758 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2687 3674 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2807 3951 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2888 3961 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2853 3906 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2846 3905 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2863 3927 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2804 3870 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2832 3886 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2818 3870 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2816 3852 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2869 3882 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2899 3939 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2926 3956 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2927 3948 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2902 3924 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2899 3901 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2946 3937 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2945 3926 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2963 3924 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2958 3919 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3005 3896 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2929 3855 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2961 3875 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2990 3858 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2957 3851 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2825 3732 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2818 3666 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2920 3691 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2913 3687 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3008 3737 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2979 3704 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2988 3730 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2980 3623 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2989 3682 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2994 3626 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2194 3423 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2253 3349 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2097 2904 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2140 2866 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2218 2864 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2315 2784 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2869 3570 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2679 3487 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1433 2641 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1688 2622 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1769 2700 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1709 2461 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1875 2754 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1909 2724 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1956 2722 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1871 2687 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2059 2630 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2015 2584 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2061 2610 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1957 2548 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2022 2559 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1992 2461 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1986 2455 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2035 2379 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1882 2352 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1982 2306 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2049 2374 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2023 2292 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1277 1714 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1333 1642 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1361 1632 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1440 1954 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1432 1842 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1572 1811 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1454 1733 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1450 1710 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1508 1774 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1505 1772 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1455 1640 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1422 1611 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1478 1658 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1509 1646 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1563 1758 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1595 1622 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1611 1622 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1622 1580 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1171 1516 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1331 1492 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1383 1491 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1292 1418 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1362 1306 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1424 1514 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1405 1506 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1435 1475 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1486 1539 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1492 1526 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1430 1433 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1463 1470 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1526 1477 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1625 1536 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1539 1411 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1593 1439 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1504 1223 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1600 1229 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1520 1171 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1685 1716 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1699 1677 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1696 1642 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1718 1625 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1705 1603 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1763 1616 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1954 1676 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2069 1590 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1696 1498 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1722 1519 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1641 1446 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1679 1411 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1723 1384 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1798 1500 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1641 1262 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1741 1212 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1814 1357 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1771 1216 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 1901 1523 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2165 2599 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2134 2598 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2165 2589 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2223 2774 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2247 2711 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2149 2554 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2113 2438 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2204 2453 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2157 2384 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2255 2541 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2305 2522 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2304 2425 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2319 2605 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2186 2311 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2119 2300 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2306 2248 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2240 2185 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2133 2087 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2091 1981 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2308 2049 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2367 2365 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2345 2313 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2498 2293 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2325 2105 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2388 1985 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2417 2074 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2410 2046 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2446 2099 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2450 2081 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2517 2132 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2483 2057 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2525 2041 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2624 2433 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2803 2678 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2877 2486 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2822 2475 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2801 2414 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2876 2454 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2947 2493 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2907 2485 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2978 2544 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2981 2449 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2991 2388 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2579 2233 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2698 2341 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2725 2367 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2696 2210 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2709 2181 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2750 2250 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2777 2253 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2770 2238 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2566 2078 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2716 2101 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2851 2294 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2889 2349 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2889 2205 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2917 2325 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2916 2215 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2802 2164 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2816 2144 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2791 2081 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2825 2159 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2886 2010 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2948 2111 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2974 2157 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2985 2101 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2175 1939 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2174 1883 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2277 1946 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2294 1861 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2319 1870 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2168 1743 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2214 1735 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2306 1728 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2378 1944 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2335 1792 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2373 1820 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2435 1959 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2529 1937 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2482 1833 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2484 1806 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2358 1591 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2409 1712 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2452 1566 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2582 1965 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2559 1953 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2604 1972 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2620 1815 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2624 1873 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2636 1869 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2696 1973 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2717 1891 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2725 1912 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2729 1843 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2554 1779 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2661 1717 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2555 1650 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2724 1639 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2937 1930 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3005 1954 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2960 1929 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2802 1825 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 2920 1614 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3080 4181 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3042 4133 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3056 4015 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3053 3989 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3057 4018 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3162 4153 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3146 4066 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3188 4068 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3320 4016 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3010 3971 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3044 3988 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3033 3948 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3048 3957 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3078 3959 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3076 3938 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3102 3952 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3047 3923 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3011 3888 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3092 3900 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3121 3969 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3130 3967 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3129 3962 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3023 3879 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3043 3830 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3013 3821 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3094 3834 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3137 3845 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3202 3878 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3164 3856 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3126 3815 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3140 3812 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3225 3939 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3228 3904 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3211 3792 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3035 3764 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3053 3763 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3067 3728 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3114 3760 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3116 3783 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3129 3729 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3036 3684 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3049 3677 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3049 3646 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3073 3587 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3141 3627 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3123 3611 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3260 3742 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3242 3654 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3233 3571 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3168 3535 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3404 4164 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3015 2762 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3092 2492 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3290 2531 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3032 2386 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3069 2244 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3083 2261 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3112 2396 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3038 2177 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3118 2135 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3039 2046 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3080 2084 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3200 2149 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3230 2112 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3425 2356 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3466 2364 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3363 2196 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3490 2572 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3492 2426 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3628 2440 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3666 2437 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3737 2567 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3751 2472 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3805 2409 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3818 2551 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3874 2504 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3910 2436 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3620 2298 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3684 2348 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3698 2318 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3687 2293 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3626 2252 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3668 2242 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3535 2198 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3520 2150 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3676 2067 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3780 2306 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3812 2355 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3737 2270 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3737 2305 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3817 2394 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3836 2336 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3907 2347 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3892 2333 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3858 2279 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3740 2067 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3817 2193 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3884 2198 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3922 2155 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3836 2150 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3893 2021 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3991 2638 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3996 2600 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3977 2510 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3937 2451 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4104 2458 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4030 2280 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4086 2353 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4066 2325 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4128 2302 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4130 2290 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4071 2246 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4081 2182 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4158 2276 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4140 2197 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3978 2149 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 3937 2069 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4152 2088 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4106 2052 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4155 1978 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4198 2342 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4162 2279 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4205 2299 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4221 2332 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4236 2289 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4253 2282 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4167 2224 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4214 2271 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4319 2340 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4320 2313 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4306 2272 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4287 2182 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4372 2261 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4346 2243 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4176 2154 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4194 2122 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4229 2089 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4252 2084 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4188 2019 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4303 2099 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4306 2093 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4375 2120 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4318 2079 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4404 2251 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4438 2214 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4462 2172 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4403 2101 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4420 2096 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4395 2092 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4471 2238 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4051 1972 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4102 1869 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4165 1943 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4192 1884 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4246 1863 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4300 1935 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4308 1910 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4346 1944 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4317 1905 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4266 1687 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4186 1561 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4414 1966 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4435 1875 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4469 1867 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4551 1908 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4850 1948 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 4619 1790 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5802 4070 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5806 4035 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5755 3910 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5952 4116 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5904 3913 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5916 3913 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5672 3744 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5675 3739 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5724 3730 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5838 3764 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5728 3636 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5800 3710 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5854 3717 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5837 3669 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5912 3826 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5927 3812 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5876 3780 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5889 3744 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5950 3761 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5935 3728 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5968 3791 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5913 3703 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6014 3620 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5875 3559 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5954 3553 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5865 3490 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6018 3518 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5828 2893 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5806 2858 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5947 2887 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5942 2790 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6174 4187 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6433 4285 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6445 4252 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6352 4086 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6485 4136 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6470 4054 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6498 4059 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6048 3835 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6138 3880 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6163 3926 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6254 3960 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6252 3888 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6258 3840 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6069 3779 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6130 3674 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6222 3755 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6353 3908 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6463 3864 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6477 3627 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6509 4232 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6681 4286 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6666 4245 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6710 4274 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6521 4168 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6528 4162 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6593 4159 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6597 4140 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6616 4155 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6584 4116 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6593 4108 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6605 4079 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6599 4054 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6601 4049 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6564 4011 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6604 4008 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6694 4148 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6661 4106 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6672 4105 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6756 4218 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6765 4209 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6901 4390 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6805 4117 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6802 4089 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6835 4104 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6769 4022 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6778 4029 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6758 3998 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6774 4003 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6792 4077 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6819 3991 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6906 4082 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6925 4087 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6542 3980 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6552 3954 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6560 3964 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6553 3934 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6552 3904 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6570 3954 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6597 3953 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6619 3922 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6595 3893 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6545 3854 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6557 3836 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6564 3806 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6619 3817 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6663 3953 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6692 3964 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6622 3886 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6631 3861 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6663 3872 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6656 3809 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6698 3826 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6606 3781 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6566 3734 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6569 3698 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6512 3612 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6624 3748 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6660 3784 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6683 3764 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6730 3758 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6642 3674 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6761 3951 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6843 3961 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6817 3927 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6800 3905 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6807 3906 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6758 3870 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6772 3870 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6786 3886 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6770 3852 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6823 3882 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6853 3939 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6880 3956 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6881 3948 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6856 3924 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6853 3901 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6900 3937 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6900 3926 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6912 3919 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6918 3924 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6959 3896 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6884 3855 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6916 3875 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6911 3851 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6945 3858 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6779 3732 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6772 3666 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6868 3687 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6875 3691 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6942 3730 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6963 3737 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6933 3704 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6944 3682 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6934 3623 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6948 3626 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6148 3423 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6208 3349 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6051 2904 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6094 2866 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6172 2864 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6269 2784 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6633 3487 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6824 3570 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5387 2641 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5643 2622 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5723 2700 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5663 2461 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5830 2754 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5825 2687 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5864 2724 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5911 2722 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6013 2630 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6016 2610 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5969 2584 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5911 2548 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5976 2559 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5940 2455 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5946 2461 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5989 2379 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5836 2352 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5937 2306 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5978 2292 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6003 2374 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5232 1714 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5288 1642 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5316 1632 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5394 1954 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5386 1842 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5526 1811 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5409 1733 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5404 1710 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5459 1772 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5463 1774 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5377 1611 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5410 1640 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5433 1658 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5463 1646 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5518 1758 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5550 1622 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5565 1622 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5576 1580 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5125 1516 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5285 1492 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5338 1491 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5246 1418 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5316 1306 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5360 1506 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5379 1514 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5389 1475 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5440 1539 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5446 1526 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5417 1470 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5385 1433 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5480 1477 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5579 1536 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5494 1411 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5547 1439 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5458 1223 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5475 1171 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5554 1229 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5640 1716 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5654 1677 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5651 1642 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5673 1625 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5718 1616 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5659 1603 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5908 1676 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6023 1590 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5651 1498 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5676 1519 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5596 1446 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5634 1411 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5677 1384 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5752 1500 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5596 1262 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5696 1212 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5769 1357 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5726 1216 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 5856 1523 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6088 2598 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6119 2599 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6119 2589 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6178 2774 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6201 2711 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6274 2605 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6104 2554 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6068 2438 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6159 2453 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6111 2384 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6209 2541 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6259 2522 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6258 2425 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6073 2300 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6140 2311 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6194 2185 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6260 2248 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6087 2087 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6045 1981 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6262 2049 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6321 2365 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6300 2313 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6453 2293 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6279 2105 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6371 2074 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6365 2046 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6342 1985 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6400 2099 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6404 2081 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6471 2132 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6437 2057 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6479 2041 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6578 2433 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6758 2678 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6831 2486 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6777 2475 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6756 2414 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6830 2454 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6861 2485 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6901 2493 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6933 2544 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6935 2449 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6945 2388 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6533 2233 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6679 2367 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6653 2341 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6650 2210 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6664 2181 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6705 2250 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6731 2253 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6724 2238 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6520 2078 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6670 2101 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6844 2349 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6806 2294 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6843 2205 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6872 2325 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6871 2215 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6757 2164 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6780 2159 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6770 2144 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6746 2081 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6841 2010 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6929 2157 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6903 2111 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6940 2101 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6129 1939 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6128 1883 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6231 1946 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6248 1861 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6274 1870 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6123 1743 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6169 1735 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6261 1728 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6332 1944 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6290 1792 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6328 1820 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6390 1959 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6483 1937 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6437 1833 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6438 1806 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6363 1712 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6312 1591 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6406 1566 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6513 1953 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6536 1965 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6559 1972 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6509 1779 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6578 1873 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6590 1869 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6575 1815 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6651 1973 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6671 1891 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6679 1912 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6683 1843 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6510 1650 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6616 1717 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6678 1639 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6757 1825 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6891 1930 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6914 1929 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6960 1954 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6875 1614 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7034 4181 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6996 4133 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7116 4153 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7012 4018 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7011 4015 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6965 3971 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6998 3988 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7007 3989 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7100 4066 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7143 4068 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7076 3969 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7084 3967 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7359 4164 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7275 4016 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6987 3948 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7003 3957 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7002 3923 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7032 3959 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7031 3938 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7056 3952 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6965 3888 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6977 3879 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7047 3900 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7084 3962 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7119 3856 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7157 3878 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6968 3821 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6997 3830 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7049 3834 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6989 3764 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7008 3763 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7091 3845 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7080 3815 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7094 3812 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7071 3783 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7069 3760 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7179 3939 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7182 3904 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7166 3792 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7022 3728 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6990 3684 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7003 3677 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7003 3646 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7084 3729 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7028 3587 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7078 3611 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7095 3627 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7123 3535 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7215 3742 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7196 3654 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7187 3571 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6969 2762 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7047 2492 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6986 2386 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7067 2396 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7244 2531 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7037 2261 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7023 2244 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6992 2177 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7072 2135 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7035 2084 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 6994 2046 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7154 2149 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7184 2112 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7379 2356 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7420 2364 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7318 2196 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7444 2572 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7446 2426 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7582 2440 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7621 2437 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7692 2567 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7705 2472 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7759 2409 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7772 2551 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7829 2504 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7772 2394 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7864 2436 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7490 2198 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7574 2298 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7639 2348 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7653 2318 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7642 2293 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7581 2252 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7623 2242 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7475 2150 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7631 2067 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7692 2305 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7766 2355 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7734 2306 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7691 2270 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7791 2336 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7813 2279 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7846 2333 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7862 2347 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7772 2193 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7838 2198 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7695 2067 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7791 2150 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7876 2155 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7848 2021 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7946 2638 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7950 2600 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7932 2510 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7891 2451 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8058 2458 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7985 2280 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8040 2353 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8020 2325 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8082 2302 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8085 2290 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8025 2246 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8036 2182 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8112 2276 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8094 2197 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7933 2149 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 7892 2069 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8107 2088 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8061 2052 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8109 1978 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8152 2342 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8116 2279 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8159 2299 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8176 2332 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8190 2289 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8207 2282 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8122 2224 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8169 2271 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8273 2340 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8274 2313 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8261 2272 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8242 2182 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8301 2243 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8326 2261 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8130 2154 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8148 2122 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8184 2089 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8206 2084 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8142 2019 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8257 2099 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8261 2093 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8272 2079 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8329 2120 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8358 2251 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8393 2214 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8425 2238 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8417 2172 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8350 2092 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8357 2101 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8375 2096 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8006 1972 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8057 1869 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8119 1943 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8146 1884 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8200 1863 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8254 1935 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8263 1910 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8272 1905 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8301 1944 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8220 1687 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8140 1561 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8369 1966 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8390 1875 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8423 1867 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8505 1908 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8573 1790 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Ellipse n 8804 1948 12 12 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col-1 s gr % Polyline n 1171 4390 m 4850 4390 l 4850 1171 l 1171 1171 l cp gs col-1 s gr % Polyline n 1717 4390 m 1717 3585 l gs col-1 s gr % Polyline n 1717 4116 m 2091 4116 l gs col-1 s gr % Polyline n 1852 4116 m 1852 3988 l gs col-1 s gr % Polyline n 1717 3988 m 2091 3988 l gs col-1 s gr % Polyline n 1904 3988 m 1904 3786 l gs col-1 s gr % Polyline n 1961 3988 m 1961 3888 l gs col-1 s gr % Polyline n 1904 3888 m 2091 3888 l gs col-1 s gr % Polyline n 1904 3826 m 1997 3826 l gs col-1 s gr % Polyline n 1997 3888 m 1997 3786 l gs col-1 s gr % Polyline n 1717 3786 m 2091 3786 l gs col-1 s gr % Polyline n 1717 3736 m 1810 3736 l gs col-1 s gr % Polyline n 1810 3786 m 1810 3686 l gs col-1 s gr % Polyline n 1810 3736 m 1904 3736 l gs col-1 s gr % Polyline n 1857 3736 m 1857 3686 l gs col-1 s gr % Polyline n 1717 3686 m 1904 3686 l gs col-1 s gr % Polyline n 1810 3686 m 1810 3585 l gs col-1 s gr % Polyline n 1904 3786 m 1904 3585 l gs col-1 s gr % Polyline n 1935 3786 m 1935 3736 l gs col-1 s gr % Polyline n 1904 3736 m 1996 3736 l gs col-1 s gr % Polyline n 1959 3736 m 1959 3686 l gs col-1 s gr % Polyline n 1996 3786 m 1996 3686 l gs col-1 s gr % Polyline n 1904 3686 m 2091 3686 l gs col-1 s gr % Polyline n 1171 3585 m 2091 3585 l gs col-1 s gr % Polyline n 1852 3585 m 1852 2781 l gs col-1 s gr % Polyline n 1971 3585 m 1971 3490 l gs col-1 s gr % Polyline n 2031 3585 m 2031 3490 l gs col-1 s gr % Polyline n 1852 3490 m 2091 3490 l gs col-1 s gr % Polyline n 1852 3183 m 2091 3183 l gs col-1 s gr % Polyline n 1852 2893 m 2091 2893 l gs col-1 s gr % Polyline n 1988 2893 m 1988 2781 l gs col-1 s gr % Polyline n 2091 4390 m 2091 2781 l gs col-1 s gr % Polyline n 2321 4390 m 2321 3988 l gs col-1 s gr % Polyline n 2479 4390 m 2479 4189 l gs col-1 s gr % Polyline n 2321 4189 m 2550 4189 l gs col-1 s gr % Polyline n 2435 4189 m 2435 3988 l gs col-1 s gr % Polyline n 2435 4089 m 2550 4089 l gs col-1 s gr % Polyline n 2516 4089 m 2516 3988 l gs col-1 s gr % Polyline n 2091 3988 m 2550 3988 l gs col-1 s gr % Polyline n 2091 3880 m 2205 3880 l gs col-1 s gr % Polyline n 2205 3988 m 2205 3786 l gs col-1 s gr % Polyline n 2263 3988 m 2263 3888 l gs col-1 s gr % Polyline n 2263 3938 m 2321 3938 l gs col-1 s gr % Polyline n 2205 3888 m 2321 3888 l gs col-1 s gr % Polyline n 2091 3786 m 2321 3786 l gs col-1 s gr % Polyline n 2091 3686 m 2205 3686 l gs col-1 s gr % Polyline n 2205 3786 m 2205 3585 l gs col-1 s gr % Polyline n 2321 3988 m 2321 3585 l gs col-1 s gr % Polyline n 2435 3988 m 2435 3786 l gs col-1 s gr % Polyline n 2321 3786 m 2550 3786 l gs col-1 s gr % Polyline n 2550 4390 m 2550 3585 l gs col-1 s gr % Polyline n 2665 4390 m 2665 4189 l gs col-1 s gr % Polyline n 2665 4286 m 2780 4286 l gs col-1 s gr % Polyline n 2723 4286 m 2723 4189 l gs col-1 s gr % Polyline n 2550 4189 m 2780 4189 l gs col-1 s gr % Polyline n 2550 4162 m 2607 4162 l gs col-1 s gr % Polyline n 2607 4189 m 2607 4089 l gs col-1 s gr % Polyline n 2639 4189 m 2639 4139 l gs col-1 s gr % Polyline n 2639 4155 m 2665 4155 l gs col-1 s gr % Polyline n 2607 4139 m 2665 4139 l gs col-1 s gr % Polyline n 2636 4139 m 2636 4089 l gs col-1 s gr % Polyline n 2550 4089 m 2665 4089 l gs col-1 s gr % Polyline n 2609 4089 m 2609 3988 l gs col-1 s gr % Polyline n 2644 4089 m 2644 4038 l gs col-1 s gr % Polyline n 2644 4064 m 2665 4064 l gs col-1 s gr % Polyline n 2609 4038 m 2665 4038 l gs col-1 s gr % Polyline n 2665 4189 m 2665 3988 l gs col-1 s gr % Polyline n 2723 4189 m 2723 4105 l gs col-1 s gr % Polyline n 2665 4105 m 2780 4105 l gs col-1 s gr % Polyline n 2780 4390 m 2780 3988 l gs col-1 s gr % Polyline n 2780 4218 m 2895 4218 l gs col-1 s gr % Polyline n 2895 4390 m 2895 4189 l gs col-1 s gr % Polyline n 2780 4189 m 3010 4189 l gs col-1 s gr % Polyline n 2847 4189 m 2847 4089 l gs col-1 s gr % Polyline n 2847 4117 m 2895 4117 l gs col-1 s gr % Polyline n 2780 4089 m 2895 4089 l gs col-1 s gr % Polyline n 2780 4029 m 2837 4029 l gs col-1 s gr % Polyline n 2809 4029 m 2809 3988 l gs col-1 s gr % Polyline n 2809 4009 m 2837 4009 l gs col-1 s gr % Polyline n 2837 4089 m 2837 3988 l gs col-1 s gr % Polyline n 2837 4038 m 2895 4038 l gs col-1 s gr % Polyline n 2895 4189 m 2895 3988 l gs col-1 s gr % Polyline n 2895 4087 m 3010 4087 l gs col-1 s gr % Polyline n 2550 3988 m 3010 3988 l gs col-1 s gr % Polyline n 2587 3988 m 2587 3938 l gs col-1 s gr % Polyline n 2587 3963 m 2607 3963 l gs col-1 s gr % Polyline n 2550 3938 m 2607 3938 l gs col-1 s gr % Polyline n 2598 3938 m 2598 3888 l gs col-1 s gr % Polyline n 2607 3988 m 2607 3888 l gs col-1 s gr % Polyline n 2636 3988 m 2636 3938 l gs col-1 s gr % Polyline n 2607 3938 m 2665 3938 l gs col-1 s gr % Polyline n 2641 3938 m 2641 3888 l gs col-1 s gr % Polyline n 2550 3888 m 2665 3888 l gs col-1 s gr % Polyline n 2550 3837 m 2607 3837 l gs col-1 s gr % Polyline n 2607 3888 m 2607 3786 l gs col-1 s gr % Polyline n 2607 3817 m 2665 3817 l gs col-1 s gr % Polyline n 2665 3988 m 2665 3786 l gs col-1 s gr % Polyline n 2723 3988 m 2723 3888 l gs col-1 s gr % Polyline n 2665 3888 m 2780 3888 l gs col-1 s gr % Polyline n 2665 3862 m 2694 3862 l gs col-1 s gr % Polyline n 2694 3888 m 2694 3837 l gs col-1 s gr % Polyline n 2665 3837 m 2723 3837 l gs col-1 s gr % Polyline n 2723 3888 m 2723 3786 l gs col-1 s gr % Polyline n 2550 3786 m 2780 3786 l gs col-1 s gr % Polyline n 2611 3786 m 2611 3686 l gs col-1 s gr % Polyline n 2611 3736 m 2665 3736 l gs col-1 s gr % Polyline n 2550 3686 m 2665 3686 l gs col-1 s gr % Polyline n 2665 3786 m 2665 3585 l gs col-1 s gr % Polyline n 2665 3748 m 2723 3748 l gs col-1 s gr % Polyline n 2723 3786 m 2723 3686 l gs col-1 s gr % Polyline n 2723 3758 m 2780 3758 l gs col-1 s gr % Polyline n 2665 3686 m 2780 3686 l gs col-1 s gr % Polyline n 2780 3988 m 2780 3585 l gs col-1 s gr % Polyline n 2837 3988 m 2837 3888 l gs col-1 s gr % Polyline n 2837 3938 m 2895 3938 l gs col-1 s gr % Polyline n 2837 3906 m 2863 3906 l gs col-1 s gr % Polyline n 2863 3938 m 2863 3888 l gs col-1 s gr % Polyline n 2780 3888 m 2895 3888 l gs col-1 s gr % Polyline n 2809 3888 m 2809 3852 l gs col-1 s gr % Polyline n 2809 3870 m 2837 3870 l gs col-1 s gr % Polyline n 2780 3852 m 2837 3852 l gs col-1 s gr % Polyline n 2837 3888 m 2837 3786 l gs col-1 s gr % Polyline n 2895 3988 m 2895 3786 l gs col-1 s gr % Polyline n 2924 3988 m 2924 3938 l gs col-1 s gr % Polyline n 2924 3956 m 2953 3956 l gs col-1 s gr % Polyline n 2895 3938 m 2953 3938 l gs col-1 s gr % Polyline n 2895 3913 m 2924 3913 l gs col-1 s gr % Polyline n 2924 3938 m 2924 3888 l gs col-1 s gr % Polyline n 2924 3926 m 2953 3926 l gs col-1 s gr % Polyline n 2953 3988 m 2953 3888 l gs col-1 s gr % Polyline n 2953 3924 m 3010 3924 l gs col-1 s gr % Polyline n 2981 3924 m 2981 3888 l gs col-1 s gr % Polyline n 2895 3888 m 3010 3888 l gs col-1 s gr % Polyline n 2953 3888 m 2953 3786 l gs col-1 s gr % Polyline n 2981 3888 m 2981 3851 l gs col-1 s gr % Polyline n 2953 3851 m 3010 3851 l gs col-1 s gr % Polyline n 2780 3786 m 3010 3786 l gs col-1 s gr % Polyline n 2780 3686 m 2895 3686 l gs col-1 s gr % Polyline n 2895 3786 m 2895 3585 l gs col-1 s gr % Polyline n 2895 3691 m 2953 3691 l gs col-1 s gr % Polyline n 2953 3786 m 2953 3686 l gs col-1 s gr % Polyline n 2953 3736 m 3010 3736 l gs col-1 s gr % Polyline n 2981 3736 m 2981 3686 l gs col-1 s gr % Polyline n 2895 3686 m 3010 3686 l gs col-1 s gr % Polyline n 2980 3686 m 2980 3585 l gs col-1 s gr % Polyline n 2980 3636 m 3010 3636 l gs col-1 s gr % Polyline n 2091 3585 m 3010 3585 l gs col-1 s gr % Polyline n 2253 3585 m 2253 3183 l gs col-1 s gr % Polyline n 2091 3183 m 2550 3183 l gs col-1 s gr % Polyline n 2091 2904 m 2315 2904 l gs col-1 s gr % Polyline n 2203 2904 m 2203 2781 l gs col-1 s gr % Polyline n 2315 3183 m 2315 2781 l gs col-1 s gr % Polyline n 2550 3585 m 2550 2781 l gs col-1 s gr % Polyline n 2550 3487 m 3010 3487 l gs col-1 s gr % Polyline n 1171 2781 m 3010 2781 l gs col-1 s gr % Polyline n 1630 2781 m 1630 1976 l gs col-1 s gr % Polyline n 1745 2781 m 1745 2580 l gs col-1 s gr % Polyline n 1630 2580 m 1861 2580 l gs col-1 s gr % Polyline n 1861 2781 m 1861 2378 l gs col-1 s gr % Polyline n 1861 2734 m 1918 2734 l gs col-1 s gr % Polyline n 1918 2781 m 1918 2687 l gs col-1 s gr % Polyline n 1861 2687 m 1975 2687 l gs col-1 s gr % Polyline n 1975 2781 m 1975 2580 l gs col-1 s gr % Polyline n 1975 2630 m 2091 2630 l gs col-1 s gr % Polyline n 2033 2630 m 2033 2580 l gs col-1 s gr % Polyline n 1861 2580 m 2091 2580 l gs col-1 s gr % Polyline n 1975 2580 m 1975 2378 l gs col-1 s gr % Polyline n 1975 2478 m 2091 2478 l gs col-1 s gr % Polyline n 1975 2455 m 2033 2455 l gs col-1 s gr % Polyline n 2033 2478 m 2033 2378 l gs col-1 s gr % Polyline n 1630 2378 m 2091 2378 l gs col-1 s gr % Polyline n 1882 2378 m 1882 1976 l gs col-1 s gr % Polyline n 1986 2378 m 1986 2292 l gs col-1 s gr % Polyline n 1882 2292 m 2091 2292 l gs col-1 s gr % Polyline n 1171 1976 m 2091 1976 l gs col-1 s gr % Polyline n 1171 1714 m 1401 1714 l gs col-1 s gr % Polyline n 1333 1714 m 1333 1573 l gs col-1 s gr % Polyline n 1401 1976 m 1401 1573 l gs col-1 s gr % Polyline n 1401 1875 m 1516 1875 l gs col-1 s gr % Polyline n 1516 1976 m 1516 1774 l gs col-1 s gr % Polyline n 1401 1774 m 1630 1774 l gs col-1 s gr % Polyline n 1401 1724 m 1458 1724 l gs col-1 s gr % Polyline n 1458 1774 m 1458 1674 l gs col-1 s gr % Polyline n 1458 1772 m 1516 1772 l gs col-1 s gr % Polyline n 1401 1674 m 1516 1674 l gs col-1 s gr % Polyline n 1401 1623 m 1458 1623 l gs col-1 s gr % Polyline n 1458 1674 m 1458 1573 l gs col-1 s gr % Polyline n 1458 1646 m 1516 1646 l gs col-1 s gr % Polyline n 1516 1774 m 1516 1573 l gs col-1 s gr % Polyline n 1516 1674 m 1630 1674 l gs col-1 s gr % Polyline n 1595 1674 m 1595 1573 l gs col-1 s gr % Polyline n 1595 1622 m 1630 1622 l gs col-1 s gr % Polyline n 1171 1573 m 1630 1573 l gs col-1 s gr % Polyline n 1286 1573 m 1286 1372 l gs col-1 s gr % Polyline n 1343 1573 m 1343 1473 l gs col-1 s gr % Polyline n 1286 1473 m 1401 1473 l gs col-1 s gr % Polyline n 1171 1372 m 1401 1372 l gs col-1 s gr % Polyline n 1401 1573 m 1401 1171 l gs col-1 s gr % Polyline n 1401 1514 m 1458 1514 l gs col-1 s gr % Polyline n 1429 1514 m 1429 1473 l gs col-1 s gr % Polyline n 1458 1573 m 1458 1473 l gs col-1 s gr % Polyline n 1458 1526 m 1516 1526 l gs col-1 s gr % Polyline n 1401 1473 m 1516 1473 l gs col-1 s gr % Polyline n 1458 1473 m 1458 1372 l gs col-1 s gr % Polyline n 1516 1573 m 1516 1372 l gs col-1 s gr % Polyline n 1573 1573 m 1573 1473 l gs col-1 s gr % Polyline n 1516 1473 m 1630 1473 l gs col-1 s gr % Polyline n 1573 1473 m 1573 1372 l gs col-1 s gr % Polyline n 1401 1372 m 1630 1372 l gs col-1 s gr % Polyline n 1516 1372 m 1516 1171 l gs col-1 s gr % Polyline n 1516 1229 m 1630 1229 l gs col-1 s gr % Polyline n 1630 1976 m 1630 1171 l gs col-1 s gr % Polyline n 1630 1716 m 1861 1716 l gs col-1 s gr % Polyline n 1630 1645 m 1745 1645 l gs col-1 s gr % Polyline n 1696 1645 m 1696 1573 l gs col-1 s gr % Polyline n 1696 1609 m 1745 1609 l gs col-1 s gr % Polyline n 1745 1716 m 1745 1573 l gs col-1 s gr % Polyline n 1861 1976 m 1861 1573 l gs col-1 s gr % Polyline n 1861 1676 m 2091 1676 l gs col-1 s gr % Polyline n 1630 1573 m 2091 1573 l gs col-1 s gr % Polyline n 1696 1573 m 1696 1473 l gs col-1 s gr % Polyline n 1630 1473 m 1745 1473 l gs col-1 s gr % Polyline n 1630 1422 m 1688 1422 l gs col-1 s gr % Polyline n 1688 1473 m 1688 1372 l gs col-1 s gr % Polyline n 1745 1573 m 1745 1372 l gs col-1 s gr % Polyline n 1630 1372 m 1861 1372 l gs col-1 s gr % Polyline n 1630 1262 m 1745 1262 l gs col-1 s gr % Polyline n 1745 1372 m 1745 1171 l gs col-1 s gr % Polyline n 1745 1271 m 1861 1271 l gs col-1 s gr % Polyline n 1861 1573 m 1861 1171 l gs col-1 s gr % Polyline n 2091 2781 m 2091 1171 l gs col-1 s gr % Polyline n 2091 2599 m 2205 2599 l gs col-1 s gr % Polyline n 2148 2599 m 2148 2580 l gs col-1 s gr % Polyline n 2205 2781 m 2205 2580 l gs col-1 s gr % Polyline n 2205 2711 m 2319 2711 l gs col-1 s gr % Polyline n 2091 2580 m 2319 2580 l gs col-1 s gr % Polyline n 2091 2478 m 2205 2478 l gs col-1 s gr % Polyline n 2148 2478 m 2148 2378 l gs col-1 s gr % Polyline n 2148 2428 m 2205 2428 l gs col-1 s gr % Polyline n 2205 2580 m 2205 2378 l gs col-1 s gr % Polyline n 2262 2580 m 2262 2478 l gs col-1 s gr % Polyline n 2205 2478 m 2319 2478 l gs col-1 s gr % Polyline n 2319 2781 m 2319 2378 l gs col-1 s gr % Polyline n 2091 2378 m 2550 2378 l gs col-1 s gr % Polyline n 2091 2300 m 2205 2300 l gs col-1 s gr % Polyline n 2205 2378 m 2205 2177 l gs col-1 s gr % Polyline n 2205 2248 m 2321 2248 l gs col-1 s gr % Polyline n 2091 2177 m 2321 2177 l gs col-1 s gr % Polyline n 2091 2076 m 2205 2076 l gs col-1 s gr % Polyline n 2205 2177 m 2205 1976 l gs col-1 s gr % Polyline n 2321 2378 m 2321 1976 l gs col-1 s gr % Polyline n 2321 2313 m 2435 2313 l gs col-1 s gr % Polyline n 2435 2378 m 2435 2177 l gs col-1 s gr % Polyline n 2321 2177 m 2550 2177 l gs col-1 s gr % Polyline n 2321 2076 m 2435 2076 l gs col-1 s gr % Polyline n 2388 2076 m 2388 1976 l gs col-1 s gr % Polyline n 2388 2046 m 2435 2046 l gs col-1 s gr % Polyline n 2435 2177 m 2435 1976 l gs col-1 s gr % Polyline n 2435 2099 m 2493 2099 l gs col-1 s gr % Polyline n 2493 2177 m 2493 2076 l gs col-1 s gr % Polyline n 2435 2076 m 2550 2076 l gs col-1 s gr % Polyline n 2493 2076 m 2493 1976 l gs col-1 s gr % Polyline n 2550 2781 m 2550 1976 l gs col-1 s gr % Polyline n 2780 2781 m 2780 2378 l gs col-1 s gr % Polyline n 2780 2580 m 3010 2580 l gs col-1 s gr % Polyline n 2780 2478 m 2895 2478 l gs col-1 s gr % Polyline n 2780 2428 m 2837 2428 l gs col-1 s gr % Polyline n 2837 2478 m 2837 2378 l gs col-1 s gr % Polyline n 2895 2580 m 2895 2378 l gs col-1 s gr % Polyline n 2895 2493 m 2953 2493 l gs col-1 s gr % Polyline n 2953 2580 m 2953 2478 l gs col-1 s gr % Polyline n 2895 2478 m 3010 2478 l gs col-1 s gr % Polyline n 2981 2478 m 2981 2378 l gs col-1 s gr % Polyline n 2550 2378 m 3010 2378 l gs col-1 s gr % Polyline n 2665 2378 m 2665 2177 l gs col-1 s gr % Polyline n 2723 2378 m 2723 2277 l gs col-1 s gr % Polyline n 2665 2277 m 2780 2277 l gs col-1 s gr % Polyline n 2665 2210 m 2723 2210 l gs col-1 s gr % Polyline n 2723 2277 m 2723 2177 l gs col-1 s gr % Polyline n 2752 2277 m 2752 2238 l gs col-1 s gr % Polyline n 2723 2238 m 2780 2238 l gs col-1 s gr % Polyline n 2550 2177 m 2780 2177 l gs col-1 s gr % Polyline n 2665 2177 m 2665 1976 l gs col-1 s gr % Polyline n 2780 2378 m 2780 1976 l gs col-1 s gr % Polyline n 2851 2378 m 2851 2277 l gs col-1 s gr % Polyline n 2780 2277 m 2895 2277 l gs col-1 s gr % Polyline n 2895 2378 m 2895 2177 l gs col-1 s gr % Polyline n 2895 2277 m 3010 2277 l gs col-1 s gr % Polyline n 2780 2177 m 3010 2177 l gs col-1 s gr % Polyline n 2780 2152 m 2825 2152 l gs col-1 s gr % Polyline n 2780 2127 m 2825 2127 l gs col-1 s gr % Polyline n 2825 2177 m 2825 2076 l gs col-1 s gr % Polyline n 2780 2076 m 2895 2076 l gs col-1 s gr % Polyline n 2895 2177 m 2895 1976 l gs col-1 s gr % Polyline n 2953 2177 m 2953 2101 l gs col-1 s gr % Polyline n 2895 2101 m 3010 2101 l gs col-1 s gr % Polyline n 2091 1976 m 3010 1976 l gs col-1 s gr % Polyline n 2091 1883 m 2205 1883 l gs col-1 s gr % Polyline n 2205 1976 m 2205 1774 l gs col-1 s gr % Polyline n 2205 1875 m 2321 1875 l gs col-1 s gr % Polyline n 2294 1875 m 2294 1774 l gs col-1 s gr % Polyline n 2091 1774 m 2321 1774 l gs col-1 s gr % Polyline n 2205 1774 m 2205 1573 l gs col-1 s gr % Polyline n 2205 1728 m 2321 1728 l gs col-1 s gr % Polyline n 2321 1976 m 2321 1573 l gs col-1 s gr % Polyline n 2321 1875 m 2435 1875 l gs col-1 s gr % Polyline n 2373 1875 m 2373 1774 l gs col-1 s gr % Polyline n 2435 1976 m 2435 1774 l gs col-1 s gr % Polyline n 2493 1976 m 2493 1875 l gs col-1 s gr % Polyline n 2435 1875 m 2550 1875 l gs col-1 s gr % Polyline n 2484 1875 m 2484 1774 l gs col-1 s gr % Polyline n 2321 1774 m 2550 1774 l gs col-1 s gr % Polyline n 2409 1774 m 2409 1573 l gs col-1 s gr % Polyline n 2091 1573 m 2550 1573 l gs col-1 s gr % Polyline n 2550 1976 m 2550 1171 l gs col-1 s gr % Polyline n 2550 1953 m 2604 1953 l gs col-1 s gr % Polyline n 2604 1976 m 2604 1885 l gs col-1 s gr % Polyline n 2550 1885 m 2665 1885 l gs col-1 s gr % Polyline n 2620 1885 m 2620 1794 l gs col-1 s gr % Polyline n 2620 1869 m 2665 1869 l gs col-1 s gr % Polyline n 2665 1976 m 2665 1794 l gs col-1 s gr % Polyline n 2665 1930 m 2723 1930 l gs col-1 s gr % Polyline n 2723 1976 m 2723 1885 l gs col-1 s gr % Polyline n 2665 1885 m 2780 1885 l gs col-1 s gr % Polyline n 2550 1794 m 2780 1794 l gs col-1 s gr % Polyline n 2607 1794 m 2607 1704 l gs col-1 s gr % Polyline n 2550 1704 m 2665 1704 l gs col-1 s gr % Polyline n 2665 1794 m 2665 1614 l gs col-1 s gr % Polyline n 2780 1976 m 2780 1614 l gs col-1 s gr % Polyline n 2937 1976 m 2937 1825 l gs col-1 s gr % Polyline n 2937 1929 m 3010 1929 l gs col-1 s gr % Polyline n 2780 1825 m 3010 1825 l gs col-1 s gr % Polyline n 2550 1614 m 3010 1614 l gs col-1 s gr % Polyline n 3010 4390 m 3010 1171 l gs col-1 s gr % Polyline n 3010 4181 m 3404 4181 l gs col-1 s gr % Polyline n 3010 4084 m 3108 4084 l gs col-1 s gr % Polyline n 3010 4015 m 3057 4015 l gs col-1 s gr % Polyline n 3057 4084 m 3057 3988 l gs col-1 s gr % Polyline n 3108 4181 m 3108 3988 l gs col-1 s gr % Polyline n 3108 4084 m 3207 4084 l gs col-1 s gr % Polyline n 3158 4084 m 3158 3988 l gs col-1 s gr % Polyline n 3207 4181 m 3207 3988 l gs col-1 s gr % Polyline n 3010 3988 m 3404 3988 l gs col-1 s gr % Polyline n 3035 3988 m 3035 3963 l gs col-1 s gr % Polyline n 3010 3963 m 3059 3963 l gs col-1 s gr % Polyline n 3035 3963 m 3035 3938 l gs col-1 s gr % Polyline n 3059 3988 m 3059 3938 l gs col-1 s gr % Polyline n 3059 3959 m 3108 3959 l gs col-1 s gr % Polyline n 3084 3959 m 3084 3938 l gs col-1 s gr % Polyline n 3010 3938 m 3108 3938 l gs col-1 s gr % Polyline n 3010 3913 m 3059 3913 l gs col-1 s gr % Polyline n 3059 3938 m 3059 3888 l gs col-1 s gr % Polyline n 3108 3988 m 3108 3888 l gs col-1 s gr % Polyline n 3130 3988 m 3130 3962 l gs col-1 s gr % Polyline n 3108 3962 m 3207 3962 l gs col-1 s gr % Polyline n 3010 3888 m 3207 3888 l gs col-1 s gr % Polyline n 3010 3837 m 3108 3837 l gs col-1 s gr % Polyline n 3010 3821 m 3059 3821 l gs col-1 s gr % Polyline n 3059 3837 m 3059 3786 l gs col-1 s gr % Polyline n 3108 3888 m 3108 3786 l gs col-1 s gr % Polyline n 3158 3888 m 3158 3837 l gs col-1 s gr % Polyline n 3158 3862 m 3207 3862 l gs col-1 s gr % Polyline n 3108 3837 m 3207 3837 l gs col-1 s gr % Polyline n 3140 3837 m 3140 3786 l gs col-1 s gr % Polyline n 3207 3988 m 3207 3786 l gs col-1 s gr % Polyline n 3228 3988 m 3228 3888 l gs col-1 s gr % Polyline n 3207 3888 m 3404 3888 l gs col-1 s gr % Polyline n 3010 3786 m 3404 3786 l gs col-1 s gr % Polyline n 3053 3786 m 3053 3736 l gs col-1 s gr % Polyline n 3010 3736 m 3108 3736 l gs col-1 s gr % Polyline n 3108 3786 m 3108 3686 l gs col-1 s gr % Polyline n 3116 3786 m 3116 3736 l gs col-1 s gr % Polyline n 3108 3736 m 3207 3736 l gs col-1 s gr % Polyline n 3010 3686 m 3207 3686 l gs col-1 s gr % Polyline n 3010 3677 m 3049 3677 l gs col-1 s gr % Polyline n 3049 3686 m 3049 3636 l gs col-1 s gr % Polyline n 3010 3636 m 3108 3636 l gs col-1 s gr % Polyline n 3108 3686 m 3108 3585 l gs col-1 s gr % Polyline n 3108 3627 m 3207 3627 l gs col-1 s gr % Polyline n 3207 3786 m 3207 3585 l gs col-1 s gr % Polyline n 3207 3686 m 3404 3686 l gs col-1 s gr % Polyline n 3010 3585 m 3404 3585 l gs col-1 s gr % Polyline n 3010 3535 m 3404 3535 l gs col-1 s gr % Polyline n 3404 4390 m 3404 2781 l gs col-1 s gr % Polyline n 3010 2781 m 4850 2781 l gs col-1 s gr % Polyline n 3010 2591 m 3240 2591 l gs col-1 s gr % Polyline n 3240 2781 m 3240 2401 l gs col-1 s gr % Polyline n 3010 2401 m 3470 2401 l gs col-1 s gr % Polyline n 3010 2306 m 3112 2306 l gs col-1 s gr % Polyline n 3069 2306 m 3069 2211 l gs col-1 s gr % Polyline n 3112 2401 m 3112 2211 l gs col-1 s gr % Polyline n 3010 2211 m 3240 2211 l gs col-1 s gr % Polyline n 3067 2211 m 3067 2116 l gs col-1 s gr % Polyline n 3010 2116 m 3125 2116 l gs col-1 s gr % Polyline n 3067 2116 m 3067 2021 l gs col-1 s gr % Polyline n 3125 2211 m 3125 2021 l gs col-1 s gr % Polyline n 3125 2116 m 3240 2116 l gs col-1 s gr % Polyline n 3240 2401 m 3240 2021 l gs col-1 s gr % Polyline n 3425 2401 m 3425 2211 l gs col-1 s gr % Polyline n 3240 2211 m 3470 2211 l gs col-1 s gr % Polyline n 3470 2781 m 3470 2021 l gs col-1 s gr % Polyline n 3470 2572 m 3700 2572 l gs col-1 s gr % Polyline n 3585 2572 m 3585 2401 l gs col-1 s gr % Polyline n 3585 2440 m 3700 2440 l gs col-1 s gr % Polyline n 3700 2781 m 3700 2401 l gs col-1 s gr % Polyline n 3700 2567 m 3930 2567 l gs col-1 s gr % Polyline n 3700 2472 m 3815 2472 l gs col-1 s gr % Polyline n 3815 2567 m 3815 2401 l gs col-1 s gr % Polyline n 3872 2567 m 3872 2483 l gs col-1 s gr % Polyline n 3815 2483 m 3930 2483 l gs col-1 s gr % Polyline n 3470 2401 m 3930 2401 l gs col-1 s gr % Polyline n 3620 2401 m 3620 2211 l gs col-1 s gr % Polyline n 3620 2348 m 3700 2348 l gs col-1 s gr % Polyline n 3620 2306 m 3700 2306 l gs col-1 s gr % Polyline n 3620 2258 m 3700 2258 l gs col-1 s gr % Polyline n 3660 2258 m 3660 2211 l gs col-1 s gr % Polyline n 3470 2211 m 3700 2211 l gs col-1 s gr % Polyline n 3470 2150 m 3585 2150 l gs col-1 s gr % Polyline n 3585 2211 m 3585 2021 l gs col-1 s gr % Polyline n 3700 2401 m 3700 2021 l gs col-1 s gr % Polyline n 3780 2401 m 3780 2306 l gs col-1 s gr % Polyline n 3700 2306 m 3815 2306 l gs col-1 s gr % Polyline n 3737 2306 m 3737 2211 l gs col-1 s gr % Polyline n 3815 2401 m 3815 2211 l gs col-1 s gr % Polyline n 3815 2353 m 3872 2353 l gs col-1 s gr % Polyline n 3872 2401 m 3872 2306 l gs col-1 s gr % Polyline n 3872 2347 m 3930 2347 l gs col-1 s gr % Polyline n 3815 2306 m 3930 2306 l gs col-1 s gr % Polyline n 3700 2211 m 3930 2211 l gs col-1 s gr % Polyline n 3815 2211 m 3815 2021 l gs col-1 s gr % Polyline n 3872 2211 m 3872 2150 l gs col-1 s gr % Polyline n 3872 2181 m 3930 2181 l gs col-1 s gr % Polyline n 3815 2150 m 3930 2150 l gs col-1 s gr % Polyline n 3010 2021 m 3930 2021 l gs col-1 s gr % Polyline n 3930 2781 m 3930 1171 l gs col-1 s gr % Polyline n 3930 2638 m 4104 2638 l gs col-1 s gr % Polyline n 3930 2580 m 4104 2580 l gs col-1 s gr % Polyline n 3930 2478 m 4104 2478 l gs col-1 s gr % Polyline n 4104 2781 m 4104 2378 l gs col-1 s gr % Polyline n 3930 2378 m 4390 2378 l gs col-1 s gr % Polyline n 4045 2378 m 4045 2177 l gs col-1 s gr % Polyline n 4045 2328 m 4102 2328 l gs col-1 s gr % Polyline n 4102 2378 m 4102 2277 l gs col-1 s gr % Polyline n 4102 2302 m 4160 2302 l gs col-1 s gr % Polyline n 4045 2277 m 4160 2277 l gs col-1 s gr % Polyline n 4045 2227 m 4102 2227 l gs col-1 s gr % Polyline n 4102 2277 m 4102 2177 l gs col-1 s gr % Polyline n 4102 2227 m 4160 2227 l gs col-1 s gr % Polyline n 3930 2177 m 4160 2177 l gs col-1 s gr % Polyline n 3930 2076 m 4045 2076 l gs col-1 s gr % Polyline n 4045 2177 m 4045 1976 l gs col-1 s gr % Polyline n 4045 2076 m 4160 2076 l gs col-1 s gr % Polyline n 4106 2076 m 4106 1976 l gs col-1 s gr % Polyline n 4160 2378 m 4160 1976 l gs col-1 s gr % Polyline n 4160 2328 m 4217 2328 l gs col-1 s gr % Polyline n 4188 2328 m 4188 2277 l gs col-1 s gr % Polyline n 4217 2378 m 4217 2277 l gs col-1 s gr % Polyline n 4217 2328 m 4274 2328 l gs col-1 s gr % Polyline n 4246 2328 m 4246 2277 l gs col-1 s gr % Polyline n 4160 2277 m 4274 2277 l gs col-1 s gr % Polyline n 4214 2277 m 4214 2177 l gs col-1 s gr % Polyline n 4274 2378 m 4274 2177 l gs col-1 s gr % Polyline n 4320 2378 m 4320 2277 l gs col-1 s gr % Polyline n 4274 2277 m 4390 2277 l gs col-1 s gr % Polyline n 4274 2227 m 4332 2227 l gs col-1 s gr % Polyline n 4332 2277 m 4332 2177 l gs col-1 s gr % Polyline n 4332 2243 m 4390 2243 l gs col-1 s gr % Polyline n 4160 2177 m 4390 2177 l gs col-1 s gr % Polyline 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col-1 s gr % Polyline n 5858 3984 m 6045 3984 l gs col-1 s gr % Polyline n 5904 3913 m 5916 3913 l 5916 3913 l 5904 3913 l cp gs col-1 s gr % Polyline n 5910 3913 m 5910 3913 l gs col-1 s gr % Polyline n 5672 3851 m 6045 3851 l gs col-1 s gr % Polyline n 5672 3744 m 5724 3744 l 5724 3718 l 5672 3718 l cp gs col-1 s gr % Polyline n 5672 3744 m 5675 3744 l 5675 3739 l 5672 3739 l cp gs col-1 s gr % Polyline n 5672 3742 m 5675 3742 l gs col-1 s gr % Polyline n 5698 3744 m 5698 3718 l gs col-1 s gr % Polyline n 5765 3851 m 5765 3718 l gs col-1 s gr % Polyline n 5672 3718 m 5858 3718 l gs col-1 s gr % Polyline n 5765 3718 m 5765 3585 l gs col-1 s gr % Polyline n 5800 3718 m 5858 3718 l 5858 3669 l 5800 3669 l cp gs col-1 s gr % Polyline n 5829 3718 m 5829 3669 l gs col-1 s gr % Polyline n 5829 3694 m 5858 3694 l gs col-1 s gr % Polyline n 5858 3851 m 5858 3585 l gs col-1 s gr % Polyline n 5912 3826 m 5927 3826 l 5927 3812 l 5912 3812 l cp gs col-1 s gr % Polyline n 5920 3826 m 5920 3812 l 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5969 2580 l cp gs col-1 s gr % Polyline n 5992 2630 m 5992 2605 l gs col-1 s gr % Polyline n 5992 2618 m 6016 2618 l gs col-1 s gr % Polyline n 5969 2605 m 6016 2605 l gs col-1 s gr % Polyline n 5815 2580 m 6045 2580 l gs col-1 s gr % Polyline n 5930 2580 m 5930 2378 l gs col-1 s gr % Polyline n 5930 2478 m 6045 2478 l gs col-1 s gr % Polyline n 5940 2461 m 5946 2461 l 5946 2455 l 5940 2455 l cp gs col-1 s gr % Polyline n 5943 2461 m 5943 2455 l gs col-1 s gr % Polyline n 5987 2478 m 5987 2378 l gs col-1 s gr % Polyline n 5585 2378 m 6045 2378 l gs col-1 s gr % Polyline n 5836 2378 m 6045 2378 l 6045 2292 l 5836 2292 l cp gs col-1 s gr % Polyline n 5888 2378 m 5888 2292 l gs col-1 s gr % Polyline n 5940 2378 m 5940 2292 l gs col-1 s gr % Polyline n 5992 2378 m 5992 2292 l gs col-1 s gr % Polyline n 5125 1976 m 6045 1976 l gs col-1 s gr % Polyline n 5232 1714 m 5355 1714 l 5355 1632 l 5232 1632 l cp gs col-1 s gr % Polyline n 5232 1673 m 5293 1673 l gs col-1 s gr % Polyline n 5293 1714 m 5293 1632 l gs col-1 s gr % Polyline n 5355 1976 m 5355 1573 l gs col-1 s gr % Polyline n 5355 1976 m 5394 1976 l 5394 1842 l 5355 1842 l cp gs col-1 s gr % Polyline n 5355 1908 m 5394 1908 l gs col-1 s gr % Polyline n 5470 1976 m 5470 1774 l gs col-1 s gr % Polyline n 5355 1774 m 5585 1774 l gs col-1 s gr % Polyline n 5404 1774 m 5470 1774 l 5470 1710 l 5404 1710 l cp gs col-1 s gr % Polyline n 5404 1733 m 5409 1733 l 5409 1710 l 5404 1710 l cp gs col-1 s gr % Polyline n 5404 1721 m 5409 1721 l gs col-1 s gr % Polyline n 5437 1774 m 5437 1710 l gs col-1 s gr % Polyline n 5459 1774 m 5463 1774 l 5463 1772 l 5459 1772 l cp gs col-1 s gr % Polyline n 5461 1774 m 5461 1772 l gs col-1 s gr % Polyline n 5355 1674 m 5470 1674 l gs col-1 s gr % Polyline n 5377 1640 m 5412 1640 l 5412 1611 l 5377 1611 l cp gs col-1 s gr % Polyline n 5395 1640 m 5395 1611 l gs col-1 s gr % Polyline n 5412 1674 m 5412 1573 l gs col-1 s gr % Polyline n 5433 1658 m 5470 1658 l 5470 1646 l 5433 1646 l cp gs col-1 s gr % Polyline n 5452 1658 m 5452 1646 l gs col-1 s gr % Polyline n 5470 1774 m 5470 1573 l gs col-1 s gr % Polyline n 5470 1674 m 5585 1674 l gs col-1 s gr % Polyline n 5550 1622 m 5585 1622 l 5585 1573 l 5550 1573 l cp gs col-1 s gr % Polyline n 5550 1622 m 5565 1622 l 5565 1622 l 5550 1622 l cp gs col-1 s gr % Polyline n 5557 1622 m 5557 1622 l gs col-1 s gr % Polyline n 5550 1598 m 5585 1598 l gs col-1 s gr % Polyline n 5125 1573 m 5585 1573 l gs col-1 s gr % Polyline n 5240 1573 m 5240 1372 l gs col-1 s gr % Polyline n 5285 1492 m 5355 1492 l 5355 1473 l 5285 1473 l cp gs col-1 s gr % Polyline n 5320 1492 m 5320 1473 l gs col-1 s gr % Polyline n 5240 1473 m 5355 1473 l gs col-1 s gr % Polyline n 5125 1372 m 5355 1372 l gs col-1 s gr % Polyline n 5355 1573 m 5355 1171 l gs col-1 s gr % Polyline n 5355 1514 m 5389 1514 l 5389 1473 l 5355 1473 l cp gs col-1 s gr % Polyline n 5355 1514 m 5379 1514 l 5379 1506 l 5355 1506 l cp gs col-1 s gr % Polyline n 5367 1514 m 5367 1506 l gs col-1 s gr % Polyline n 5355 1493 m 5389 1493 l gs col-1 s gr % Polyline n 5412 1573 m 5412 1473 l gs col-1 s gr % Polyline n 5440 1539 m 5446 1539 l 5446 1526 l 5440 1526 l cp gs col-1 s gr % Polyline n 5440 1532 m 5446 1532 l gs col-1 s gr % Polyline n 5355 1473 m 5470 1473 l gs col-1 s gr % Polyline n 5385 1473 m 5417 1473 l 5417 1433 l 5385 1433 l cp gs col-1 s gr % Polyline n 5385 1452 m 5417 1452 l gs col-1 s gr % Polyline n 5470 1573 m 5470 1372 l gs col-1 s gr % Polyline n 5528 1573 m 5528 1473 l gs col-1 s gr % Polyline n 5470 1473 m 5585 1473 l gs col-1 s gr % Polyline n 5470 1439 m 5547 1439 l 5547 1411 l 5470 1411 l cp gs col-1 s gr % Polyline n 5509 1439 m 5509 1411 l gs col-1 s gr % Polyline n 5355 1372 m 5585 1372 l gs col-1 s gr % Polyline n 5458 1229 m 5585 1229 l 5585 1171 l 5458 1171 l cp gs col-1 s gr % Polyline n 5458 1200 m 5490 1200 l gs col-1 s gr % Polyline n 5490 1229 m 5490 1171 l gs col-1 s gr % Polyline n 5522 1229 m 5522 1171 l gs col-1 s gr % Polyline n 5585 1976 m 5585 1171 l gs col-1 s gr % Polyline n 5585 1716 m 5718 1716 l 5718 1573 l 5585 1573 l cp gs col-1 s gr % Polyline n 5640 1716 m 5654 1716 l 5654 1677 l 5640 1677 l cp gs col-1 s gr % Polyline n 5640 1697 m 5654 1697 l gs col-1 s gr % Polyline n 5585 1645 m 5718 1645 l gs col-1 s gr % Polyline n 5651 1645 m 5651 1573 l gs col-1 s gr % Polyline n 5685 1645 m 5685 1609 l gs col-1 s gr % Polyline n 5651 1609 m 5718 1609 l gs col-1 s gr % Polyline n 5815 1976 m 5815 1573 l gs col-1 s gr % Polyline n 5908 1676 m 6045 1676 l 6045 1573 l 5908 1573 l cp gs col-1 s gr % Polyline n 5976 1676 m 5976 1573 l gs col-1 s gr % Polyline n 5585 1573 m 6045 1573 l gs col-1 s gr % Polyline n 5651 1519 m 5676 1519 l 5676 1498 l 5651 1498 l cp gs col-1 s gr % Polyline n 5663 1519 m 5663 1498 l gs col-1 s gr % Polyline n 5585 1473 m 5700 1473 l gs col-1 s gr % Polyline n 5585 1446 m 5642 1446 l 5642 1411 l 5585 1411 l cp gs col-1 s gr % Polyline n 5613 1446 m 5613 1411 l gs col-1 s gr % Polyline n 5642 1473 m 5642 1372 l gs col-1 s gr % Polyline n 5700 1573 m 5700 1372 l gs col-1 s gr % Polyline n 5585 1372 m 5815 1372 l gs col-1 s gr % Polyline n 5585 1271 m 5700 1271 l gs col-1 s gr % Polyline n 5642 1271 m 5642 1171 l gs col-1 s gr % Polyline n 5700 1372 m 5700 1171 l gs col-1 s gr % Polyline n 5700 1271 m 5815 1271 l gs col-1 s gr % Polyline n 5815 1573 m 5815 1171 l gs col-1 s gr % Polyline n 6045 2781 m 6045 1171 l gs col-1 s gr % Polyline n 6088 2599 m 6119 2599 l 6119 2580 l 6088 2580 l cp gs col-1 s gr % Polyline n 6104 2599 m 6104 2580 l gs col-1 s gr % Polyline n 6119 2599 m 6119 2599 l 6119 2589 l 6119 2589 l cp gs col-1 s gr % Polyline n 6119 2594 m 6119 2594 l gs col-1 s gr % Polyline n 6160 2781 m 6160 2580 l gs col-1 s gr % Polyline n 6160 2781 m 6201 2781 l 6201 2711 l 6160 2711 l cp gs col-1 s gr % Polyline n 6160 2746 m 6201 2746 l gs col-1 s gr % Polyline n 6160 2680 m 6275 2680 l gs col-1 s gr % Polyline n 6045 2580 m 6275 2580 l gs col-1 s gr % Polyline n 6045 2478 m 6160 2478 l gs col-1 s gr % Polyline n 6102 2478 m 6102 2378 l gs col-1 s gr % Polyline n 6102 2428 m 6160 2428 l gs col-1 s gr % Polyline n 6160 2580 m 6160 2378 l gs col-1 s gr % Polyline n 6209 2541 m 6275 2541 l 6275 2522 l 6209 2522 l cp gs col-1 s gr % Polyline n 6242 2541 m 6242 2522 l gs col-1 s gr % Polyline n 6160 2478 m 6275 2478 l gs col-1 s gr % Polyline n 6275 2781 m 6275 2378 l gs col-1 s gr % Polyline n 6045 2378 m 6504 2378 l gs col-1 s gr % Polyline n 6045 2311 m 6160 2311 l 6160 2300 l 6045 2300 l cp gs col-1 s gr % Polyline n 6102 2311 m 6102 2300 l gs col-1 s gr % Polyline n 6160 2378 m 6160 2177 l gs col-1 s gr % Polyline n 6194 2248 m 6275 2248 l 6275 2177 l 6194 2177 l cp gs col-1 s gr % Polyline n 6235 2248 m 6235 2177 l gs col-1 s gr % Polyline n 6045 2177 m 6275 2177 l gs col-1 s gr % Polyline n 6045 2087 m 6087 2087 l 6087 1976 l 6045 1976 l cp gs col-1 s gr % Polyline n 6045 2031 m 6087 2031 l gs col-1 s gr % Polyline n 6160 2177 m 6160 1976 l gs col-1 s gr % Polyline n 6275 2378 m 6275 1976 l gs col-1 s gr % Polyline n 6275 2378 m 6321 2378 l 6321 2313 l 6275 2313 l cp gs col-1 s gr % Polyline n 6275 2345 m 6321 2345 l gs col-1 s gr % Polyline n 6390 2378 m 6390 2177 l gs col-1 s gr % Polyline n 6275 2177 m 6504 2177 l gs col-1 s gr % Polyline n 6275 2076 m 6390 2076 l gs col-1 s gr % Polyline n 6332 2076 m 6332 1976 l gs col-1 s gr % Polyline n 6365 2076 m 6371 2076 l 6371 2046 l 6365 2046 l cp gs col-1 s gr % Polyline n 6365 2061 m 6371 2061 l gs col-1 s gr % Polyline n 6332 2026 m 6390 2026 l gs col-1 s gr % Polyline n 6390 2177 m 6390 1976 l gs col-1 s gr % Polyline n 6400 2099 m 6404 2099 l 6404 2076 l 6400 2076 l cp gs col-1 s gr % Polyline n 6400 2087 m 6404 2087 l gs col-1 s gr % Polyline n 6447 2177 m 6447 2076 l gs col-1 s gr % Polyline n 6390 2076 m 6504 2076 l gs col-1 s gr % Polyline n 6437 2076 m 6479 2076 l 6479 2041 l 6437 2041 l cp gs col-1 s gr % Polyline n 6458 2076 m 6458 2041 l gs col-1 s gr % Polyline n 6504 2781 m 6504 1976 l gs col-1 s gr % Polyline n 6735 2781 m 6735 2378 l gs col-1 s gr % Polyline n 6735 2580 m 6965 2580 l gs col-1 s gr % Polyline n 6735 2478 m 6849 2478 l gs col-1 s gr % Polyline n 6735 2428 m 6792 2428 l gs col-1 s gr % Polyline n 6792 2478 m 6792 2378 l gs col-1 s gr % Polyline n 6849 2580 m 6849 2378 l gs col-1 s gr % Polyline n 6849 2529 m 6907 2529 l gs col-1 s gr % Polyline n 6878 2529 m 6878 2478 l gs col-1 s gr % Polyline n 6907 2580 m 6907 2478 l gs col-1 s gr % Polyline n 6849 2478 m 6965 2478 l gs col-1 s gr % Polyline n 6907 2478 m 6907 2378 l gs col-1 s gr % Polyline n 6907 2428 m 6965 2428 l gs col-1 s gr % Polyline n 6504 2378 m 6965 2378 l gs col-1 s gr % Polyline n 6620 2378 m 6620 2177 l gs col-1 s gr % Polyline n 6653 2378 m 6679 2378 l 6679 2341 l 6653 2341 l cp gs col-1 s gr % Polyline n 6653 2360 m 6679 2360 l gs col-1 s gr % Polyline n 6620 2277 m 6735 2277 l gs col-1 s gr % Polyline n 6650 2210 m 6677 2210 l 6677 2177 l 6650 2177 l cp gs col-1 s gr % Polyline n 6650 2193 m 6677 2193 l gs col-1 s gr % Polyline n 6677 2277 m 6677 2177 l gs col-1 s gr % Polyline n 6705 2253 m 6735 2253 l 6735 2238 l 6705 2238 l cp gs col-1 s gr % Polyline n 6719 2253 m 6719 2238 l gs col-1 s gr % Polyline n 6719 2246 m 6735 2246 l gs col-1 s gr % Polyline n 6504 2177 m 6735 2177 l gs col-1 s gr % Polyline n 6504 2101 m 6735 2101 l 6735 2078 l 6504 2078 l cp gs col-1 s gr % Polyline n 6620 2101 m 6620 2078 l gs col-1 s gr % Polyline n 6735 2378 m 6735 1976 l gs col-1 s gr % Polyline n 6806 2349 m 6849 2349 l 6849 2277 l 6806 2277 l cp gs col-1 s gr % Polyline n 6806 2314 m 6849 2314 l gs col-1 s gr % Polyline n 6735 2277 m 6849 2277 l gs col-1 s gr % Polyline n 6849 2378 m 6849 2177 l gs col-1 s gr % Polyline n 6849 2277 m 6965 2277 l gs col-1 s gr % Polyline n 6735 2177 m 6965 2177 l gs col-1 s gr % Polyline n 6757 2164 m 6780 2164 l 6780 2144 l 6757 2144 l cp gs col-1 s gr % Polyline n 6769 2164 m 6769 2144 l gs col-1 s gr % Polyline n 6769 2154 m 6780 2154 l gs col-1 s gr % Polyline n 6735 2127 m 6792 2127 l gs col-1 s gr % Polyline n 6792 2177 m 6792 2076 l gs col-1 s gr % Polyline n 6735 2076 m 6849 2076 l gs col-1 s gr % Polyline n 6849 2177 m 6849 1976 l gs col-1 s gr % Polyline n 6903 2177 m 6965 2177 l 6965 2101 l 6903 2101 l cp gs col-1 s gr % Polyline n 6903 2139 m 6965 2139 l gs col-1 s gr % Polyline n 6903 2111 m 6940 2111 l 6940 2101 l 6903 2101 l cp gs col-1 s gr % Polyline n 6921 2111 m 6921 2101 l gs col-1 s gr % Polyline n 6045 1976 m 6965 1976 l gs col-1 s gr % Polyline n 6128 1976 m 6275 1976 l 6275 1861 l 6128 1861 l cp gs col-1 s gr % Polyline n 6128 1939 m 6129 1939 l 6129 1861 l 6128 1861 l cp gs col-1 s gr % Polyline n 6128 1900 m 6129 1900 l gs col-1 s gr % Polyline n 6201 1976 m 6201 1861 l gs col-1 s gr % Polyline n 6201 1919 m 6275 1919 l gs col-1 s gr % Polyline n 6248 1870 m 6275 1870 l 6275 1861 l 6248 1861 l cp gs col-1 s gr % Polyline n 6262 1870 m 6262 1861 l gs col-1 s gr % Polyline n 6045 1774 m 6275 1774 l gs col-1 s gr % Polyline n 6123 1774 m 6275 1774 l 6275 1728 l 6123 1728 l cp gs col-1 s gr % Polyline n 6123 1743 m 6169 1743 l 6169 1728 l 6123 1728 l cp gs col-1 s gr % Polyline n 6146 1743 m 6146 1728 l gs col-1 s gr % Polyline n 6199 1774 m 6199 1728 l gs col-1 s gr % Polyline n 6275 1976 m 6275 1573 l gs col-1 s gr % Polyline n 6275 1875 m 6390 1875 l gs col-1 s gr % Polyline n 6275 1820 m 6328 1820 l 6328 1774 l 6275 1774 l cp gs col-1 s gr % Polyline n 6301 1820 m 6301 1774 l gs col-1 s gr % Polyline n 6390 1976 m 6390 1774 l gs col-1 s gr % Polyline n 6447 1976 m 6447 1875 l gs col-1 s gr % Polyline n 6390 1875 m 6504 1875 l gs col-1 s gr % Polyline n 6437 1833 m 6438 1833 l 6438 1806 l 6437 1806 l cp gs col-1 s gr % Polyline n 6437 1819 m 6438 1819 l gs col-1 s gr % Polyline n 6275 1774 m 6504 1774 l gs col-1 s gr % Polyline n 6275 1712 m 6363 1712 l 6363 1573 l 6275 1573 l cp gs col-1 s gr % Polyline n 6275 1642 m 6363 1642 l gs col-1 s gr % Polyline n 6045 1573 m 6504 1573 l gs col-1 s gr % Polyline n 6504 1976 m 6504 1171 l gs col-1 s gr % Polyline n 6504 1976 m 6559 1976 l 6559 1953 l 6504 1953 l cp gs col-1 s gr % Polyline n 6532 1976 m 6532 1953 l gs col-1 s gr % Polyline n 6545 1976 m 6545 1953 l gs col-1 s gr % Polyline n 6504 1875 m 6620 1875 l gs col-1 s gr % Polyline n 6562 1875 m 6562 1774 l gs col-1 s gr % Polyline n 6562 1875 m 6590 1875 l 6590 1815 l 6562 1815 l cp gs col-1 s gr % Polyline n 6578 1875 m 6590 1875 l 6590 1869 l 6578 1869 l cp gs col-1 s gr % Polyline n 6584 1875 m 6584 1869 l gs col-1 s gr % Polyline n 6562 1845 m 6590 1845 l gs col-1 s gr % Polyline n 6620 1976 m 6620 1774 l gs col-1 s gr % Polyline n 6620 1926 m 6677 1926 l gs col-1 s gr % Polyline n 6677 1976 m 6677 1875 l gs col-1 s gr % Polyline n 6620 1875 m 6735 1875 l gs col-1 s gr % Polyline n 6504 1774 m 6735 1774 l gs col-1 s gr % Polyline n 6504 1717 m 6620 1717 l 6620 1650 l 6504 1650 l cp gs col-1 s gr % Polyline n 6562 1717 m 6562 1650 l gs col-1 s gr % Polyline n 6620 1774 m 6620 1573 l gs col-1 s gr % Polyline n 6735 1976 m 6735 1573 l gs col-1 s gr % Polyline n 6849 1976 m 6849 1774 l gs col-1 s gr % Polyline n 6891 1976 m 6965 1976 l 6965 1929 l 6891 1929 l cp gs col-1 s gr % Polyline n 6891 1930 m 6914 1930 l 6914 1929 l 6891 1929 l cp gs col-1 s gr % Polyline n 6903 1930 m 6903 1929 l gs col-1 s gr % Polyline n 6928 1976 m 6928 1929 l gs col-1 s gr % Polyline n 6735 1774 m 6965 1774 l gs col-1 s gr % Polyline n 6504 1573 m 6965 1573 l gs col-1 s gr % Polyline n 6965 4390 m 6965 1171 l gs col-1 s gr % Polyline n 6965 4390 m 7359 4390 l 7359 3535 l 6965 3535 l cp gs col-1 s gr % Polyline n 6965 4176 m 7359 4176 l gs col-1 s gr % Polyline n 7063 4176 m 7063 4070 l gs col-1 s gr % Polyline n 6965 4070 m 7162 4070 l gs col-1 s gr % Polyline n 6965 4018 m 7012 4018 l 7012 3962 l 6965 3962 l cp gs col-1 s gr % Polyline n 7011 4018 m 7012 4018 l 7012 4015 l 7011 4015 l cp gs col-1 s gr % Polyline n 7011 4017 m 7012 4017 l gs col-1 s gr % Polyline n 6965 3991 m 7012 3991 l gs col-1 s gr % Polyline n 6988 3991 m 6988 3962 l gs col-1 s gr % Polyline n 6998 3991 m 7007 3991 l 7007 3988 l 6998 3988 l cp gs col-1 s gr % Polyline n 7003 3991 m 7003 3988 l gs col-1 s gr % Polyline n 7063 4070 m 7063 3962 l gs col-1 s gr % Polyline n 7100 4070 m 7162 4070 l 7162 4066 l 7100 4066 l cp gs col-1 s gr % Polyline n 7131 4070 m 7131 4066 l gs col-1 s gr % Polyline n 7063 4016 m 7162 4016 l gs col-1 s gr % Polyline n 7076 3969 m 7084 3969 l 7084 3967 l 7076 3967 l cp gs col-1 s gr % Polyline n 7080 3969 m 7080 3967 l gs col-1 s gr % Polyline n 7162 4176 m 7162 3962 l gs col-1 s gr % Polyline n 7162 4070 m 7359 4070 l gs col-1 s gr % Polyline n 6965 3962 m 7359 3962 l gs col-1 s gr % Polyline n 6987 3962 m 7003 3962 l 7003 3948 l 6987 3948 l cp gs col-1 s gr % Polyline n 6995 3962 m 6995 3948 l gs col-1 s gr % Polyline n 6965 3935 m 7014 3935 l gs col-1 s gr % Polyline n 7014 3962 m 7014 3909 l gs col-1 s gr % Polyline n 7031 3962 m 7063 3962 l 7063 3938 l 7031 3938 l cp gs col-1 s gr % Polyline n 7031 3950 m 7047 3950 l gs col-1 s gr % Polyline n 7047 3962 m 7047 3938 l gs col-1 s gr % Polyline n 6965 3909 m 7063 3909 l gs col-1 s gr % Polyline n 6965 3888 m 6977 3888 l 6977 3879 l 6965 3879 l cp gs col-1 s gr % Polyline n 6971 3888 m 6971 3879 l gs col-1 s gr % Polyline n 7014 3909 m 7014 3856 l gs col-1 s gr % Polyline n 7063 3962 m 7063 3856 l gs col-1 s gr % Polyline n 7063 3909 m 7162 3909 l gs col-1 s gr % Polyline n 7119 3878 m 7162 3878 l 7162 3856 l 7119 3856 l cp gs col-1 s gr % Polyline n 7140 3878 m 7140 3856 l gs col-1 s gr % Polyline n 6965 3856 m 7162 3856 l gs col-1 s gr % Polyline n 6965 3830 m 6997 3830 l 6997 3821 l 6965 3821 l cp gs col-1 s gr % Polyline n 6981 3830 m 6981 3821 l gs col-1 s gr % Polyline n 7014 3856 m 7014 3802 l gs col-1 s gr % Polyline n 6965 3802 m 7063 3802 l gs col-1 s gr % Polyline n 6989 3764 m 7008 3764 l 7008 3763 l 6989 3763 l cp gs col-1 s gr % Polyline n 6998 3764 m 6998 3763 l gs col-1 s gr % Polyline n 7063 3856 m 7063 3748 l gs col-1 s gr % Polyline n 7080 3856 m 7094 3856 l 7094 3802 l 7080 3802 l cp gs col-1 s gr % Polyline n 7080 3829 m 7094 3829 l gs col-1 s gr % Polyline n 7080 3815 m 7094 3815 l 7094 3812 l 7080 3812 l cp gs col-1 s gr % Polyline n 7087 3815 m 7087 3812 l gs col-1 s gr % Polyline n 7063 3802 m 7162 3802 l gs col-1 s gr % Polyline n 7063 3783 m 7071 3783 l 7071 3760 l 7063 3760 l cp gs col-1 s gr % Polyline n 7063 3771 m 7071 3771 l gs col-1 s gr % Polyline n 7162 3962 m 7162 3748 l gs col-1 s gr % Polyline n 7179 3939 m 7182 3939 l 7182 3904 l 7179 3904 l cp gs col-1 s gr % Polyline n 7179 3921 m 7182 3921 l gs col-1 s gr % Polyline n 7162 3856 m 7359 3856 l gs col-1 s gr % Polyline n 6965 3748 m 7359 3748 l gs col-1 s gr % Polyline n 6965 3695 m 7063 3695 l gs col-1 s gr % Polyline n 6990 3695 m 7003 3695 l 7003 3641 l 6990 3641 l cp gs col-1 s gr % Polyline n 6990 3684 m 7003 3684 l 7003 3677 l 6990 3677 l cp gs col-1 s gr % Polyline n 6997 3684 m 6997 3677 l gs col-1 s gr % Polyline n 6990 3668 m 7003 3668 l gs col-1 s gr % Polyline n 7063 3748 m 7063 3641 l gs col-1 s gr % Polyline n 6965 3641 m 7162 3641 l gs col-1 s gr % Polyline n 7063 3641 m 7063 3535 l gs col-1 s gr % Polyline n 7078 3627 m 7095 3627 l 7095 3611 l 7078 3611 l cp gs col-1 s gr % Polyline n 7086 3627 m 7086 3611 l gs col-1 s gr % Polyline n 7063 3588 m 7162 3588 l gs col-1 s gr % Polyline n 7162 3748 m 7162 3535 l gs col-1 s gr % Polyline n 7162 3695 m 7260 3695 l gs col-1 s gr % Polyline n 7260 3748 m 7260 3641 l gs col-1 s gr % Polyline n 7162 3641 m 7359 3641 l gs col-1 s gr % Polyline n 6965 2781 m 8804 2781 l gs col-1 s gr % Polyline n 6965 2580 m 7194 2580 l gs col-1 s gr % Polyline n 6965 2492 m 7067 2492 l 7067 2378 l 6965 2378 l cp gs col-1 s gr % Polyline n 6965 2435 m 7067 2435 l gs col-1 s gr % Polyline n 7016 2435 m 7016 2378 l gs col-1 s gr % Polyline n 7194 2781 m 7194 2378 l gs 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2641 1445 2654 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1688 2622 12 12 1688 2622 1701 2634 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1769 2700 12 12 1769 2700 1781 2712 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1709 2461 12 12 1709 2461 1721 2473 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1875 2754 12 12 1875 2754 1888 2766 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1909 2724 12 12 1909 2724 1921 2736 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1956 2722 12 12 1956 2722 1969 2735 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1871 2687 12 12 1871 2687 1883 2700 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2059 2630 12 12 2059 2630 2071 2643 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2015 2584 12 12 2015 2584 2027 2596 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2061 2610 12 12 2061 2610 2073 2622 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1957 2548 12 12 1957 2548 1969 2560 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2022 2559 12 12 2022 2559 2034 2571 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1992 2461 12 12 1992 2461 2004 2473 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1986 2455 12 12 1986 2455 1998 2467 1 3 0 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12 1424 1514 1436 1526 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1405 1506 12 12 1405 1506 1417 1519 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1435 1475 12 12 1435 1475 1447 1487 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1486 1539 12 12 1486 1539 1498 1551 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1492 1526 12 12 1492 1526 1504 1538 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1430 1433 12 12 1430 1433 1443 1445 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1463 1470 12 12 1463 1470 1475 1482 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1526 1477 12 12 1526 1477 1538 1489 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1625 1536 12 12 1625 1536 1637 1549 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1539 1411 12 12 1539 1411 1552 1423 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1593 1439 12 12 1593 1439 1605 1452 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1504 1223 12 12 1504 1223 1516 1235 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1600 1229 12 12 1600 1229 1612 1241 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1520 1171 12 12 1520 1171 1533 1183 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1685 1716 12 12 1685 1716 1698 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0 0 0.000 1 0.0000 1741 1212 12 12 1741 1212 1753 1224 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1814 1357 12 12 1814 1357 1826 1369 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1771 1216 12 12 1771 1216 1783 1229 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 1901 1523 12 12 1901 1523 1913 1536 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2165 2599 12 12 2165 2599 2177 2611 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2134 2598 12 12 2134 2598 2146 2610 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2165 2589 12 12 2165 2589 2177 2601 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2223 2774 12 12 2223 2774 2235 2787 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2247 2711 12 12 2247 2711 2259 2724 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2149 2554 12 12 2149 2554 2162 2566 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2113 2438 12 12 2113 2438 2126 2450 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2204 2453 12 12 2204 2453 2216 2466 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2157 2384 12 12 2157 2384 2169 2396 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2255 2541 12 12 2255 2541 2267 2553 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2305 2522 12 12 2305 2522 2317 2534 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2304 2425 12 12 2304 2425 2316 2437 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2319 2605 12 12 2319 2605 2332 2618 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2186 2311 12 12 2186 2311 2198 2323 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2119 2300 12 12 2119 2300 2131 2312 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2306 2248 12 12 2306 2248 2318 2260 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2240 2185 12 12 2240 2185 2252 2197 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2133 2087 12 12 2133 2087 2145 2099 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2091 1981 12 12 2091 1981 2103 1993 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2308 2049 12 12 2308 2049 2320 2061 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2367 2365 12 12 2367 2365 2379 2377 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2345 2313 12 12 2345 2313 2357 2325 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2498 2293 12 12 2498 2293 2511 2305 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2325 2105 12 12 2325 2105 2337 2117 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2388 1985 12 12 2388 1985 2400 1997 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2417 2074 12 12 2417 2074 2429 2087 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2410 2046 12 12 2410 2046 2422 2058 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2446 2099 12 12 2446 2099 2458 2111 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2450 2081 12 12 2450 2081 2462 2093 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2517 2132 12 12 2517 2132 2529 2144 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2483 2057 12 12 2483 2057 2495 2070 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2525 2041 12 12 2525 2041 2537 2053 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2624 2433 12 12 2624 2433 2636 2445 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2803 2678 12 12 2803 2678 2815 2691 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2877 2486 12 12 2877 2486 2889 2498 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2822 2475 12 12 2822 2475 2834 2488 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2801 2414 12 12 2801 2414 2813 2426 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2876 2454 12 12 2876 2454 2888 2466 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2947 2493 12 12 2947 2493 2959 2505 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2907 2485 12 12 2907 2485 2919 2497 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2978 2544 12 12 2978 2544 2991 2556 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2981 2449 12 12 2981 2449 2993 2461 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2991 2388 12 12 2991 2388 3003 2401 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2579 2233 12 12 2579 2233 2591 2245 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2698 2341 12 12 2698 2341 2710 2353 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2725 2367 12 12 2725 2367 2737 2380 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2696 2210 12 12 2696 2210 2708 2222 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2709 2181 12 12 2709 2181 2722 2193 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2750 2250 12 12 2750 2250 2763 2263 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2777 2253 12 12 2777 2253 2789 2266 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2770 2238 12 12 2770 2238 2782 2250 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2566 2078 12 12 2566 2078 2578 2090 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2716 2101 12 12 2716 2101 2728 2113 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2851 2294 12 12 2851 2294 2864 2306 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2889 2349 12 12 2889 2349 2902 2361 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2889 2205 12 12 2889 2205 2901 2217 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2917 2325 12 12 2917 2325 2929 2337 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2916 2215 12 12 2916 2215 2929 2228 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2802 2164 12 12 2802 2164 2815 2176 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2816 2144 12 12 2816 2144 2828 2157 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2791 2081 12 12 2791 2081 2804 2093 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2825 2159 12 12 2825 2159 2837 2171 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2886 2010 12 12 2886 2010 2899 2022 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2948 2111 12 12 2948 2111 2961 2123 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2974 2157 12 12 2974 2157 2986 2169 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2985 2101 12 12 2985 2101 2997 2114 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2175 1939 12 12 2175 1939 2187 1951 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 2174 1883 12 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2279 4174 2291 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4205 2299 12 12 4205 2299 4217 2311 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4221 2332 12 12 4221 2332 4233 2344 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4236 2289 12 12 4236 2289 4248 2301 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4253 2282 12 12 4253 2282 4265 2295 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4167 2224 12 12 4167 2224 4179 2236 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4214 2271 12 12 4214 2271 4227 2284 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4319 2340 12 12 4319 2340 4331 2352 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4320 2313 12 12 4320 2313 4332 2325 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4306 2272 12 12 4306 2272 4319 2284 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4287 2182 12 12 4287 2182 4300 2195 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4372 2261 12 12 4372 2261 4384 2274 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4346 2243 12 12 4346 2243 4358 2255 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4176 2154 12 12 4176 2154 4188 2166 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 4194 2122 12 12 4194 2122 4206 2134 1 3 0 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8040 2353 12 12 8040 2353 8052 2365 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8020 2325 12 12 8020 2325 8033 2337 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8082 2302 12 12 8082 2302 8095 2314 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8085 2290 12 12 8085 2290 8097 2302 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8025 2246 12 12 8025 2246 8038 2258 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8036 2182 12 12 8036 2182 8048 2195 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8112 2276 12 12 8112 2276 8125 2288 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8094 2197 12 12 8094 2197 8106 2209 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 7933 2149 12 12 7933 2149 7945 2161 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 7892 2069 12 12 7892 2069 7904 2081 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8107 2088 12 12 8107 2088 8119 2100 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8061 2052 12 12 8061 2052 8073 2064 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8109 1978 12 12 8109 1978 8122 1990 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8152 2342 12 12 8152 2342 8165 2354 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8116 2279 12 12 8116 2279 8128 2291 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8159 2299 12 12 8159 2299 8171 2311 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8176 2332 12 12 8176 2332 8188 2344 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8190 2289 12 12 8190 2289 8203 2301 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8207 2282 12 12 8207 2282 8220 2295 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8122 2224 12 12 8122 2224 8134 2236 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8169 2271 12 12 8169 2271 8181 2284 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8273 2340 12 12 8273 2340 8285 2352 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8274 2313 12 12 8274 2313 8287 2325 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8261 2272 12 12 8261 2272 8273 2284 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8242 2182 12 12 8242 2182 8254 2195 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8301 2243 12 12 8301 2243 8313 2255 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8326 2261 12 12 8326 2261 8339 2274 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8130 2154 12 12 8130 2154 8142 2166 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8148 2122 12 12 8148 2122 8160 2134 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8184 2089 12 12 8184 2089 8196 2101 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8206 2084 12 12 8206 2084 8219 2096 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8142 2019 12 12 8142 2019 8155 2032 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8257 2099 12 12 8257 2099 8269 2111 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8261 2093 12 12 8261 2093 8273 2105 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8272 2079 12 12 8272 2079 8285 2092 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8329 2120 12 12 8329 2120 8342 2133 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8358 2251 12 12 8358 2251 8371 2263 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8393 2214 12 12 8393 2214 8405 2226 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8425 2238 12 12 8425 2238 8437 2250 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8417 2172 12 12 8417 2172 8429 2184 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8350 2092 12 12 8350 2092 8362 2104 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8357 2101 12 12 8357 2101 8369 2113 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8375 2096 12 12 8375 2096 8387 2108 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8006 1972 12 12 8006 1972 8018 1984 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8057 1869 12 12 8057 1869 8069 1881 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8119 1943 12 12 8119 1943 8131 1955 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8146 1884 12 12 8146 1884 8158 1897 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8200 1863 12 12 8200 1863 8212 1875 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8254 1935 12 12 8254 1935 8266 1948 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8263 1910 12 12 8263 1910 8275 1922 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8272 1905 12 12 8272 1905 8284 1917 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8301 1944 12 12 8301 1944 8313 1956 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8220 1687 12 12 8220 1687 8233 1699 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8140 1561 12 12 8140 1561 8152 1574 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8369 1966 12 12 8369 1966 8381 1978 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8390 1875 12 12 8390 1875 8402 1887 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8423 1867 12 12 8423 1867 8436 1879 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8505 1908 12 12 8505 1908 8518 1920 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8573 1790 12 12 8573 1790 8586 1802 1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 8804 1948 12 12 8804 1948 8816 1960 2 2 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 5 1171 4390 4850 4390 4850 1171 1171 1171 1171 4390 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1717 4390 1717 3585 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1717 4116 2091 4116 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1852 4116 1852 3988 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1717 3988 2091 3988 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1904 3988 1904 3786 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1961 3988 1961 3888 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1904 3888 2091 3888 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1904 3826 1997 3826 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1997 3888 1997 3786 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1717 3786 2091 3786 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1717 3736 1810 3736 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1810 3786 1810 3686 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1810 3736 1904 3736 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1857 3736 1857 3686 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1717 3686 1904 3686 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1810 3686 1810 3585 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1904 3786 1904 3585 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1935 3786 1935 3736 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1904 3736 1996 3736 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1959 3736 1959 3686 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1996 3786 1996 3686 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1904 3686 2091 3686 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1171 3585 2091 3585 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1852 3585 1852 2781 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1971 3585 1971 3490 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 2031 3585 2031 3490 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1852 3490 2091 3490 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1852 3183 2091 3183 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2 1852 2893 2091 2893 2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 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ffffffffffffdbffffffbfeffefffffffffffffffffffffffffffffffffffffffffe fffeffffdffffff7fffeffff7fffffffeffffffffffffffffffffffffffffffffffe fffffffffeffffffffffffffffffffbefffffffffffffffffffffffffffffffffffe ffffffffff7fdffdfffffffff7fffffdfffffffffffffffffffffffffffffffffffe ffffbfffffffff7ffffffffffffffffffffffffffffffffffffffffffffffffffffe fffdffffffffffffffffffffffffff4ffffffffffffffffffffffffffffffffffffe fffffffbfffffffffdeffff7efbffffffffffffffffffffffffffffffffffffffffe fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe showpage % stop using temporary dictionary end % restore original state origstate restore %%Trailer ann-1.1.2+doc/doc/ReadMe.txt0000644000175000017500000000463410464722022016363 0ustar sylvestresylvestreANN: Approximate Nearest Neighbors Version: 1.1.1 Release date: Aug 4, 2006 ---------------------------------------------------------------------------- Copyright (c) 1997-2005 University of Maryland and Sunil Arya and David Mount. All Rights Reserved. See Copyright.txt and License.txt for complete information on terms and conditions of use and distribution of this software. ---------------------------------------------------------------------------- Authors ------- David Mount Dept of Computer Science University of Maryland, College Park, MD 20742 USA mount@cs.umd.edu http://www.cs.umd.edu/~mount/ Sunil Arya Dept of Computer Science Hong University of Science and Technology Clearwater Bay, HONG KONG arya@cs.ust.hk http://www.cs.ust.hk/faculty/arya/ Introduction ------------ ANN is a library written in the C++ programming language to support both exact and approximate nearest neighbor searching in spaces of various dimensions. It was implemented by David M. Mount of the University of Maryland, and Sunil Arya of the Hong Kong University of Science and Technology. ANN (pronounced like the name ``Ann'') stands for Approximate Nearest Neighbors. ANN is also a testbed containing programs and procedures for generating data sets, collecting and analyzing statistics on the performance of nearest neighbor algorithms and data structures, and visualizing the geometric structure of these data structures. The ANN source code and documentation is available from the following web page: http://www.cs.umd.edu/~mount/ANN For more information on ANN and its use, see the ``ANN Programming Manual,'' which is provided with the software distribution. ---------------------------------------------------------------------------- History Version 0.1 03/04/98 Preliminary release Version 0.2 06/24/98 Changes for SGI compiler. Version 1.0 04/01/05 Fixed a number of small bugs Added dump/load operations Added annClose to eliminate minor memory leak Improved compatibility with current C++ compilers Added compilation for Microsoft Visual Studio.NET Added compilation for Linux 2.x Version 1.1 05/03/05 Added make target for Mac OS X Added fixed-radius range searching and counting Added instructions on compiling/using ANN on Windows platforms Fixed minor output bug in ann2fig Version 1.1.1 08/04/06 Added "planted" distribution Updated old source comments for GNU LPL. ann-1.1.2+doc/doc/ANNmanual.pdf0000644000175000017500000127273610464722024017007 0ustar sylvestresylvestre%PDF-1.3 %Çì¢ 6 0 obj <> stream xœµUMoÓ@=pó¯Ø#HtÙ™ýæ8´¢%p·'b;ulPÅŸgv½“–ïò!ÊÌxæíÛ7Ï7BI*=åwÝU7Õ“k#vÇêF@NñϺ/V”¤¿à%‚µbµ­–÷@ Š2h+œ³R+/V]õðùåå£Õ§Ê(#F*[mª‡oÇa7Ö]×ö»”ŒQj«MI^Ô} j%ƒñ¾çzŸ‚4Y ­…4ù H¥AœQ¹̵/ëT F‹®¼ÿ¥Ýä D¯y’Ì1/ƒ‹\x1Ìyå&ã7nÇv÷1G-éý´/SÆA(]ôL1*år%ÙAT|åÿi_­ÄUò$GMôb:†v+ DKûï„Ž6Hg“‡=¹F%^ÕÙS[yL¦Œ€à‘VV™ÄØTÛ?Zj‘oÃ}‹ 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the terms and conditions of the GNU Lesser General Public Library, which is stated below. 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IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE LIBRARY AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE LIBRARY (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE LIBRARY TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. ann-1.1.2+doc/bin/0000755000175000017500000000000011330212441014451 5ustar sylvestresylvestreann-1.1.2+doc/ann2fig/0000755000175000017500000000000011330212441015225 5ustar sylvestresylvestreann-1.1.2+doc/ann2fig/Makefile0000644000175000017500000000554711330212441016700 0ustar sylvestresylvestre#----------------------------------------------------------------------------- # Makefile for ann2fig # # ANN: Approximate Nearest Neighbors # Version: 1.1.1 08/04/06 #----------------------------------------------------------------------------- # Copyright (c) 1997-2005 University of Maryland and Sunil Arya and # David Mount. All Rights Reserved. # # This software and related documentation is part of the Approximate # Nearest Neighbor Library (ANN). This software is provided under # the provisions of the Lesser GNU Public License (LGPL). See the # file ../ReadMe.txt for further information. # # The University of Maryland (U.M.) and the authors make no # representations about the suitability or fitness of this software for # any purpose. It is provided "as is" without express or implied # warranty. #----------------------------------------------------------------------------- # Revision 0.1 03/04/98 # Initial release # Revision 1.1.1 08/04/06 # Added copyright/license #----------------------------------------------------------------------------- #----------------------------------------------------------------------------- # Basic definitions # BASEDIR where include, src, lib, ... are # INCDIR include directory # LIBDIR library directory # BINDIR bin directory # LDFLAGS loader flags # ANNLIB ANN library # OTHERLIB other libraries #----------------------------------------------------------------------------- BASEDIR = .. INCDIR = $(BASEDIR)/include LIBDIR = $(BASEDIR)/lib BINDIR = $(BASEDIR)/bin LDFLAGS = -L$(LIBDIR) ANNLIBS = -lANN OTHERLIBS = -lm #----------------------------------------------------------------------------- # Some more definitions # ANN2FIG name of executable #----------------------------------------------------------------------------- ANN2FIG = ann2fig SOURCES = ann2fig.cpp OBJECTS = $(SOURCES:.cpp=.o) #----------------------------------------------------------------------------- # Make the program #----------------------------------------------------------------------------- default: @echo "Specify a target configuration" targets: $(BINDIR)/$(ANN2FIG) $(BINDIR)/$(ANN2FIG): $(OBJECTS) $(C++) $(OBJECTS) -o $(ANN2FIG) $(LDFLAGS) $(ANNLIBS) $(OTHERLIBS) mv $(ANN2FIG) $(BINDIR) #----------------------------------------------------------------------------- # configuration definitions #----------------------------------------------------------------------------- include ../Make-config #----------------------------------------------------------------------------- # Objects #----------------------------------------------------------------------------- ann2fig.o: ann2fig.cpp $(C++) -c -I$(INCDIR) ann2fig.cpp #----------------------------------------------------------------------------- # Cleaning #----------------------------------------------------------------------------- clean: -rm -f *.o core realclean: clean ann-1.1.2+doc/ann2fig/ann2fig.cpp0000644000175000017500000005200311330212441017255 0ustar sylvestresylvestre//---------------------------------------------------------------------- // File: ann2fig.cpp // Programmer: David Mount // Last modified: 05/03/05 // Description: convert ann dump file to fig file //---------------------------------------------------------------------- // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and // David Mount. All Rights Reserved. // // This software and related documentation is part of the Approximate // Nearest Neighbor Library (ANN). This software is provided under // the provisions of the Lesser GNU Public License (LGPL). See the // file ../ReadMe.txt for further information. // // The University of Maryland (U.M.) and the authors make no // representations about the suitability or fitness of this software for // any purpose. It is provided "as is" without express or implied // warranty. //---------------------------------------------------------------------- // History: // Revision 0.1 03/04/98 // Initial release // Revision 1.0 04/01/05 // Changed dump file suffix from .ann to .dmp. // Revision 1.1 05/03/05 // Fixed usage output string. //---------------------------------------------------------------------- // This program inputs an ann dump file of a search structure // perhaps along with point coordinates, and outputs a fig (Ver 3.1) // file (see fig2dev (1)) displaying the tree. The fig file may // then be displayed using xfig, or converted to any of a number of // other formats using fig2dev. // // If the dimension is 2 then the entire tree is display. If the // dimension is larger than 2 then the user has the option of // selecting which two dimensions will be displayed, and the slice // value for each of the remaining dimensions. All leaf cells // intersecting the slice are shown along with the points in these // cells. See the procedure getArgs() below for the command-line // arguments. //---------------------------------------------------------------------- #include // C standard I/O #include // standard lib defs #include // C strings #include // file I/O #include // string manipulation #include // all ANN includes using namespace std; // make std:: accessible //---------------------------------------------------------------------- // Globals and their defaults //---------------------------------------------------------------------- const int STRING_LEN = 500; // string lengths const int MAX_DIM = 1000; // maximum dimension const double DEF_SLICE_VAL = 0; // default slice value const char FIG_HEAD[] = {"#FIG 3.1"}; // fig file header const char DUMP_SUFFIX[] = {".dmp"}; // suffix for dump file const char FIG_SUFFIX[] = {".fig"}; // suffix for fig file char file_name[STRING_LEN]; // (root) file name (say xxx) char infile_name[STRING_LEN];// input file name (xxx.dmp) char outfile_name[STRING_LEN];// output file name (xxx.fig) char caption[STRING_LEN]; // caption line (= command line) ofstream ofile; // output file stream ifstream ifile; // input file stream int dim_x = 0; // horizontal dimension int dim_y = 1; // vertical dimension double slice_val[MAX_DIM]; // array of slice values double u_per_in = 1200; // fig units per inch (version 3.1) double in_size = 5; // size of figure (in inches) double in_low_x = 1; // fig upper left corner (in inches) double in_low_y = 1; // fig upper left corner (in inches) double u_size = 6000; // size of figure (in units) double u_low_x = 1200; // fig upper left corner (in units) double u_low_y = 1200; // fig upper left corner (in units) int pt_size = 10; // point size (in fig units) int dim; // dimension int n_pts; // number of points ANNpointArray pts = NULL; // point array double scale; // scale factor for transformation double offset_x; // offsets for transformation double offset_y; // transformations #define TRANS_X(p) (offset_x + scale*(p[dim_x])) #define TRANS_Y(p) (offset_y - scale*(p[dim_y])) //---------------------------------------------------------------------- // Error handler //---------------------------------------------------------------------- void Error(const char* msg, ANNerr level) { if (level == ANNabort) { cerr << "ann2fig: ERROR------->" << msg << "<-------------ERROR\n"; exit(1); } else { cerr << "ann2fig: WARNING----->" << msg << "<-------------WARNING\n"; } } //---------------------------------------------------------------------- // set_slice_val - set all slice values to given value //---------------------------------------------------------------------- void set_slice_val(double val) { for (int i = 0; i < MAX_DIM; i++) { slice_val[i] = val; } } //---------------------------------------------------------------------- // getArgs - get input arguments // // Syntax: // ann2fig [-upi scale] [-x low_x] [-y low_y] // [-sz size] [-dx dim_x] [-dy dim_y] [-sl dim value]* // [-ps pointsize] // file // // where: // -upi scale fig units per inch (default = 1200) // -x low_x x and y offset of upper left corner (inches) // -y low_y ...(default = 1) // -sz size maximum side length of figure (in inches) // ...(default = 5) // -dx dim_x horizontal dimension (default = 0) // -dy dim_y vertical dimension (default = 1) // -sv value default slice value (default = 0) // -sl dim value each such pair defines the value along the // ...given dimension at which to slice. This // ...may be supplied for all dimensions except // ...dim_x and dim_y. // -ps pointsize size of points in fig units (def = 10) // file file (input=file.dmp, output=file.fig) // //---------------------------------------------------------------------- void getArgs(int argc, char **argv) { int i; int sl_dim; // temp slice dimension double sl_val; // temp slice value set_slice_val(DEF_SLICE_VAL); // set initial slice-values if (argc <= 1) { cerr << "Syntax:\n\ ann2fig [-upi scale] [-x low_x] [-y low_y]\n\ [-sz size] [-dx dim_x] [-dy dim_y] [-sl dim value]*\n\ file\n\ \n\ where:\n\ -upi scale fig units per inch (default = 1200)\n\ -x low_x x and y offset of upper left corner (inches)\n\ -y low_y ...(default = 1)\n\ -sz size maximum side length of figure (in inches)\n\ ...(default = 5)\n\ -dx dim_x horizontal dimension (default = 0)\n\ -dy dim_y vertical dimension (default = 1)\n\ -sv value default slice value (default = 0)\n\ -sl dim value each such pair defines the value along the\n\ ...given dimension at which to slice. This\n\ ...may be supplied for each dimension except\n\ ...dim_x and dim_y.\n\ -ps pointsize size of points in fig units (def = 10)\n\ file file (input=file.dmp, output=file.fig)\n"; exit(0); } ANNbool fileSeen = ANNfalse; // file argument seen? for (i = 1; i < argc; i++) { if (!strcmp(argv[i], "-upi")) { // process -upi option sscanf(argv[++i], "%lf", &u_per_in); } else if (!strcmp(argv[i], "-x")) { // process -x option sscanf(argv[++i], "%lf", &in_low_x); } else if (!strcmp(argv[i], "-y")) { // process -y option sscanf(argv[++i], "%lf", &in_low_y); } else if (!strcmp(argv[i], "-sz")) { // process -sz option sscanf(argv[++i], "%lf", &in_size); } else if (!strcmp(argv[i], "-dx")) { // process -dx option sscanf(argv[++i], "%d", &dim_x); } else if (!strcmp(argv[i], "-dy")) { // process -dy option sscanf(argv[++i], "%d", &dim_y); } else if (!strcmp(argv[i], "-sv")) { // process -sv option sscanf(argv[++i], "%lf", &sl_val); set_slice_val(sl_val); // set slice values } else if (!strcmp(argv[i], "-sl")) { // process -sl option sscanf(argv[++i], "%d", &sl_dim); if (sl_dim < 0 || sl_dim >= MAX_DIM) { Error("Slice dimension out of bounds", ANNabort); } sscanf(argv[++i], "%lf", &slice_val[sl_dim]); } if (!strcmp(argv[i], "-ps")) { // process -ps option sscanf(argv[++i], "%i", &pt_size); } else { // must be file name fileSeen = ANNtrue; sscanf(argv[i], "%s", file_name); strcpy(infile_name, file_name); // copy to input file name strcat(infile_name, DUMP_SUFFIX); strcpy(outfile_name, file_name); // copy to output file name strcat(outfile_name, FIG_SUFFIX); } } if (!fileSeen) { // no file seen Error("File argument is required", ANNabort); } ifile.open(infile_name, ios::in); // open for reading if (!ifile) { Error("Cannot open input file", ANNabort); } ofile.open(outfile_name, ios::out); // open for writing if (!ofile) { Error("Cannot open output file", ANNabort); } u_low_x = u_per_in * in_low_x; // convert inches to fig units u_low_y = u_per_in * in_low_y; u_size = u_per_in * in_size; strcpy(caption, argv[0]); // copy command line to caption for (i = 1; i < argc; i++) { strcat(caption, " "); strcat(caption, argv[i]); } } //---------------------------------------------------------------------- // Graphics utilities for fig output // // writeHeader write header for fig file // writePoint write a point // writeBox write a box // writeLine write a line //---------------------------------------------------------------------- void writeHeader() { ofile << FIG_HEAD << "\n" // fig file header << "Portrait\n" << "Center\n" << "Inches\n" << (int) u_per_in << " 2\n"; } void writePoint(ANNpoint p) // write a single point { // filled black point object ofile << "1 3 0 1 -1 7 0 0 0 0.000 1 0.0000 "; int cent_x = (int) TRANS_X(p); // transform center coords int cent_y = (int) TRANS_Y(p); ofile << cent_x << " " << cent_y << " " // write center, radius, bounds << pt_size << " " << pt_size << " " << cent_x << " " << cent_y << " " << cent_x + pt_size << " " << cent_y + pt_size << "\n"; } void writeBox(const ANNorthRect &r) // write box { // unfilled box object ofile << "2 2 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 5\n"; int p0_x = (int) TRANS_X(r.lo); // transform endpoints int p0_y = (int) TRANS_Y(r.lo); int p1_x = (int) TRANS_X(r.hi); int p1_y = (int) TRANS_Y(r.hi); ofile << "\t" << p0_x << " " << p0_y << " " // write vertices << p1_x << " " << p0_y << " " << p1_x << " " << p1_y << " " << p0_x << " " << p1_y << " " << p0_x << " " << p0_y << "\n"; } void writeLine(ANNpoint p0, ANNpoint p1) // write line { // unfilled line object ofile << "2 1 0 1 -1 7 0 0 -1 0.000 0 0 -1 0 0 2\n"; int p0_x = (int) TRANS_X(p0); // transform endpoints int p0_y = (int) TRANS_Y(p0); int p1_x = (int) TRANS_X(p1); int p1_y = (int) TRANS_Y(p1); ofile << "\t" << p0_x << " " << p0_y << " " // write vertices << p1_x << " " << p1_y << "\n"; } void writeCaption( // write caption text const ANNorthRect &bnd_box, // bounding box char *caption) // caption { if (!strcmp(caption, "\0")) return; // null string? int px = (int) TRANS_X(bnd_box.lo); // put .5 in. lower left int py = (int) (TRANS_Y(bnd_box.lo) + 0.50 * u_per_in); ofile << "4 0 -1 0 0 0 20 0.0000 4 255 2000 "; ofile << px << " " << py << " " << caption << "\\001\n"; } //---------------------------------------------------------------------- // overlap - test whether a box overlap slicing region // // The slicing region is a 2-dimensional plane in space // which contains points (x1, x2, ..., xn) satisfying the // n-2 linear equalities: // // xi == slice_val[i] for i != dim_x, dim_y // // This procedure returns true of the box defined by // corner points box.lo and box.hi overlap this plane. //---------------------------------------------------------------------- ANNbool overlap(const ANNorthRect &box) { for (int i = 0; i < dim; i++) { if (i != dim_x && i != dim_y && (box.lo[i] > slice_val[i] || box.hi[i] < slice_val[i])) return ANNfalse; } return ANNtrue; } //---------------------------------------------------------------------- // readTree, recReadTree - inputs tree and outputs figure // // readTree procedure initializes things and then calls recReadTree // which does all the work. // // recReadTree reads in a node of the tree, makes any recursive // calls as needed to input the children of this node (if internal) // and maintains the bounding box. Note that the bounding box // is modified within this procedure, but it is the responsibility // of the procedure that it be restored to its original value // on return. // // Recall that these are the formats. The tree is given in // preorder. // // Leaf node: // leaf ... // Splitting nodes: // split // Shrinking nodes: // shrink // // // ... (repeated n_bnds times) // // On reading a leaf we determine whether we should output the // cell's points (if dimension = 2 or this cell overlaps the // slicing region). For splitting nodes we check whether the // current cell overlaps the slicing plane and whether the // cutting dimension coincides with either the x or y drawing // dimensions. If so, we output the corresponding splitting // segment. //---------------------------------------------------------------------- void recReadTree(ANNorthRect &box) { char tag[STRING_LEN]; // tag (leaf, split, shrink) int n_pts; // number of points in leaf int idx; // point index int cd; // cut dimension ANNcoord cv; // cut value ANNcoord lb; // low bound ANNcoord hb; // high bound int n_bnds; // number of bounding sides int sd; // which side ifile >> tag; // input node tag if (strcmp(tag, "leaf") == 0) { // leaf node ifile >> n_pts; // input number of points // check for overlap if (dim == 2 || overlap(box)) { for (int i = 0; i < n_pts; i++) { // yes, write the points ifile >> idx; writePoint(pts[idx]); } } else { // input but ignore points for (int i = 0; i < n_pts; i++) { ifile >> idx; } } } else if (strcmp(tag, "split") == 0) { // splitting node ifile >> cd >> cv >> lb >> hb; if (lb != box.lo[cd] || hb != box.hi[cd]) { Error("Bounding box coordinates are fishy", ANNwarn); } ANNcoord lv = box.lo[cd]; // save bounds for cutting dim ANNcoord hv = box.hi[cd]; //-------------------------------------------------------------- // The following code is rather fragile so modify at your // own risk. We first decrease the high-end of the bounding // box down to the cutting plane and then read the left subtree. // Then we increase the low-end of the bounding box up to the // cutting plane (thus collapsing the bounding box to a d-1 // dimensional hyperrectangle). Then we draw the projection of // its diagonal if it crosses the slicing plane. This will have // the effect of drawing its intersection on the slicing plane. // Then we restore the high-end of the bounding box and read // the right subtree. Finally we restore the low-end of the // bounding box, before returning. //-------------------------------------------------------------- box.hi[cd] = cv; // decrease high bounds recReadTree(box); // read left subtree // check for overlap box.lo[cd] = cv; // increase low bounds if (dim == 2 || overlap(box)) { // check for overlap if (cd == dim_x || cd == dim_y) { // cut through slice plane writeLine(box.lo, box.hi); // draw cutting line } } box.hi[cd] = hv; // restore high bounds recReadTree(box); // read right subtree box.lo[cd] = lv; // restore low bounds } else if (strcmp(tag, "shrink") == 0) { // splitting node ANNorthRect inner(dim, box); // copy bounding box ifile >> n_bnds; // number of bounding sides for (int i = 0; i < n_bnds; i++) { ifile >> cd >> cv >> sd; // input bounding halfspace ANNorthHalfSpace hs(cd, cv, sd); // create orthogonal halfspace hs.project(inner.lo); // intersect by projecting hs.project(inner.hi); } if (dim == 2 || overlap(inner)) { writeBox(inner); // draw inner rectangle } recReadTree(inner); // read inner subtree recReadTree(box); // read outer subtree } else { Error("Illegal node type in dump file", ANNabort); } } void readTree(ANNorthRect &bnd_box) { writeHeader(); // output header writeBox(bnd_box); // draw bounding box writeCaption(bnd_box, caption); // write caption recReadTree(bnd_box); // do it } //---------------------------------------------------------------------- // readANN - read the ANN dump file // // This procedure reads in the dump file. See the format below. // It first reads the header line with version number. If the // points section is present it reads them (otherwise just leaves // points = NULL), and then it reads the tree section. It inputs // the bounding box and determines the parameters for transforming // the image to figure units. It then invokes the procedure // readTree to do all the real work. // // Dump File Format: = coordinate value (ANNcoord) // // #ANN [END_OF_LINE] // points (point coordinates: this is optional) // 0 ... (point indices and coordinates) // 1 ... // ... // tree // ... (lower end of bounding box) // ... (upper end of bounding box) // If the tree is null, then a single line "null" is // output. Otherwise the nodes of the tree are printed // one per line in preorder. Leaves and splitting nodes // have the following formats: // Leaf node: // leaf ... // Splitting nodes: // split // Shrinking nodes: // shrink // // // ... (repeated n_bnds times) // // Note: Infinite lo_ and hi_bounds are printed as the special // values "-INF" and "+INF", respectively. We do not // check for this, because the current version of ANN // starts with a finite bounding box if the tree is // nonempty. //---------------------------------------------------------------------- void readANN() { int j; char str[STRING_LEN]; // storage for string char version[STRING_LEN]; // storage for version int bkt_size; // bucket size ifile >> str; // input header if (strcmp(str, "#ANN") != 0) { // incorrect header Error("Incorrect header for dump file", ANNabort); } ifile.getline(version, STRING_LEN); // get version (ignore) ifile >> str; // get major heading if (strcmp(str, "points") == 0) { // points section ifile >> dim; // read dimension ifile >> n_pts; // number of points pts = annAllocPts(n_pts, dim); // allocate points for (int i = 0; i < n_pts; i++) { // input point coordinates int idx; // point index ifile >> idx; // input point index if (idx < 0 || idx >= n_pts) { Error("Point index is out of range", ANNabort); } for (j = 0; j < dim; j++) { ifile >> pts[idx][j]; // read point coordinates } } ifile >> str; // get next major heading } if (strcmp(str, "tree") == 0) { // tree section ifile >> dim; // read dimension if (dim_x > dim || dim_y > dim) { Error("Dimensions out of bounds", ANNabort); } ifile >> n_pts; // number of points ifile >> bkt_size; // bucket size (ignored) // read bounding box ANNorthRect bnd_box(dim); // create bounding box for (j = 0; j < dim; j++) { ifile >> bnd_box.lo[j]; // read box low coordinates } for (j = 0; j < dim; j++) { ifile >> bnd_box.hi[j]; // read box high coordinates } // compute scaling factors double box_len_x = bnd_box.hi[dim_x] - bnd_box.lo[dim_x]; double box_len_y = bnd_box.hi[dim_y] - bnd_box.lo[dim_y]; // longer side determines scale if (box_len_x > box_len_y) scale = u_size/box_len_x; else scale = u_size/box_len_y; // compute offsets offset_x = u_low_x - scale*bnd_box.lo[dim_x]; offset_y = u_low_y + scale*bnd_box.hi[dim_y]; readTree(bnd_box); // read the tree and process } else if (strcmp(str, "null") == 0) return; // empty tree else { cerr << "Input string: " << str << "\n"; Error("Illegal ann format. Expecting section heading", ANNabort); } } //---------------------------------------------------------------------- // Main program // // Gets the command-line arguments and invokes the main scanning // procedure. //---------------------------------------------------------------------- main(int argc, char **argv) { getArgs(argc, argv); // get input arguments readANN(); // read the dump file } ann-1.1.2+doc/License.txt0000644000175000017500000005776411330212441016047 0ustar sylvestresylvestre---------------------------------------------------------------------- The ANN Library (all versions) is provided under the terms and conditions of the GNU Lesser General Public Library, which is stated below. 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