pax_global_header00006660000000000000000000000064141571375340014524gustar00rootroot0000000000000052 comment=6132750a8792ec87518c05e178cccd29dfa1834b meshzoo-0.9.2/000077500000000000000000000000001415713753400132205ustar00rootroot00000000000000meshzoo-0.9.2/.codecov.yml000066400000000000000000000000141415713753400154360ustar00rootroot00000000000000comment: no meshzoo-0.9.2/.flake8000066400000000000000000000001531415713753400143720ustar00rootroot00000000000000[flake8] ignore = E203, E266, E501, W503 max-line-length = 80 max-complexity = 18 select = B,C,E,F,W,T4,B9 meshzoo-0.9.2/.github/000077500000000000000000000000001415713753400145605ustar00rootroot00000000000000meshzoo-0.9.2/.github/workflows/000077500000000000000000000000001415713753400166155ustar00rootroot00000000000000meshzoo-0.9.2/.github/workflows/ci.yml000066400000000000000000000015071415713753400177360ustar00rootroot00000000000000name: ci on: push: branches: - main pull_request: branches: - main jobs: lint: runs-on: ubuntu-latest steps: - name: Check out repo uses: actions/checkout@v2 - name: Set up Python uses: actions/setup-python@v2 - name: Run pre-commit uses: pre-commit/action@v2.0.3 build: runs-on: ubuntu-latest strategy: matrix: python-version: ["3.7", "3.8", "3.9", "3.10"] steps: - uses: actions/setup-python@v2 with: python-version: ${{ matrix.python-version }} - uses: actions/checkout@v2 - name: Test with tox run: | pip install tox tox -- --cov meshzoo --cov-report xml --cov-report term - uses: codecov/codecov-action@v1 if: ${{ matrix.python-version == '3.10' }} meshzoo-0.9.2/.gitignore000066400000000000000000000001471415713753400152120ustar00rootroot00000000000000*.pyc *.e README.rst dist/ meshzoo.egg-info/ .cache/ build/ .pytest_cache/ .coverage *.vtu *.vtk .tox/ meshzoo-0.9.2/.pre-commit-config.yaml000066400000000000000000000004561415713753400175060ustar00rootroot00000000000000repos: - repo: https://github.com/PyCQA/isort rev: 5.9.1 hooks: - id: isort - repo: https://github.com/python/black rev: 21.6b0 hooks: - id: black language_version: python3 - repo: https://gitlab.com/pycqa/flake8 rev: 3.9.2 hooks: - id: flake8 meshzoo-0.9.2/LICENSE.txt000066400000000000000000001045201415713753400150450ustar00rootroot00000000000000 GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. 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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 MODIFIES AND/OR CONVEYS THE PROGRAM 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 PROGRAM (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 PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. 17. Interpretation of Sections 15 and 16. If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS How to Apply These Terms to Your New Programs If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively state the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. 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But first, please read . meshzoo-0.9.2/README.md000066400000000000000000000175611415713753400145110ustar00rootroot00000000000000# meshzoo [![PyPi Version](https://img.shields.io/pypi/v/meshzoo.svg?style=flat-square)](https://pypi.org/project/meshzoo/) [![PyPI pyversions](https://img.shields.io/pypi/pyversions/meshzoo.svg?style=flat-square)](https://pypi.org/project/meshzoo/) [![GitHub stars](https://img.shields.io/github/stars/nschloe/meshzoo.svg?style=flat-square&logo=github&label=Stars&logoColor=white)](https://github.com/nschloe/meshzoo) [![Downloads](https://pepy.tech/badge/meshzoo/month?style=flat-square)](https://pepy.tech/project/meshzoo) [![Discord](https://img.shields.io/static/v1?logo=discord&label=chat&message=on%20discord&color=7289da&style=flat-square)](https://discord.gg/PBCCvwHqpv) [![gh-actions](https://img.shields.io/github/workflow/status/nschloe/meshzoo/ci?style=flat-square)](https://github.com/nschloe/meshzoo/actions?query=workflow%3Aci) [![codecov](https://img.shields.io/codecov/c/github/nschloe/meshzoo.svg?style=flat-square)](https://codecov.io/gh/nschloe/meshzoo) [![LGTM](https://img.shields.io/lgtm/grade/python/github/nschloe/meshzoo.svg?style=flat-square)](https://lgtm.com/projects/g/nschloe/meshzoo) [![Code style: black](https://img.shields.io/badge/code%20style-black-000000.svg?style=flat-square)](https://github.com/psf/black) When generating meshes for FEM/FVM computations, sometimes your geometry is so simple that you don't need a complex mesh generator (like [pygmsh](https://github.com/nschloe/pygmsh/), [MeshPy](https://github.com/inducer/meshpy), [mshr](https://bitbucket.org/fenics-project/mshr), [pygalmesh](https://github.com/nschloe/pygalmesh/), [dmsh](https://github.com/nschloe/dmsh/)), but something simple and fast that makes use of the structure of the domain. Enter meshzoo. ### Examples #### Triangle ```python import meshzoo bary, cells = meshzoo.triangle(8) # corners = numpy.array( # [ # [0.0, -0.5 * numpy.sqrt(3.0), +0.5 * numpy.sqrt(3.0)], # [1.0, -0.5, -0.5], # ] # ) # points = numpy.dot(corners, bary).T # Process the mesh, e.g., write it to a file using meshio # meshio.write_points_cells("triangle.vtk", points, {"triangle": cells}) ``` #### Rectangle
```python import meshzoo import numpy as np points, cells = meshzoo.rectangle_tri( np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11), variant="zigzag", # or "up", "down", "center" ) points, cells = meshzoo.rectangle_quad( np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11), cell_type="quad4", # or "quad8", "quad9" ) ``` #### Regular polygon | | | | | :----------------------------------------------------------------: | :----------------------------------------------------------------: | :----------------------------------------------------------------: | | `meshzoo.ngon(4, 8)` | `meshzoo.ngon(6, 8)` | `meshzoo.ngon(9, 8)` | ```python import meshzoo points, cells = meshzoo.ngon(5, 11) ``` #### Disk | | | | | :---------------------------------------------------------------------: | :---------------------------------------------------------------------: | :---------------------------------------------------------------------: | | `meshzoo.disk(4, 8)` | `meshzoo.disk(6, 8)` | `meshzoo.disk(9, 8)` | The disk meshes are inflations of regular polygons. ```python import meshzoo points, cells = meshzoo.disk(6, 11) points, cells = meshzoo.disk_quad(10, cell_type="quad4") # or "quad8", "quad9" ``` #### Möbius strip ```python import meshzoo points, cells = meshzoo.moebius(num_twists=1, nl=60, nw=11) ``` #### Sphere (surface) | | | | :---------------------------------------------------------------------: | :----------------------------------------------------------------------: | ```python import meshzoo points, cells = meshzoo.uv_sphere(num_points_per_circle=20, num_circles=10, radius=1.0) points, tri, quad = meshzoo.geo_sphere( num_points_per_circle=20, num_circles=10, radius=1.0 ) ``` Spheres can also be generated by refining the faces of [platonic solids](https://en.wikipedia.org/wiki/Platonic_solid) and then "inflating" them. meshzoo implements a few of them. The sphere generated from the icosahedron has the highest-quality (most equilateral) triangles. All cells are oriented such that its normals point outwards. | | | | | :------------------------------------------------------------------------: | :-----------------------------------------------------------------------: | :------------------------------------------------------------------------: | | `meshzoo.tetra_sphere(10)` | `meshzoo.octa_sphere(10)` | `meshzoo.icosa_sphere(10)` | #### Ball (solid) | | | | :----------------------------------------------------------------------: | :---------------------------------------------------------------------: | ```python import meshzoo points, cells = meshzoo.ball_tetra(10) points, cells = meshzoo.ball_hexa(10) ``` #### Tube ```python import meshzoo points, cells = meshzoo.tube(length=1.0, radius=1.0, n=30) ``` #### Cube | | | | :----------------------------------------------------------------: | :---------------------------------------------------------------------: | ```python import meshzoo import numpy as np points, cells = meshzoo.cube_tetra( np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11) ) points, cells = meshzoo.cube_hexa( np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11) ) ``` ### Extra, extra In addition to this, the [`examples/`](https://github.com/nschloe/meshzoo/tree/main/examples) directory contains a couple of instructive examples for other mesh generators. ### Installation meshzoo is [available from the Python Package Index](https://pypi.org/project/meshzoo/), so simply do ``` pip install meshzoo ``` to install. ### Testing To run the meshzoo unit tests, check out this repository and run ``` pytest ``` ### License This software is published under the [GPLv3 license](https://www.gnu.org/licenses/gpl-3.0.en.html). meshzoo-0.9.2/examples/000077500000000000000000000000001415713753400150365ustar00rootroot00000000000000meshzoo-0.9.2/examples/meshpy/000077500000000000000000000000001415713753400163435ustar00rootroot00000000000000meshzoo-0.9.2/examples/meshpy/__init__.py000066400000000000000000000005151415713753400204550ustar00rootroot00000000000000import ball import cube import ellipse import lshape import lshape3d import pacman import rectangle import rectangle_with_hole import tetrahedron import torus __all__ = [ "ball", "cube", "ellipse", "lshape", "lshape3d", "pacman", "rectangle", "rectangle_with_hole", "tetrahedron", "torus", ] meshzoo-0.9.2/examples/meshpy/ball.py000066400000000000000000000024231415713753400176300ustar00rootroot00000000000000import numpy as np from meshpy.geometry import EXT_OPEN, GeometryBuilder, generate_surface_of_revolution from meshpy.tet import MeshInfo, build def create_ball_mesh(num_longi_points=10): radius = 5.0 radial_subdiv = 2 * num_longi_points dphi = np.pi / num_longi_points # Make sure the nodes meet at the poles of the ball. def truncate(r): if abs(r) < 1e-10: return 0 else: return r # Compute the volume of a canonical tetrahedron # with edgelength radius*dphi. a = radius * dphi canonical_tet_volume = np.sqrt(2.0) / 12 * a ** 3 # Build outline for surface of revolution. rz = [ (truncate(radius * np.sin(i * dphi)), radius * np.cos(i * dphi)) for i in range(num_longi_points + 1) ] geob = GeometryBuilder() geob.add_geometry( *generate_surface_of_revolution( rz, closure=EXT_OPEN, radial_subdiv=radial_subdiv ) ) mesh_info = MeshInfo() geob.set(mesh_info) meshpy_mesh = build(mesh_info, max_volume=canonical_tet_volume) return np.array(meshpy_mesh.points), np.array(meshpy_mesh.elements) if __name__ == "__main__": import meshio points, cells = create_ball_mesh() meshio.write("ball.e", points, {"tetra": cells}) meshzoo-0.9.2/examples/meshpy/cube.py000066400000000000000000000022241415713753400176330ustar00rootroot00000000000000""" Creates meshes on a cube. """ import meshpy.tet import numpy as np def create_mesh(maxvol): # get the file name to be written to # circumcirlce radius cc_radius = 5.0 lx = 2.0 / np.sqrt(3.0) * cc_radius ly = lx lz = lx # Corner points of the cube points = [ (-0.5 * lx, -0.5 * ly, -0.5 * lz), (0.5 * lx, -0.5 * ly, -0.5 * lz), (0.5 * lx, 0.5 * ly, -0.5 * lz), (-0.5 * lx, 0.5 * ly, -0.5 * lz), (-0.5 * lx, -0.5 * ly, 0.5 * lz), (0.5 * lx, -0.5 * ly, 0.5 * lz), (0.5 * lx, 0.5 * ly, 0.5 * lz), (-0.5 * lx, 0.5 * ly, 0.5 * lz), ] facets = [ [0, 1, 2, 3], [4, 5, 6, 7], [0, 4, 5, 1], [1, 5, 6, 2], [2, 6, 7, 3], [3, 7, 4, 0], ] # create the mesh info = meshpy.tet.MeshInfo() info.set_points(points) info.set_facets(facets) meshpy_mesh = meshpy.tet.build(info, max_volume=maxvol) return np.array(meshpy_mesh.points), np.array(meshpy_mesh.elements) if __name__ == "__main__": import meshio points, cells = create_mesh(0.1) meshio.write("cube.e", points, {"tetra": cells}) meshzoo-0.9.2/examples/meshpy/ellipse.py000066400000000000000000000032141415713753400203520ustar00rootroot00000000000000#!/usr/bin/env python import meshpy.triangle import numpy as np from scipy import special def create_mesh(axis0=1, axis1=0.5, num_boundary_points=100): # lengths of major and minor axes a = max(axis0, axis1) b = min(axis0, axis1) # Choose the maximum area of a triangle equal to the area of # an equilateral triangle on the boundary. # For circumference of an ellipse, see # https://en.wikipedia.org/wiki/Ellipse#Circumference eccentricity = np.sqrt(1.0 - (b / a) ** 2) length_boundary = float(4 * a * special.ellipe(eccentricity)) a_boundary = length_boundary / num_boundary_points max_area = a_boundary ** 2 * np.sqrt(3) / 4 # generate points on the circle Phi = np.linspace(0, 2 * np.pi, num_boundary_points, endpoint=False) boundary_points = np.column_stack((a * np.cos(Phi), b * np.sin(Phi))) info = meshpy.triangle.MeshInfo() info.set_points(boundary_points) def _round_trip_connect(start, end): result = [] for i in range(start, end): result.append((i, i + 1)) result.append((end, start)) return result info.set_facets(_round_trip_connect(0, len(boundary_points) - 1)) def _needs_refinement(vertices, area): return bool(area > max_area) meshpy_mesh = meshpy.triangle.build(info, refinement_func=_needs_refinement) # append column pts = np.array(meshpy_mesh.points) points = np.c_[pts[:, 0], pts[:, 1], np.zeros(len(pts))] return points, np.array(meshpy_mesh.elements) if __name__ == "__main__": import meshio points, cells = create_mesh() meshio.write("ellipse.e", points, {"triangle": cells}) meshzoo-0.9.2/examples/meshpy/lshape.py000066400000000000000000000022601415713753400201710ustar00rootroot00000000000000import meshpy.triangle import numpy as np def create_mesh(maxarea=1.0): # dimensions of the rectangle cc_radius = 5.0 # circumcircle radius lx = np.sqrt(2.0) * cc_radius ly = lx # corner points points = [ (-0.5 * lx, -0.5 * ly), (0.5 * lx, -0.5 * ly), (0.5 * lx, 0.0), (0.0, 0.0), (0.0, 0.5 * ly), (-0.5 * lx, 0.5 * ly), ] info = meshpy.triangle.MeshInfo() info.set_points(points) def _round_trip_connect(start, end): result = [] for i in range(start, end): result.append((i, i + 1)) result.append((end, start)) return result info.set_facets(_round_trip_connect(0, len(points) - 1)) def _needs_refinement(vertices, area): return bool(area > maxarea) meshpy_mesh = meshpy.triangle.build(info, refinement_func=_needs_refinement) # append column pts = np.array(meshpy_mesh.points) points = np.c_[pts[:, 0], pts[:, 1], np.zeros(len(pts))] return points, np.array(meshpy_mesh.elements) if __name__ == "__main__": import meshio points, cells = create_mesh() meshio.write("lshape.e", points, {"triangle": cells}) meshzoo-0.9.2/examples/meshpy/lshape3d.py000066400000000000000000000027311415713753400204230ustar00rootroot00000000000000"""Creates meshes on a 3D L-shape. """ import meshpy.tet import numpy as np def create_mesh(maxvol): # circumcirlce radius cc_radius = 10.0 lx = 2.0 / np.sqrt(3.0) * cc_radius ly = lx lz = lx # create the mesh data structure # Corner points of the cube points = [ (-0.5 * lx, -0.5 * ly, -0.5 * lz), (0.5 * lx, -0.5 * ly, -0.5 * lz), (0.5 * lx, 0.5 * ly, -0.5 * lz), (-0.5 * lx, 0.5 * ly, -0.5 * lz), (-0.5 * lx, -0.5 * ly, 0.5 * lz), (0.5 * lx, 0.5 * ly, 0.5 * lz), (-0.5 * lx, 0.5 * ly, 0.5 * lz), (0.0, -0.5 * ly, 0.5 * lz), (0.0, -0.5 * ly, 0.0), (0.5 * lx, -0.5 * ly, 0.0), (0.5 * lx, 0.0, 0.0), (0.5 * lx, 0.0, 0.5 * lz), (0.0, 0.0, 0.5 * lz), (0.0, 0.0, 0.0), ] facets = [ [0, 1, 2, 3], [4, 7, 12, 11, 5, 6], [0, 1, 9, 8, 7, 4], [1, 2, 5, 11, 10, 9], [2, 5, 6, 3], [3, 6, 4, 0], [8, 13, 12, 7], [8, 9, 10, 13], [10, 11, 12, 13], ] # create the mesh # Set the geometry and build the mesh. info = meshpy.tet.MeshInfo() info.set_points(points) info.set_facets(facets) meshpy_mesh = meshpy.tet.build(info, max_volume=maxvol) return np.array(meshpy_mesh.points), np.array(meshpy_mesh.elements) if __name__ == "__main__": import meshio points, cells = create_mesh(0.1) meshio.write("lshape3d.e", points, {"tetra": cells}) meshzoo-0.9.2/examples/meshpy/pacman.py000066400000000000000000000034141415713753400201560ustar00rootroot00000000000000""" Creates a mesh for a circle with a cut. """ import meshpy.triangle import numpy as np def create_pacman_mesh(num_boundary_points=50): n_phi = num_boundary_points radius = 5.0 # set those to 0.0 for perfect circle cut_angle = 0.1 * 2 * np.pi cut_depth = 0.5 * radius # Choose the maximum area of a triangle equal to the area of # an equilateral triangle on the boundary. a_boundary = (2 * np.pi - cut_angle) * radius / n_phi max_area = a_boundary ** 2 * np.sqrt(3.0) / 4.0 max_area = float(max_area) # meshpy can't deal with np.float64 # generate points on the boundary Phi = np.linspace( 0.5 * cut_angle, 2 * np.pi - 0.5 * cut_angle, n_phi, endpoint=False ) boundary_points = [] if abs(cut_angle) > 0.0 or cut_depth != 0.0: boundary_points.append((radius - cut_depth, 0.0)) for phi in Phi: boundary_points.append((radius * np.cos(phi), radius * np.sin(phi))) # create the mesh info = meshpy.triangle.MeshInfo() info.set_points(boundary_points) def _round_trip_connect(start, end): result = [] for i in range(start, end): result.append((i, i + 1)) result.append((end, start)) return result info.set_facets(_round_trip_connect(0, len(boundary_points) - 1)) def _needs_refinement(vertices, area): return bool(area > max_area) meshpy_mesh = meshpy.triangle.build(info, refinement_func=_needs_refinement) # append column pts = np.array(meshpy_mesh.points) points = np.c_[pts[:, 0], pts[:, 1], np.zeros(len(pts))] return points, np.array(meshpy_mesh.elements) if __name__ == "__main__": import meshio points, cells = create_pacman_mesh() meshio.write("pacman.vtu", points, {"triangle": cells}) meshzoo-0.9.2/examples/meshpy/rectangle.py000066400000000000000000000023001415713753400206540ustar00rootroot00000000000000""" Creates a mesh on a rectangle in the x-y-plane. """ import meshpy.triangle import numpy as np def create_mesh(edgelength=1.0, max_area=0.01): # dimensions of the rectangle lx = edgelength ly = edgelength # corner points boundary_points = [ (-0.5 * lx, -0.5 * ly), (0.5 * lx, -0.5 * ly), (0.5 * lx, 0.5 * ly), (-0.5 * lx, 0.5 * ly), ] info = meshpy.triangle.MeshInfo() info.set_points(boundary_points) def _round_trip_connect(start, end): result = [] for i in range(start, end): result.append((i, i + 1)) result.append((end, start)) return result info.set_facets(_round_trip_connect(0, len(boundary_points) - 1)) def _needs_refinement(vertices, area): return bool(area > max_area) meshpy_mesh = meshpy.triangle.build(info, refinement_func=_needs_refinement) # append column pts = np.array(meshpy_mesh.points) points = np.c_[pts[:, 0], pts[:, 1], np.zeros(len(pts))] return points, np.array(meshpy_mesh.elements) if __name__ == "__main__": import meshio points, cells = create_mesh() meshio.write("rectangle.e", points, {"triangle": cells}) meshzoo-0.9.2/examples/meshpy/rectangle_with_hole.py000066400000000000000000000030631415713753400227250ustar00rootroot00000000000000import meshpy.triangle import numpy as np def create_mesh(max_area=1.0): # dimensions of the rectangle cc_radius = 15.0 # circumcircle radius lx = np.sqrt(2.0) * cc_radius ly = lx h_radius = 1.0 # corner points boundary_points = [ (0.5 * lx, 0.0), (0.5 * lx, 0.5 * ly), (-0.5 * lx, 0.5 * ly), (-0.5 * lx, -0.5 * ly), (0.5 * lx, -0.5 * ly), (0.5 * lx, 0.0), ] # create circular boundary on the inside segments = 100 for k in range(segments + 1): angle = k * 2.0 * np.pi / segments boundary_points.append((h_radius * np.cos(angle), h_radius * np.sin(angle))) # mark the hole by an interior point holes = [(0, 0)] info = meshpy.triangle.MeshInfo() info.set_points(boundary_points) info.set_holes(holes) def _round_trip_connect(start, end): result = [] for i in range(start, end): result.append((i, i + 1)) result.append((end, start)) return result info.set_facets(_round_trip_connect(0, len(boundary_points) - 1)) def _needs_refinement(vertices, area): return bool(area > max_area) meshpy_mesh = meshpy.triangle.build(info, refinement_func=_needs_refinement) # append column pts = np.array(meshpy_mesh.points) points = np.c_[pts[:, 0], pts[:, 1], np.zeros(len(pts))] return points, np.array(meshpy_mesh.elements) if __name__ == "__main__": import meshio points, cells = create_mesh() meshio.write("rectangle_with_hole.e", points, {"triangle": cells}) meshzoo-0.9.2/examples/meshpy/tetrahedron.py000066400000000000000000000025511415713753400212370ustar00rootroot00000000000000#!/usr/bin/env python """ Create irregular mesh on a regular tetrahedron centered at the origin. """ import meshpy.tet import numpy as np def create_tetrahedron_mesh(maxvol=0.1): # circumcircle radius r = 5.0 # boundary points points = [] points.append((0.0, 0.0, r)) # theta = arccos(-1/3) (tetrahedral angle) costheta = -1.0 / 3.0 sintheta = 2.0 / 3.0 * np.sqrt(2.0) # phi = 0.0 sinphi = 0.0 cosphi = 1.0 points.append((r * cosphi * sintheta, r * sinphi * sintheta, r * costheta)) # phi = np.pi * 2.0 / 3.0 sinphi = np.sqrt(3.0) / 2.0 cosphi = -0.5 points.append((r * cosphi * sintheta, r * sinphi * sintheta, r * costheta)) # phi = - np.pi * 2.0 / 3.0 sinphi = -np.sqrt(3.0) / 2.0 cosphi = -0.5 points.append((r * cosphi * sintheta, r * sinphi * sintheta, r * costheta)) # boundary faces facets = [[0, 1, 2], [0, 2, 3], [0, 3, 1], [1, 2, 3]] # create the mesh # Set the geometry and build the mesh. info = meshpy.tet.MeshInfo() info.set_points(points) info.set_facets(facets) meshpy_mesh = meshpy.tet.build(info, max_volume=maxvol) return np.array(meshpy_mesh.points), np.array(meshpy_mesh.elements) if __name__ == "__main__": import meshio points, cells = create_tetrahedron_mesh(10.0) meshio.write("tetrahedron.vtu", points, {"tetra": cells}) meshzoo-0.9.2/examples/meshpy/torus.py000066400000000000000000000021621415713753400200720ustar00rootroot00000000000000#!/usr/bin/env python import numpy as np from meshpy.geometry import ( EXT_CLOSED_IN_RZ, GeometryBuilder, generate_surface_of_revolution, ) from meshpy.tet import MeshInfo, build def create_mesh(big_r=1.0, small_r=0.5, num_points=10): dphi = 2 * np.pi / num_points # Compute the volume of a canonical tetrahedron # with edgelength radius2*dphi. a = small_r * dphi canonical_tet_volume = np.sqrt(2.0) / 12 * a ** 3 radial_subdiv = int(2 * np.pi * big_r / a) rz = [ (big_r + small_r * np.cos(i * dphi), 0.5 * small_r * np.sin(i * dphi)) for i in range(num_points) ] geob = GeometryBuilder() geob.add_geometry( *generate_surface_of_revolution( rz, closure=EXT_CLOSED_IN_RZ, radial_subdiv=radial_subdiv ) ) mesh_info = MeshInfo() geob.set(mesh_info) meshpy_mesh = build(mesh_info, max_volume=canonical_tet_volume) return np.array(meshpy_mesh.points), np.array(meshpy_mesh.elements) if __name__ == "__main__": import meshio points, cells = create_mesh() meshio.write("torus.e", points, {"tetra": cells}) meshzoo-0.9.2/examples/mshr/000077500000000000000000000000001415713753400160075ustar00rootroot00000000000000meshzoo-0.9.2/examples/mshr/__init__.py000066400000000000000000000000361415713753400201170ustar00rootroot00000000000000import toy __all__ = ["toy"] meshzoo-0.9.2/examples/mshr/toy.py000066400000000000000000000014341415713753400171760ustar00rootroot00000000000000import dolfin import mshr def create_toy_mesh(): box = mshr.Box(dolfin.Point(-3, -1, -0.5), dolfin.Point(3, 1, 0.5)) c1 = mshr.Cylinder(dolfin.Point(0, 0, -2), dolfin.Point(0, 0, 2), 0.6, 0.6) b1 = mshr.Box(dolfin.Point(-2.5, -0.5, -2), dolfin.Point(-1.5, 0.5, 2)) # "triangle" t1 = mshr.Polygon( [ dolfin.Point(2.5, -0.5, 0), dolfin.Point(2.5, 0.5, 0), dolfin.Point(1.5, -0.5, 0), ] ) g3d = mshr.Extrude2D(t1, -2) g3d = mshr.CSGTranslation(g3d, dolfin.Point(0, 0, 1)) m = mshr.generate_mesh(box - c1 - b1 - g3d, 40, "cgal") return m.coordinates(), m.cells() if __name__ == "__main__": import meshio points, cells = create_toy_mesh() meshio.write("toy.e", points, {"tetra": cells}) meshzoo-0.9.2/justfile000066400000000000000000000016661415713753400150010ustar00rootroot00000000000000version := `python3 -c "from configparser import ConfigParser; p = ConfigParser(); p.read('setup.cfg'); print(p['metadata']['version'])"` name := `python3 -c "from configparser import ConfigParser; p = ConfigParser(); p.read('setup.cfg'); print(p['metadata']['name'])"` default: @echo "\"just publish\"?" tag: @if [ "$(git rev-parse --abbrev-ref HEAD)" != "main" ]; then exit 1; fi curl -H "Authorization: token `cat ~/.github-access-token`" -d '{"tag_name": "v{{version}}"}' https://api.github.com/repos/nschloe/{{name}}/releases upload: clean @if [ "$(git rev-parse --abbrev-ref HEAD)" != "main" ]; then exit 1; fi # https://stackoverflow.com/a/58756491/353337 python3 -m build --sdist --wheel . twine upload dist/* publish: tag upload clean: @find . | grep -E "(__pycache__|\.pyc|\.pyo$)" | xargs rm -rf @rm -rf src/*.egg-info/ build/ dist/ .tox/ format: isort . black . blacken-docs README.md lint: black --check . flake8 . meshzoo-0.9.2/pyproject.toml000066400000000000000000000001761415713753400161400ustar00rootroot00000000000000[build-system] requires = ["setuptools>=42", "wheel"] build-backend = "setuptools.build_meta" [tool.isort] profile = "black" meshzoo-0.9.2/setup.cfg000066400000000000000000000023121415713753400150370ustar00rootroot00000000000000[metadata] name = meshzoo version = 0.9.2 author = Nico Schlömer author_email = nico.schloemer@gmail.com description = Collection of explicitly constructed meshes url = https://github.com/nschloe/meshzoo project_urls = Code=https://github.com/nschloe/meshzoo Issues=https://github.com/nschloe/meshzoo/issues Funding=https://github.com/sponsors/nschloe long_description = file: README.md long_description_content_type = text/markdown license = GPL-3.0-or-later classifiers = Development Status :: 5 - Production/Stable Intended Audience :: Science/Research License :: OSI Approved :: GNU General Public License v3 or later (GPLv3+) Operating System :: OS Independent Programming Language :: Python Programming Language :: Python :: 3 Programming Language :: Python :: 3.7 Programming Language :: Python :: 3.8 Programming Language :: Python :: 3.9 Programming Language :: Python :: 3.10 Topic :: Scientific/Engineering Topic :: Scientific/Engineering :: Mathematics [options] package_dir = =src packages = find: install_requires = numpy python_requires = >=3.7 [options.packages.find] where=src [options.extras_require] all = matplotlib plot = matplotlib meshzoo-0.9.2/src/000077500000000000000000000000001415713753400140075ustar00rootroot00000000000000meshzoo-0.9.2/src/meshzoo/000077500000000000000000000000001415713753400154735ustar00rootroot00000000000000meshzoo-0.9.2/src/meshzoo/__init__.py000066400000000000000000000016021415713753400176030ustar00rootroot00000000000000from ._ball import ball_hexa, ball_tetra from ._cube import cube, cube_hexa, cube_tetra from ._disk import disk, disk_quad from ._helpers import create_edges, insert_midpoints_edges, plot2d, save2d, show2d from ._moebius import moebius from ._ngon import ngon from ._rectangle import rectangle, rectangle_quad, rectangle_tri from ._sphere import geo_sphere, icosa_sphere, octa_sphere, tetra_sphere, uv_sphere from ._triangle import triangle from ._tube import tube __all__ = [ "ball_hexa", "ball_tetra", "cube", "cube_tetra", "cube_hexa", "disk", "disk_quad", "moebius", "ngon", "rectangle", "rectangle_tri", "rectangle_quad", "uv_sphere", "icosa_sphere", "octa_sphere", "tetra_sphere", "geo_sphere", "triangle", "tube", # "save2d", "show2d", "plot2d", "create_edges", "insert_midpoints_edges", ] meshzoo-0.9.2/src/meshzoo/_ball.py000066400000000000000000000017511415713753400171220ustar00rootroot00000000000000import numpy as np from ._cube import cube_hexa, cube_tetra def ball_hexa(n: int): a = 1 / np.sqrt(3) ls = np.linspace(-a, a, n + 1) nodes, cells = cube_hexa(ls, ls, ls) # Inflate the nodes towards the circle boundary. # Inflate each point such that the 2-norm of the new point is the max-norm of the # old. alpha = np.max(np.abs(nodes), axis=1) beta = np.linalg.norm(nodes, axis=1) idx = beta > 1.0e-13 nodes[idx] = (nodes[idx].T * (alpha[idx] / beta[idx])).T return nodes, cells def ball_tetra(n: int): a = 1 / np.sqrt(3) ls = np.linspace(-a, a, n + 1) nodes, cells = cube_tetra(ls, ls, ls) # Inflate the nodes towards the circle boundary. # Inflate each point such that the 2-norm of the new point is the max-norm of the # old. alpha = np.max(np.abs(nodes), axis=1) beta = np.linalg.norm(nodes, axis=1) idx = beta > 1.0e-13 nodes[idx] = (nodes[idx].T * (alpha[idx] / beta[idx])).T return nodes, cells meshzoo-0.9.2/src/meshzoo/_cube.py000066400000000000000000000104341415713753400171240ustar00rootroot00000000000000from __future__ import annotations import numpy as np from numpy.typing import ArrayLike # backwards compatibility def cube( x0: float, x1: float, y0: float, y1: float, z0: float, z1: float, nx: int, ny: int, nz: int, ): return cube_tetra( np.linspace(x0, x1, nx + 1), np.linspace(y0, y1, ny + 1), np.linspace(z0, z1, nz + 1), ) def cube_hexa( x_range: ArrayLike, y_range: ArrayLike, z_range: ArrayLike ) -> tuple[np.ndarray, np.ndarray]: x_range = np.asarray(x_range) y_range = np.asarray(y_range) z_range = np.asarray(z_range) nx1 = len(x_range) ny1 = len(y_range) nz1 = len(z_range) # Create the vertices. x, y, z = np.meshgrid(x_range, y_range, z_range, indexing="ij") # Alternative with slightly different order: # ``` # points = np.stack([x, y, z]).T.reshape(-1, 3) # ``` points = np.array([x, y, z]).T.reshape(-1, 3) # Create the cells. a = np.arange(len(points)).reshape(nz1, ny1, nx1) a = np.transpose(a, [2, 1, 0]) # `c` contains the indices of each "cube" like # # # c[7] c[6] # ________ # / /| # c[4] /_______/ | c[5] # | | | # | | | # | | / c[2] # |________|/ # # c[0] c[1] # cells = ( np.array( [ a[:-1, :-1, :-1], a[1:, :-1, :-1], a[1:, 1:, :-1], a[:-1, 1:, :-1], a[:-1, :-1, 1:], a[1:, :-1, 1:], a[1:, 1:, 1:], a[:-1, 1:, 1:], ] ) .reshape(8, -1) .T ) return points, cells def cube_tetra(x_range: ArrayLike, y_range: ArrayLike, z_range: ArrayLike): x_range = np.asarray(x_range) y_range = np.asarray(y_range) z_range = np.asarray(z_range) nx1 = len(x_range) ny1 = len(y_range) nz1 = len(z_range) # Create the vertices. x, y, z = np.meshgrid(x_range, y_range, z_range, indexing="ij") # Alternative with slightly different order: # ``` # points = np.stack([x, y, z]).T.reshape(-1, 3) # ``` points = np.array([x, y, z]).T.reshape(-1, 3) # Create the elements (cells). a = np.arange(len(points)).reshape(nz1, ny1, nx1) a = np.transpose(a, [2, 1, 0]) # # `c` contains the indices of each "cube" like # # # c[7] c[6] # ________ # / /| # c[4] /_______/ | c[5] # | | | # | | | # | | / c[2] # |________|/ # # c[0] c[1] # c = [ a[:-1, :-1, :-1], a[1:, :-1, :-1], a[1:, 1:, :-1], a[:-1, 1:, :-1], a[:-1, :-1, 1:], a[1:, :-1, 1:], a[1:, 1:, 1:], a[:-1, 1:, 1:], ] # 3D checkers idx = np.ones((nx1 - 1, ny1 - 1, nz1 - 1), dtype=bool) idx[::2, 1::2, ::2] = False idx[::2, ::2, 1::2] = False idx[1::2, ::2, ::2] = False idx[1::2, 1::2, 1::2] = False # There is 1 way to split a cube into 5 tetrahedra, # and 12 ways to split it into 6 tetrahedra. # See # # Also interesting: . cells = [ # regular; make sure the order of the points is such that the signed volume is # positive [c[0][idx], c[1][idx], c[3][idx], c[4][idx]], [c[1][idx], c[2][idx], c[3][idx], c[6][idx]], [c[1][idx], c[3][idx], c[4][idx], c[6][idx]], [c[1][idx], c[4][idx], c[5][idx], c[6][idx]], [c[3][idx], c[4][idx], c[6][idx], c[7][idx]], # the rest rotated such that it fits with the others; basically we change # "bottom" and "top" of the dice [c[4][~idx], c[5][~idx], c[0][~idx], c[7][~idx]], [c[5][~idx], c[6][~idx], c[2][~idx], c[7][~idx]], [c[5][~idx], c[7][~idx], c[2][~idx], c[0][~idx]], [c[5][~idx], c[0][~idx], c[2][~idx], c[1][~idx]], [c[7][~idx], c[0][~idx], c[3][~idx], c[2][~idx]], ] cells = np.column_stack([np.array(c).reshape(4, -1) for c in cells]).T return points, cells meshzoo-0.9.2/src/meshzoo/_disk.py000066400000000000000000000031241415713753400171360ustar00rootroot00000000000000import numpy as np from ._helpers import _compose_from_faces from ._rectangle import rectangle_quad def disk(p: int, n: int, offset: float = np.pi / 2): x = np.linspace(offset, offset + 2 * np.pi, p, endpoint=False) corners = np.vstack( [ [[0.0, 0.0]], np.array([np.cos(x), np.sin(x)]).T, ] ) faces = [(0, k + 1, k + 2) for k in range(p - 1)] + [(0, p, 1)] def edge_adjust(edge, verts): if 0 in edge: return verts dist = np.sqrt(np.einsum("ij,ij->i", verts, verts)) return verts / dist[:, None] def face_adjust(face, bary, verts, corner_verts): assert face[0] == 0 z = np.zeros_like(bary[1]) edge_proj_bary = np.array([z, bary[1], bary[2]]) / (bary[1] + bary[2]) edge_proj_cart = np.dot(corner_verts.T, edge_proj_bary).T dist = np.sqrt(np.einsum("ij,ij->i", edge_proj_cart, edge_proj_cart)) return verts / dist[:, None] return _compose_from_faces( corners, faces, n, edge_adjust=edge_adjust, face_adjust=face_adjust ) def disk_quad(n: int, cell_type: str = "quad4"): a = 1 / np.sqrt(2) nodes, cells = rectangle_quad( np.linspace(-a, a, n + 1), np.linspace(-a, a, n + 1), cell_type ) # Inflate the nodes towards the circle boundary. # Inflate each point such that the 2-norm of the new point is the max-norm of the # old. alpha = np.max(np.abs(nodes), axis=1) beta = np.linalg.norm(nodes, axis=1) idx = beta > 1.0e-13 nodes[idx] = (nodes[idx].T * (alpha[idx] / beta[idx])).T return nodes, cells meshzoo-0.9.2/src/meshzoo/_helpers.py000066400000000000000000000207661415713753400176610ustar00rootroot00000000000000import numpy as np def create_edges(cells_nodes): """Setup edge-node and edge-cell relations. Adapted from voropy.""" # Create the idx_hierarchy (nodes->edges->cells), i.e., the value of # `self.idx_hierarchy[0, 2, 27]` is the index of the node of cell 27, edge # 2, node 0. The shape of `self.idx_hierarchy` is `(2, 3, n)`, where `n` is # the number of cells. Make sure that the k-th edge is opposite of the k-th # point in the triangle. local_idx = np.array([[1, 2], [2, 0], [0, 1]]).T # Map idx back to the nodes. This is useful if quantities which are in # idx shape need to be added up into nodes (e.g., equation system rhs). nds = cells_nodes.T idx_hierarchy = nds[local_idx] s = idx_hierarchy.shape a = np.sort(idx_hierarchy.reshape(s[0], s[1] * s[2]).T) b = np.ascontiguousarray(a).view(np.dtype((np.void, a.dtype.itemsize * a.shape[1]))) _, idx, inv, cts = np.unique( b, return_index=True, return_inverse=True, return_counts=True ) # No edge has more than 2 cells. This assertion fails, for example, if # cells are listed twice. assert all(cts < 3) edge_nodes = a[idx] cells_edges = inv.reshape(3, -1).T return edge_nodes, cells_edges def show2d(*args, **kwargs): import matplotlib.pyplot as plt plot2d(*args, **kwargs) plt.show() def save2d(filename, *args, **kwargs): import matplotlib.pyplot as plt plot2d(*args, **kwargs) plt.savefig(filename, transparent=True, bbox_inches="tight") def plot2d( points, cells, show_axes=False, # ParaView's default colors fill: str = "#c8c5bd", stroke: str = "#000080", ): """Plot a 2D mesh using matplotlib.""" import matplotlib.pyplot as plt fig = plt.figure() ax = fig.gca() plt.axis("equal") if not show_axes: ax.set_axis_off() assert points.shape[1] == 2 xmin = np.amin(points[:, 0]) xmax = np.amax(points[:, 0]) ymin = np.amin(points[:, 1]) ymax = np.amax(points[:, 1]) width = xmax - xmin xmin -= 0.1 * width xmax += 0.1 * width height = ymax - ymin ymin -= 0.1 * height ymax += 0.1 * height ax.set_xlim(xmin, xmax) ax.set_ylim(ymin, ymax) for cell in cells: import matplotlib.patches poly = matplotlib.patches.Polygon(points[cell], ec=stroke, fc=fill) ax.add_patch(poly) # import matplotlib.tri # tri = matplotlib.tri.Triangulation(points[:,0], points[:,1], triangles=cells) # ax.triplot(tri, '-', lw=1, color="k") return fig def _compose_from_faces(corners, faces, n, edge_adjust=None, face_adjust=None): # create corner nodes vertices = [corners] vertex_count = len(corners) corner_nodes = np.arange(len(corners)) # create edges edges = set() for face in faces: edges.add(tuple(sorted([face[0], face[1]]))) edges.add(tuple(sorted([face[1], face[2]]))) edges.add(tuple(sorted([face[2], face[0]]))) edges = list(edges) # create edge nodes: edge_nodes = {} t = np.linspace(1 / n, 1.0, n - 1, endpoint=False) corners = vertices[0] k = corners.shape[0] for edge in edges: i0, i1 = edge new_vertices = np.outer(1 - t, corners[i0]) + np.outer(t, corners[i1]) if edge_adjust: new_vertices = edge_adjust(edge, new_vertices) vertices.append(new_vertices) vertex_count += len(vertices[-1]) edge_nodes[edge] = np.arange(k, k + len(t)) k += len(t) # This is the same code as appearing for cell in a single triangle. On each face, # those indices are translated into the actual indices. triangle_cells = [] k = 0 for i in range(n): j = np.arange(n - i) triangle_cells.append(np.column_stack([k + j, k + j + 1, k + n - i + j + 1])) j = j[:-1] triangle_cells.append( np.column_stack([k + j + 1, k + n - i + j + 2, k + n - i + j + 1]) ) k += n - i + 1 triangle_cells = np.vstack(triangle_cells) cells = [] for face in faces: corners = face edges = [(face[0], face[1]), (face[1], face[2]), (face[2], face[0])] is_edge_reverted = [False, False, False] for k, edge in enumerate(edges): if edge[0] > edge[1]: edges[k] = (edge[1], edge[0]) is_edge_reverted[k] = True # First create the interior points in barycentric coordinates if n == 1: num_new_vertices = 0 else: bary = ( np.hstack( [[np.full(n - i - 1, i), np.arange(1, n - i)] for i in range(1, n)] ) / n ) bary = np.array([1.0 - bary[0] - bary[1], bary[1], bary[0]]) corner_verts = np.array([vertices[0][i] for i in corners]) vertices_cart = np.dot(corner_verts.T, bary).T if face_adjust: vertices_cart = face_adjust(face, bary, vertices_cart, corner_verts) vertices.append(vertices_cart) num_new_vertices = len(vertices[-1]) # translation table num_nodes_per_triangle = (n + 1) * (n + 2) // 2 tt = np.empty(num_nodes_per_triangle, dtype=int) # first the corners tt[0] = corner_nodes[corners[0]] tt[n] = corner_nodes[corners[1]] tt[num_nodes_per_triangle - 1] = corner_nodes[corners[2]] # then the edges. # edge 0 tt[1:n] = edge_nodes[edges[0]] if is_edge_reverted[0]: tt[1:n] = tt[1:n][::-1] # # edge 1 idx = 2 * n for k in range(n - 1): if is_edge_reverted[1]: tt[idx] = edge_nodes[edges[1]][n - 2 - k] else: tt[idx] = edge_nodes[edges[1]][k] idx += n - k - 1 # # edge 2 idx = n + 1 for k in range(n - 1): if is_edge_reverted[2]: tt[idx] = edge_nodes[edges[2]][k] else: tt[idx] = edge_nodes[edges[2]][n - 2 - k] idx += n - k # now the remaining interior nodes idx = n + 2 j = vertex_count for k in range(n - 2): for _ in range(n - k - 2): tt[idx] = j j += 1 idx += 1 idx += 2 cells += [tt[triangle_cells]] vertex_count += num_new_vertices vertices = np.concatenate(vertices) cells = np.concatenate(cells) return vertices, cells def insert_midpoints_edges(points, cells, cell_type): """Collect all unique edges, calculate and return points including midpoints on edges as well as the extended cells array.""" number_of_points = {"triangle": 3, "tetra": 4, "quad": 4, "hexahedron": 8} if cells.shape[1] != number_of_points[cell_type]: raise ValueError("Mismatch of cell type and shape of cells array.") if cell_type == "triangle": # k-th edge between cell points no. (ij[k]) ij = [[0, 1], [1, 2], [2, 0]] elif cell_type == "tetra": # k-th edge between cell points no. (ij[k]) ij = [[0, 1], [1, 2], [2, 0], [3, 0], [3, 1], [3, 2]] elif cell_type == "quad": # k-th edge between cell points no. (ij[k]) ij = [[0, 1], [1, 2], [2, 3], [3, 0]] elif cell_type == "hexahedron": # k-th edge between cell points no. (ij[k]) ij = [ [0, 1], [1, 2], [2, 3], [3, 0], [4, 5], [5, 6], [6, 7], [7, 4], [0, 4], [1, 5], [2, 6], [3, 7], ] else: raise TypeError("Cell type not implemented.") # obtain edges from cells (contains duplicates) edges = cells[:, ij] # sort points of edges edges_sorted = np.sort(edges.reshape(-1, 2), axis=1) # obtain unique edges and inverse mapping edges_unique, inverse = np.unique( edges_sorted, return_index=False, return_inverse=True, return_counts=False, axis=0, ) # calculate midpoints on edges as mean of edge-based pairs of points midpoints_on_edges = np.mean(points[edges_unique.T], axis=0) # create the additional cells array # add offset to point index for midpoints on edges cells_edges = inverse.reshape(len(cells), -1) + len(points) # vertical stack of points and horizontal stack of edges points_new = np.vstack((points, midpoints_on_edges)) cells_new = np.hstack((cells, cells_edges)) return points_new, cells_new meshzoo-0.9.2/src/meshzoo/_moebius.py000066400000000000000000000100451415713753400176470ustar00rootroot00000000000000import numpy as np def moebius( num_twists: int = 1, # How many twists are there in the 'paper'? nl: int = 60, # Number of nodes along the length of the strip nw: int = 11, # Number of nodes along the width of the strip (>= 2) variant: str = "classical", ): """Creates a simplistic triangular mesh on a slightly Möbius strip. The Möbius strip here deviates slightly from the ordinary geometry in that it is constructed in such a way that the two halves can be exchanged as to allow better comparison with the pseudo-Möbius geometry. The variant is either `'classical'` or `'smooth'`. The first is the classical Möbius band parametrization, the latter a smoothed variant matching `'pseudo'`. """ # The width of the strip width = 1.0 scale = 10.0 # radius of the strip when flattened out r = 1.0 # seam displacement alpha0 = 0.0 # pi / 2 # How flat the strip will be. # Positive values result in left-turning Möbius strips, negative in # right-turning ones. # Also influences the width of the strip. flatness = 1.0 # Generate suitable ranges for parametrization u_range = np.linspace(0.0, 2 * np.pi, num=nl, endpoint=False) v_range = np.linspace(-0.5 * width, 0.5 * width, num=nw) # Create the vertices. This is based on the parameterization # of the Möbius strip as given in # sin_u = np.sin(u_range) cos_u = np.cos(u_range) alpha = num_twists * 0.5 * u_range + alpha0 sin_alpha = np.sin(alpha) cos_alpha = np.cos(alpha) if variant == "classical": a = cos_alpha b = sin_alpha reverse_seam = num_twists % 2 == 1 elif variant == "smooth": # The fundamental difference with the ordinary Möbius band here are the # squares. # It is also possible to to abs() the respective sines and cosines, but # this results in a non-smooth manifold. a = np.copysign(cos_alpha ** 2, cos_alpha) b = np.copysign(sin_alpha ** 2, sin_alpha) reverse_seam = num_twists % 2 == 1 else: assert variant == "pseudo" a = cos_alpha ** 2 b = sin_alpha ** 2 reverse_seam = False nodes = ( scale * np.array( [ np.outer(a * cos_u, v_range) + r * cos_u[:, np.newaxis], np.outer(a * sin_u, v_range) + r * sin_u[:, np.newaxis], np.outer(b, v_range) * flatness, ] ) .reshape(3, -1) .T ) cells = _create_elements(nl, nw, reverse_seam) return nodes, cells def _create_elements(nl, nw, reverse_seam): cells = [] for i in range(nl - 1): for j in range(nw - 1): if (i + j) % 2 == 0: cells.append([i * nw + j, (i + 1) * nw + j + 1, i * nw + j + 1]) cells.append([i * nw + j, (i + 1) * nw + j, (i + 1) * nw + j + 1]) else: cells.append([i * nw + j, i * nw + j + 1, (i + 1) * nw + j]) cells.append([i * nw + j + 1, (i + 1) * nw + j, (i + 1) * nw + j + 1]) # close the geometry i = nl - 1 if reverse_seam: # Close the geometry upside down (odd Möbius fold) for j in range(nw - 1): if (i + j) % 2 == 0: cells.append([i * nw + j, (nw - 1) - (j + 1), i * nw + j + 1]) cells.append([i * nw + j, (nw - 1) - j, (nw - 1) - (j + 1)]) else: cells.append([i * nw + j, i * nw + j + 1, (nw - 1) - j]) cells.append([i * nw + j + 1, (nw - 1) - j, (nw - 1) - (j + 1)]) else: # Close the geometry upside up (even Möbius fold) for j in range(nw - 1): if (i + j) % 2 == 0: cells.append([i * nw + j, j + 1, i * nw + j + 1]) cells.append([i * nw + j, j, j + 1]) else: cells.append([i * nw + j, i * nw + j + 1, j]) cells.append([i * nw + j + 1, j, j + 1]) return np.array(cells) meshzoo-0.9.2/src/meshzoo/_ngon.py000066400000000000000000000006531415713753400171510ustar00rootroot00000000000000import numpy as np from ._helpers import _compose_from_faces def ngon(p: int, n: int, offset: float = np.pi / 2): x = np.linspace(offset, offset + 2 * np.pi, p, endpoint=False) corners = np.vstack( [ [[0.0, 0.0]], np.array([np.cos(x), np.sin(x)]).T, ] ) faces = [(0, k + 1, k + 2) for k in range(p - 1)] + [(0, p, 1)] return _compose_from_faces(corners, faces, n) meshzoo-0.9.2/src/meshzoo/_rectangle.py000066400000000000000000000121141415713753400201470ustar00rootroot00000000000000from __future__ import annotations import numpy as np from numpy.typing import ArrayLike # backwards compatibility def rectangle( x0: float, x1: float, y0: float, y1: float, nx: int, ny: int, ): x_range = np.linspace(x0, x1, nx + 1) y_range = np.linspace(y0, y1, ny + 1) return rectangle_tri(x_range, y_range) def rectangle_quad(x_range: ArrayLike, y_range: ArrayLike, cell_type: str = "quad4"): x_range = np.asarray(x_range) y_range = np.asarray(y_range) nx = len(x_range) ny = len(y_range) if cell_type == "quad4": points = np.array(np.meshgrid(x_range, y_range)).reshape(2, -1).T a = np.arange(nx * ny).reshape(ny, nx).T cells = ( np.array([a[:-1, :-1], a[1:, :-1], a[1:, 1:], a[:-1, 1:]]).reshape(4, -1).T ) elif cell_type == "quad8": k = 0 points_corner = np.array(np.meshgrid(x_range, y_range)).reshape(2, -1).T a_corner = np.arange(nx * ny).reshape(ny, nx).T k += a_corner.size x_mid = (x_range[:-1] + x_range[1:]) / 2 points_xmid = np.array(np.meshgrid(x_mid, y_range)).reshape(2, -1).T a_xmid = k + np.arange((nx - 1) * ny).reshape(ny, nx - 1).T k += a_xmid.size y_mid = (y_range[:-1] + y_range[1:]) / 2 points_ymid = np.array(np.meshgrid(x_range, y_mid)).reshape(2, -1).T a_ymid = k + np.arange(nx * (ny - 1)).reshape(ny - 1, nx).T points = np.row_stack([points_corner, points_xmid, points_ymid]) cells = ( np.array( [ a_corner[:-1, :-1], a_corner[1:, :-1], a_corner[1:, 1:], a_corner[:-1, 1:], a_xmid[:, :-1], a_ymid[1:, :], a_xmid[:, 1:], a_ymid[:-1, :], ] ) .reshape(8, -1) .T ) else: assert cell_type == "quad9" k = 0 points_corner = np.array(np.meshgrid(x_range, y_range)).reshape(2, -1).T a_corner = np.arange(nx * ny).reshape(ny, nx).T k += a_corner.size x_mid = (x_range[:-1] + x_range[1:]) / 2 points_xmid = np.array(np.meshgrid(x_mid, y_range)).reshape(2, -1).T a_xmid = k + np.arange((nx - 1) * ny).reshape(ny, nx - 1).T k += a_xmid.size y_mid = (y_range[:-1] + y_range[1:]) / 2 points_ymid = np.array(np.meshgrid(x_range, y_mid)).reshape(2, -1).T a_ymid = k + np.arange(nx * (ny - 1)).reshape(ny - 1, nx).T k += a_ymid.size points_center = np.array(np.meshgrid(x_mid, y_mid)).reshape(2, -1).T a_center = k + np.arange((nx - 1) * (ny - 1)).reshape(ny - 1, nx - 1).T points = np.row_stack([points_corner, points_xmid, points_ymid, points_center]) cells = ( np.array( [ a_corner[:-1, :-1], a_corner[1:, :-1], a_corner[1:, 1:], a_corner[:-1, 1:], a_xmid[:, :-1], a_ymid[1:, :], a_xmid[:, 1:], a_ymid[:-1, :], a_center, ] ) .reshape(9, -1) .T ) return points, cells def rectangle_tri(x_range: ArrayLike, y_range: ArrayLike, variant: str = "zigzag"): x_range = np.asarray(x_range) y_range = np.asarray(y_range) nx = len(x_range) ny = len(y_range) # Create the vertices. points = np.array(np.meshgrid(x_range, y_range)).reshape(2, -1).T a = np.arange(nx * ny).reshape(ny, nx).T # indices of corners # # c[3] c[2] # _____ # | | # |___| # # c[0] c[1] # c = [ a[:-1, :-1], a[1:, :-1], a[1:, 1:], a[:-1, 1:], ] if variant == "up": cells = [ [c[0], c[1], c[2]], [c[0], c[2], c[3]], ] elif variant == "down": cells = [ [c[0], c[1], c[3]], [c[1], c[2], c[3]], ] elif variant == "zigzag": # https://stackoverflow.com/a/68550456/353337 idx = np.ones((nx - 1, ny - 1), dtype=bool) idx[1::2, ::2] = False idx[::2, 1::2] = False cells = [ # up [c[0][idx], c[1][idx], c[2][idx]], [c[0][idx], c[2][idx], c[3][idx]], # down [c[0][~idx], c[1][~idx], c[3][~idx]], [c[1][~idx], c[2][~idx], c[3][~idx]], ] else: assert variant == "center" idx = np.ones(((nx - 1), (ny - 1)), dtype=bool) idx[: (nx - 1) // 2, : (ny - 1) // 2] = False idx[(nx - 1) // 2 :, (ny - 1) // 2 :] = False cells = [ # up [c[0][idx], c[1][idx], c[2][idx]], [c[0][idx], c[2][idx], c[3][idx]], # down [c[0][~idx], c[1][~idx], c[3][~idx]], [c[1][~idx], c[2][~idx], c[3][~idx]], ] cells = np.column_stack([np.array(c).reshape(3, -1) for c in cells]).T return points, cells meshzoo-0.9.2/src/meshzoo/_sphere.py000066400000000000000000000156741415713753400175070ustar00rootroot00000000000000import numpy as np from ._helpers import _compose_from_faces def uv_sphere(num_points_per_circle: int, num_circles: int, radius: float = 1.0): # Mesh parameters n_phi = num_points_per_circle n_theta = num_circles # Generate suitable ranges for parametrization phi_range = np.linspace(0.0, 2 * np.pi, num=n_phi, endpoint=False) theta_range = np.linspace( -np.pi / 2 + np.pi / (n_theta - 1), np.pi / 2 - np.pi / (n_theta - 1), num=n_theta - 2, ) # nodes in the circles of latitude (except poles) nodes = radius * np.array( [[0.0, 0.0, -1.0]] # south pole + [ [ np.cos(theta) * np.sin(phi), np.cos(theta) * np.cos(phi), np.sin(theta), ] for theta in theta_range for phi in phi_range ] + [[0.0, 0.0, 1.0]] # north pole ) south_pole_index = 0 north_pole_index = len(nodes) - 1 # create the elements (cells) num_cells = 2 * (n_theta - 2) * n_phi cells = [] # connections to south pole for i in range(n_phi - 1): cells.append([south_pole_index, i + 1, i + 2]) # close geometry cells.append([south_pole_index, n_phi, 1]) # non-pole elements for i in range(n_theta - 3): for j in range(n_phi - 1): cells += [ [i * n_phi + j + 2, i * n_phi + j + 1, (i + 1) * n_phi + j + 2], [i * n_phi + j + 1, (i + 1) * n_phi + j + 1, (i + 1) * n_phi + j + 2], ] # close the geometry for i in range(n_theta - 3): cells += [ [i * n_phi + 1, (i + 1) * n_phi, (i + 1) * n_phi + 1], [(i + 1) * n_phi + 1, (i + 1) * n_phi, (i + 2) * n_phi], ] # connections to the north pole for i in range(n_phi - 1): cells.append( [ i + 1 + n_phi * (n_theta - 3) + 1, i + n_phi * (n_theta - 3) + 1, north_pole_index, ] ) # close geometry cells.append( [ 0 + n_phi * (n_theta - 3) + 1, n_phi - 1 + n_phi * (n_theta - 3) + 1, north_pole_index, ] ) cells = np.array(cells) assert len(cells) == num_cells, "Wrong element count." return nodes, cells def geo_sphere(num_points_per_circle: int, num_circles: int, radius=1.0): # Mesh parameters n_phi = num_points_per_circle n_theta = num_circles # Generate suitable ranges for parametrization phi_range = np.linspace(0.0, 2 * np.pi, num=n_phi, endpoint=False) theta_range = np.linspace( -np.pi / 2 + np.pi / (n_theta - 1), np.pi / 2 - np.pi / (n_theta - 1), num=n_theta - 2, ) # nodes in the circles of latitude (except poles) nodes = radius * np.array( [[0.0, 0.0, -1.0]] # south pole + [ [ np.cos(theta) * np.sin(phi), np.cos(theta) * np.cos(phi), np.sin(theta), ] for theta in theta_range for phi in phi_range ] + [[0.0, 0.0, 1.0]] # north pole ) south_pole_index = 0 north_pole_index = len(nodes) - 1 # create the elements (cells) tri = [] quad = [] # connections to south pole for i in range(n_phi - 1): tri.append([south_pole_index, i + 1, i + 2]) # close geometry tri.append([south_pole_index, n_phi, 1]) # non-pole elements for i in range(n_theta - 3): for j in range(n_phi - 1): quad += [ [ i * n_phi + j + 1, i * n_phi + j + 2, (i + 1) * n_phi + j + 2, (i + 1) * n_phi + j + 1, ], ] # close the geometry for i in range(n_theta - 3): quad += [ [i * n_phi + 1, (i + 1) * n_phi + 1, (i + 2) * n_phi, (i + 1) * n_phi], ] # connections to the north pole for i in range(n_phi - 1): tri.append( [ i + 1 + n_phi * (n_theta - 3) + 1, i + n_phi * (n_theta - 3) + 1, north_pole_index, ] ) # close geometry tri.append( [ 0 + n_phi * (n_theta - 3) + 1, n_phi - 1 + n_phi * (n_theta - 3) + 1, north_pole_index, ] ) tri = np.array(tri) quad = np.array(quad) return nodes, tri, quad def tetra_sphere(n): corners = np.array( [ [2 * np.sqrt(2) / 3, 0.0, -1.0 / 3.0], [-np.sqrt(2) / 3, np.sqrt(2.0 / 3.0), -1.0 / 3.0], [-np.sqrt(2) / 3, -np.sqrt(2.0 / 3.0), -1.0 / 3.0], [0.0, 0.0, 1.0], ] ) # make sure the normals are pointing outwards faces = [(0, 2, 1), (0, 1, 3), (0, 3, 2), (1, 2, 3)] vertices, cells = _compose_from_faces(corners, faces, n) # push all nodes to the sphere norms = np.sqrt(np.einsum("ij,ij->i", vertices, vertices)) vertices = (vertices.T / norms).T return vertices, cells def octa_sphere(n: int): corners = np.array( [ [1.0, 0.0, 0.0], [-1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, 1.0], [0.0, 0.0, -1.0], ] ) faces = [ (0, 2, 4), (1, 4, 2), (1, 3, 4), (0, 4, 3), (0, 5, 2), (1, 2, 5), (1, 5, 3), (0, 3, 5), ] vertices, cells = _compose_from_faces(corners, faces, n) # push all nodes to the sphere norms = np.sqrt(np.einsum("ij,ij->i", vertices, vertices)) vertices = (vertices.T / norms).T return vertices, cells def icosa_sphere(n: int): assert n >= 1 # Start off with an isosahedron and refine. # Construction from # . # Create 12 vertices of a icosahedron. t = (1.0 + np.sqrt(5.0)) / 2.0 corners = np.array( [ [-1, +t, +0], [+1, +t, +0], [-1, -t, +0], [+1, -t, +0], # [+0, -1, +t], [+0, +1, +t], [+0, -1, -t], [+0, +1, -t], # [+t, +0, -1], [+t, +0, +1], [-t, +0, -1], [-t, +0, +1], ] ) faces = [ (0, 11, 5), (0, 5, 1), (0, 1, 7), (0, 7, 10), (0, 10, 11), (1, 5, 9), (5, 11, 4), (11, 10, 2), (10, 7, 6), (7, 1, 8), (3, 9, 4), (3, 4, 2), (3, 2, 6), (3, 6, 8), (3, 8, 9), (4, 9, 5), (2, 4, 11), (6, 2, 10), (8, 6, 7), (9, 8, 1), ] vertices, cells = _compose_from_faces(corners, faces, n) # push all nodes to the sphere norms = np.sqrt(np.einsum("ij,ij->i", vertices, vertices)) vertices = (vertices.T / norms).T return vertices, cells meshzoo-0.9.2/src/meshzoo/_triangle.py000066400000000000000000000016021415713753400200100ustar00rootroot00000000000000import numpy as np def triangle(n: int): # Create the mesh in barycentric coordinates bary = np.hstack( [ [ np.full(n - i + 1, i / n), # np.arange(n - i + 1) / n: np.linspace(0.0, (n - i + 1) / n, n - i + 1, endpoint=False), ] for i in range(n + 1) ] ) bary = np.array([1.0 - bary[0] - bary[1], bary[1], bary[0]]) # Some applications don't accept values like -1.4125e-16. bary[bary < 0.0] = 0.0 bary[bary > 1.0] = 1.0 cells = [] k = 0 for i in range(n): j = np.arange(n - i) cells.append(np.column_stack([k + j, k + j + 1, k + n - i + j + 1])) # j = j[:-1] cells.append(np.column_stack([k + j + 1, k + n - i + j + 2, k + n - i + j + 1])) k += n - i + 1 cells = np.vstack(cells) return bary, cells meshzoo-0.9.2/src/meshzoo/_tube.py000066400000000000000000000023241415713753400171440ustar00rootroot00000000000000import numpy as np def tube(length: float = 1.0, radius: float = 1.0, n: int = 30): # Number of points along the width of the strip (>= 2) # Choose it such that we have approximately square boxes. nw = int(round(length * n / (2 * np.pi * radius))) # Generate suitable ranges for parametrization u_range = np.linspace(0.0, 2 * np.pi, num=n, endpoint=False) v_range = np.linspace(-0.5 * length, 0.5 * length, num=nw) # Create the vertices. proto_points = np.dstack(np.meshgrid(u_range, v_range, indexing="ij")).reshape( -1, 2 ) points = np.column_stack( [ radius * np.cos(proto_points[:, 0]), radius * np.sin(proto_points[:, 0]), proto_points[:, 1], ] ) # create the elements (cells) cells = [] for i in range(n - 1): for j in range(nw - 1): cells.append([i * nw + j, (i + 1) * nw + j + 1, i * nw + j + 1]) cells.append([i * nw + j, (i + 1) * nw + j, (i + 1) * nw + j + 1]) # close the geometry for j in range(nw - 1): cells.append([(n - 1) * nw + j, j + 1, (n - 1) * nw + j + 1]) cells.append([(n - 1) * nw + j, j, j + 1]) return points, np.array(cells) meshzoo-0.9.2/tests/000077500000000000000000000000001415713753400143625ustar00rootroot00000000000000meshzoo-0.9.2/tests/__init__.py000066400000000000000000000000001415713753400164610ustar00rootroot00000000000000meshzoo-0.9.2/tests/helpers.py000066400000000000000000000015371415713753400164040ustar00rootroot00000000000000import math import numpy as np def is_near_equal(a, b, tol=1.0e-12): return np.allclose(a, b, rtol=0.0, atol=tol) def signed_simplex_volumes(coords, cells): assert len(coords.shape) == 2 assert len(cells.shape) == 2 assert ( coords.shape[1] + 1 == cells.shape[1] ), "Signed areas only make sense for n-simplices in in nD." # bc = coords[:, cells] # return np.cross((bc[:, :, 1] - bc[:, :, 0]).T, (bc[:, :, 2] - bc[:, :, 0]).T) # https://en.wikipedia.org/wiki/Simplex#Volume cp = coords[cells] n = coords.shape[1] # append ones; this appends a column instead of a row as suggested by # wikipedia, but that doesn't change the determinant cp1 = np.concatenate([cp, np.ones(cp.shape[:-1] + (1,))], axis=-1) sign = -1 if n % 2 == 1 else 1 return sign * np.linalg.det(cp1) / math.factorial(n) meshzoo-0.9.2/tests/test_ball.py000066400000000000000000000011701415713753400167040ustar00rootroot00000000000000import meshzoo from .helpers import signed_simplex_volumes def test_ball_hexa(): points, cells = meshzoo.ball_hexa(10) # import meshio # meshio.Mesh(points, {"hexahedron": cells}).write("ball-hexa.vtk") assert len(points) == 1331 assert len(cells) == 1000 def test_ball_tetra(): points, cells = meshzoo.ball_tetra(10) # import meshio # meshio.Mesh(points, {"tetra": cells}).write("ball-tetra.vtk") assert len(points) == 1331 assert len(cells) == 5000 def test_positive_volumes(): points, cells = meshzoo.ball_tetra(2) assert (signed_simplex_volumes(points, cells) > 0.0).all() meshzoo-0.9.2/tests/test_cube.py000066400000000000000000000062261415713753400167170ustar00rootroot00000000000000import numpy as np import meshzoo from .helpers import signed_simplex_volumes def test_positive_volumes(): x_range = np.linspace(0.0, 1.0, 5) y_range = np.linspace(0.0, 1.0, 5) z_range = np.linspace(0.0, 1.0, 5) points, cells = meshzoo.cube_tetra(x_range, y_range, z_range) assert np.all(signed_simplex_volumes(points, cells) > 0.0) def test_cube_tetra(): x_range = np.linspace(0.0, 1.0, 11) y_range = np.linspace(0.0, 1.0, 11) z_range = np.linspace(0.0, 1.0, 11) points, cells = meshzoo.cube_tetra(x_range, y_range, z_range) assert len(points) == 1331 assert len(cells) == 5000 def test_cube_tetra2(): x_range = np.linspace(0.0, 1.0, 3) y_range = np.linspace(0.0, 1.0, 3) z_range = np.linspace(0.0, 1.0, 3) points, cells = meshzoo.cube_tetra(x_range, y_range, z_range) assert len(points) == 27 assert all(np.sum(points, axis=0) == [13.5, 13.5, 13.5]) assert len(cells) == 40 def test_cube_tetra3(): x_range = [0.0, 1.0] y_range = [0.0, 0.5, 1.0] z_range = [0.0, 0.3, 0.7, 1.0] points, cells = meshzoo.cube_tetra(x_range, y_range, z_range) assert len(points) == 24 assert all(np.sum(points, axis=0) == [12.0, 12.0, 12.0]) assert cells.tolist() == [ [0, 1, 2, 6], [12, 13, 14, 18], [8, 9, 10, 14], [1, 3, 2, 9], [13, 15, 14, 21], [9, 11, 10, 17], [1, 2, 6, 9], [13, 14, 18, 21], [9, 10, 14, 17], [1, 6, 7, 9], [13, 18, 19, 21], [9, 14, 15, 17], [2, 6, 9, 8], [14, 18, 21, 20], [10, 14, 17, 16], [12, 13, 6, 14], [8, 9, 2, 10], [20, 21, 14, 22], [13, 15, 9, 14], [9, 11, 5, 10], [21, 23, 17, 22], [13, 14, 9, 6], [9, 10, 5, 2], [21, 22, 17, 14], [13, 6, 9, 7], [9, 2, 5, 3], [21, 14, 17, 15], [14, 6, 8, 9], [10, 2, 4, 5], [22, 14, 16, 17], ] def test_cube_hexa(): x_range = np.linspace(0.0, 1.0, 11) y_range = np.linspace(0.0, 1.0, 11) z_range = np.linspace(0.0, 1.0, 11) points, cells = meshzoo.cube_hexa(x_range, y_range, z_range) assert len(points) == 1331 assert len(cells) == 1000 # import meshio # meshio.Mesh(points, {"hexahedron": cells}).write("cube-hexa.vtk") def test_cube_hexa2(): x_range = np.linspace(0.0, 1.0, 3) y_range = np.linspace(0.0, 1.0, 3) z_range = np.linspace(0.0, 1.0, 3) points, cells = meshzoo.cube_hexa(x_range, y_range, z_range) assert len(points) == 27 assert all(np.sum(points, axis=0) == [13.5, 13.5, 13.5]) assert len(cells) == 8 def test_cube_hexa3(): x_range = [0.0, 1.0] y_range = [0.0, 0.5, 1.0] z_range = [0.0, 0.3, 0.7, 1.0] points, cells = meshzoo.cube_hexa(x_range, y_range, z_range) assert len(points) == 24 assert all(np.sum(points, axis=0) == [12.0, 12.0, 12.0]) assert cells.tolist() == [ [0, 1, 3, 2, 6, 7, 9, 8], [6, 7, 9, 8, 12, 13, 15, 14], [12, 13, 15, 14, 18, 19, 21, 20], [2, 3, 5, 4, 8, 9, 11, 10], [8, 9, 11, 10, 14, 15, 17, 16], [14, 15, 17, 16, 20, 21, 23, 22], ] meshzoo-0.9.2/tests/test_disk.py000066400000000000000000000007251415713753400167310ustar00rootroot00000000000000import meshzoo from .helpers import signed_simplex_volumes def test_disk(): points, cells = meshzoo.disk(9, 8) meshzoo.save2d("4gon_disk.svg", points, cells) assert len(points) == 325 assert len(cells) == 576 assert (signed_simplex_volumes(points, cells) > 0.0).all() def test_disk_quad(): points, cells = meshzoo.disk_quad(10) # meshzoo.save2d("disk-quad.svg", points, cells) assert len(points) == 121 assert len(cells) == 100 meshzoo-0.9.2/tests/test_midpointsedges.py000066400000000000000000000032031415713753400210070ustar00rootroot00000000000000import numpy as np import meshzoo def test_midpoints_edges_tri(): points, cells = meshzoo.rectangle_tri( np.linspace(0.0, 1.0, 2), np.linspace(0.0, 1.0, 2) ) assert len(points) == 4 assert cells.shape == (2, 3) points_new, cells_new = meshzoo.insert_midpoints_edges( points, cells, cell_type="triangle" ) assert len(points_new) == 9 assert cells_new.shape == (2, 6) def test_midpoints_edges_tetra(): ls = np.linspace(0.0, 1.0, 2) points, cells = meshzoo.cube_tetra(ls, ls, ls) assert len(points) == 8 assert cells.shape == (5, 4) points_new, cells_new = meshzoo.insert_midpoints_edges( points, cells, cell_type="tetra" ) assert len(points_new) == 26 assert cells_new.shape == (5, 10) def test_midpoints_edges_quad(): ls = np.linspace(0.0, 1.0, 3) points, cells = meshzoo.rectangle_quad(ls, ls) assert len(points) == 9 assert cells.shape == (4, 4) points_new, cells_new = meshzoo.insert_midpoints_edges( points, cells, cell_type="quad" ) assert len(points_new) == 21 assert cells_new.shape == (4, 8) def test_midpoints_edges_hexa(): ls = np.linspace(0.0, 1.0, 3) points, cells = meshzoo.cube_hexa(ls, ls, ls) assert len(points) == 27 assert cells.shape == (8, 8) points_new, cells_new = meshzoo.insert_midpoints_edges( points, cells, cell_type="hexahedron" ) assert len(points_new) == 81 assert cells_new.shape == (8, 20) if __name__ == "__main__": test_midpoints_edges_tri() test_midpoints_edges_tetra() test_midpoints_edges_quad() test_midpoints_edges_hexa() meshzoo-0.9.2/tests/test_moebius.py000066400000000000000000000051201415713753400174340ustar00rootroot00000000000000import numpy as np import pytest import meshzoo from .helpers import is_near_equal @pytest.mark.parametrize( "num_twists, num_points, num_cells, ref1, ref2", [ [1, 5890, 11400, [0, 0, 0], [2753575 / 9.0, 2724125 / 9.0, 58900 / 3.0]], [2, 5890, 11400, [0, 0, 0], [2797750 / 9.0, 2679950 / 9.0, 58900 / 3.0]], ], ) def test_moebius(num_twists, num_points, num_cells, ref1, ref2): points, cells = meshzoo.moebius(num_twists, 190, 31, variant="smooth") assert len(points) == num_points assert len(cells) == num_cells assert is_near_equal(np.sum(points, axis=0), ref1, tol=1.0e-10) sum_points2 = np.sum(points ** 2, axis=0) assert np.allclose(sum_points2, ref2, rtol=1.0e-12, atol=0.0) @pytest.mark.parametrize( "num_twists, num_points, num_cells, ref1, ref2", [ [ 1, 5700, 11020, [0, 0, 0], [[296107.21982759, 292933.72844828, 19040.94827586]], ], [ 2, 5700, 11020, [0, 0, 0], [[300867.45689655, 288173.49137931, 19040.94827586]], ], ], ) def test_moebius2(num_twists, num_points, num_cells, ref1, ref2): points, cells = meshzoo.moebius( nl=190, nw=30, num_twists=num_twists, variant="smooth" ) assert len(points) == num_points assert len(cells) == num_cells assert is_near_equal(np.sum(points, axis=0), ref1, tol=1.0e-10) sum_points2 = np.sum(points ** 2, axis=0) assert np.allclose(sum_points2, ref2, rtol=1.0e-12, atol=0.0) @pytest.mark.parametrize( "num_twists, num_points, num_cells, ref1, ref2", [ [1, 1000, 1800, [0, 0, 0], [1418750 / 27.0, 1418750 / 27.0, 137500 / 27.0]], [2, 1000, 1800, [0, 0, 0], [484375 / 9.0, 1384375 / 27.0, 137500 / 27.0]], ], ) def test_moebius3(num_twists, num_points, num_cells, ref1, ref2): points, cells = meshzoo.moebius(num_twists, 100, 10, variant="classical") assert len(points) == num_points assert len(cells) == num_cells assert is_near_equal(np.sum(points, axis=0), ref1, tol=1.0e-10) sum_points2 = np.sum(points ** 2, axis=0) assert np.allclose(sum_points2, ref2, rtol=1.0e-12, atol=0.0) def test_pseudomoebius(): points, cells = meshzoo.moebius(nl=190, nw=31, variant="pseudo") assert len(points) == 5890 assert len(cells) == 11400 assert is_near_equal(np.sum(points, axis=0), [0, 0, 0], tol=1.0e-10) sum_points2 = np.sum(points ** 2, axis=0) ref2 = [2753575 / 9.0, 2724125 / 9.0, 58900 / 3.0] assert np.allclose(sum_points2, ref2, rtol=1.0e-12, atol=0.0) meshzoo-0.9.2/tests/test_ngon.py000066400000000000000000000005411415713753400167340ustar00rootroot00000000000000import numpy as np import meshzoo from .helpers import signed_simplex_volumes def test_ngon(): points, cells = meshzoo.ngon(9, 8) # meshzoo.save2d("9gon.svg", points, cells) assert len(points) == 325 assert len(cells) == 576 assert np.all(signed_simplex_volumes(points, cells) > 0.0) if __name__ == "__main__": test_ngon() meshzoo-0.9.2/tests/test_rectangle.py000066400000000000000000000106321415713753400177410ustar00rootroot00000000000000import numpy as np import meshzoo from .helpers import is_near_equal, signed_simplex_volumes def test_up(): x_range = np.linspace(0.0, 1.0, 11) y_range = np.linspace(0.0, 1.0, 11) points, cells = meshzoo.rectangle_tri(x_range, y_range, variant="up") assert len(points) == 121 assert is_near_equal(np.sum(points, axis=0), [60.5, 60.5]) assert len(cells) == 200 assert np.all(signed_simplex_volumes(points, cells) > 0.0) def test_up2(): x_range = np.linspace(0.0, 1.0, 3) y_range = np.linspace(0.0, 1.0, 2) points, cells = meshzoo.rectangle_tri(x_range, y_range, variant="up") assert len(points) == 6 assert is_near_equal(np.sum(points, axis=0), [3.0, 3.0]) assert len(cells) == 4 assert list(cells[0]) == [0, 1, 4] assert list(cells[2]) == [0, 4, 3] assert np.all(signed_simplex_volumes(points, cells) > 0.0) def test_zigzag(): x_range = np.linspace(0.0, 1.0, 11) y_range = np.linspace(0.0, 1.0, 11) points, cells = meshzoo.rectangle_tri(x_range, y_range, variant="zigzag") assert len(points) == 121 assert is_near_equal(np.sum(points, axis=0), [60.5, 60.5]) assert len(cells) == 200 assert np.all(signed_simplex_volumes(points, cells) > 0.0) def test_zigzag2(): x_range = np.linspace(0.0, 1.0, 2) y_range = np.linspace(0.0, 1.0, 2) points, cells = meshzoo.rectangle_tri(x_range, y_range, variant="zigzag") assert len(points) == 4 assert is_near_equal(np.sum(points, axis=0), [2.0, 2.0]) assert len(cells) == 2 assert np.all(signed_simplex_volumes(points, cells) > 0.0) def test_zigzag3(): x_range = np.linspace(0.0, 1.0, 3) y_range = np.linspace(0.0, 1.0, 2) points, cells = meshzoo.rectangle_tri(x_range, y_range, variant="zigzag") assert len(points) == 6 assert is_near_equal(np.sum(points, axis=0), [3.0, 3.0]) assert len(cells) == 4 assert list(cells[0]) == [0, 1, 4] assert list(cells[2]) == [1, 2, 4] assert np.all(signed_simplex_volumes(points, cells) > 0.0) def test_down(): x_range = np.linspace(0.0, 1.0, 5) y_range = np.linspace(0.0, 1.0, 4) points, cells = meshzoo.rectangle_tri(x_range, y_range, variant="down") assert len(points) == 20 assert len(cells) == 24 assert np.all(signed_simplex_volumes(points, cells) > 0.0) # meshzoo.show2d(points, cells) def test_center(): x_range = np.linspace(0.0, 1.0, 11) y_range = np.linspace(0.0, 1.0, 9) points, cells = meshzoo.rectangle_tri(x_range, y_range, variant="center") meshzoo.show2d(points, cells) assert len(points) == 99 assert len(cells) == 160 assert np.all(signed_simplex_volumes(points, cells) > 0.0) def test_quad1(): x_range = np.linspace(0.0, 1.0, 11) y_range = np.linspace(0.0, 1.0, 11) points, cells = meshzoo.rectangle_quad(x_range, y_range) assert len(points) == 121 assert is_near_equal(np.sum(points, axis=0), [60.5, 60.5]) assert len(cells) == 100 # meshzoo.save2d("rectangle-quad.svg", points, cells) def test_quad2(): x_range = np.linspace(0.0, 1.0, 3) y_range = np.linspace(0.0, 1.0, 2) points, cells = meshzoo.rectangle_quad(x_range, y_range) assert len(points) == 6 assert is_near_equal(np.sum(points, axis=0), [3.0, 3.0]) assert np.all(cells == [[0, 1, 4, 3], [1, 2, 5, 4]]) def test_quad3(): x_range = np.linspace(0.0, 1.0, 3) y_range = np.linspace(0.0, 1.0, 3) points, cells = meshzoo.rectangle_quad(x_range, y_range) assert len(points) == 9 assert np.all(cells == [[0, 1, 4, 3], [3, 4, 7, 6], [1, 2, 5, 4], [4, 5, 8, 7]]) def test_quad8(): x_range = np.linspace(0.0, 1.0, 3) y_range = np.linspace(0.0, 1.0, 2) points, cells = meshzoo.rectangle_quad(x_range, y_range, cell_type="quad8") assert len(points) == 13 print(cells.tolist()) assert np.all(cells == [[0, 1, 4, 3, 6, 11, 8, 10], [1, 2, 5, 4, 7, 12, 9, 11]]) def test_quad9(): x_range = np.linspace(0.0, 1.0, 4) y_range = np.linspace(0.0, 1.0, 3) points, cells = meshzoo.rectangle_quad(x_range, y_range, cell_type="quad9") assert len(points) == 35 print(cells.tolist()) assert np.all( cells == [ [0, 1, 5, 4, 12, 22, 15, 21, 29], [4, 5, 9, 8, 15, 26, 18, 25, 32], [1, 2, 6, 5, 13, 23, 16, 22, 30], [5, 6, 10, 9, 16, 27, 19, 26, 33], [2, 3, 7, 6, 14, 24, 17, 23, 31], [6, 7, 11, 10, 17, 28, 20, 27, 34], ] ) meshzoo-0.9.2/tests/test_sphere.py000066400000000000000000000051661415713753400172710ustar00rootroot00000000000000import numpy as np import meshzoo from .helpers import is_near_equal def _compute_cells_normals_dir(points, cells): pc = points[cells] midpoints = np.sum(pc, axis=1) / 3.0 nrm = np.sqrt(np.einsum("ij,ij->i", midpoints, midpoints)) normals = (midpoints.T / nrm).T cross = np.cross( pc[:, 1, :] - pc[:, 0, :], pc[:, 2, :] - pc[:, 0, :], ) return np.einsum("ij,ij->i", normals, cross) def test_uv_sphere(num_points_per_circle=20, num_circles=10): points, cells = meshzoo.uv_sphere(num_points_per_circle, num_circles) assert len(points) == 162 assert is_near_equal(np.sum(points, axis=0), [0.0, 0.0, 0.0]) assert len(cells) == 320 assert (_compute_cells_normals_dir(points, cells) > 0.0).all() assert np.all(np.abs(np.einsum("ij,ij->i", points, points) - 1.0) < 1.0e-10) def test_geo_sphere(num_points_per_circle=20, num_circles=10): points, tri, quad = meshzoo.geo_sphere(num_points_per_circle, num_circles) # import meshio # meshio.write_points_cells("geo-sphere.vtk", points, {"triangle": tri, "quad": quad}) assert len(points) == 162 assert is_near_equal(np.sum(points, axis=0), [0.0, 0.0, 0.0]) assert len(tri) == 40 assert len(quad) == 140 # assert (_compute_cells_normals_dir(points, cells) > 0.0).all() assert np.all(np.abs(np.einsum("ij,ij->i", points, points) - 1.0) < 1.0e-10) def test_tetra_sphere(n=16): points, cells = meshzoo.tetra_sphere(n) # import meshio # meshio.write_points_cells("out.vtk", points, {"triangle": cells}) assert len(points) == 514 assert is_near_equal(np.sum(points, axis=0), [0.0, 0.0, 0.0]) assert len(cells) == 1024 assert (_compute_cells_normals_dir(points, cells) > 0.0).all() assert np.all(np.abs(np.einsum("ij,ij->i", points, points) - 1.0) < 1.0e-10) def test_octa_sphere(n=16): points, cells = meshzoo.octa_sphere(n) assert len(points) == 1026 assert is_near_equal(np.sum(points, axis=0), [0.0, 0.0, 0.0]) assert len(cells) == 2048 assert (_compute_cells_normals_dir(points, cells) > 0.0).all() assert np.all(np.abs(np.einsum("ij,ij->i", points, points) - 1.0) < 1.0e-10) def test_icosa_sphere(n=16): points, cells = meshzoo.icosa_sphere(n) # import meshio # meshio.write_points_cells("out.vtk", points, {"triangle": cells}) assert len(points) == 2562 assert is_near_equal(np.sum(points, axis=0), [0.0, 0.0, 0.0]) assert len(cells) == 5120 assert (_compute_cells_normals_dir(points, cells) > 0.0).all() assert np.all(np.abs(np.einsum("ij,ij->i", points, points) - 1.0) < 1.0e-10) if __name__ == "__main__": test_geo_sphere() meshzoo-0.9.2/tests/test_triangle.py000066400000000000000000000024131415713753400176000ustar00rootroot00000000000000import numpy as np import meshzoo from .helpers import is_near_equal, signed_simplex_volumes def _get_points(bary): corners = np.array( [[0.0, -0.5 * np.sqrt(3.0), +0.5 * np.sqrt(3.0)], [1.0, -0.5, -0.5]] ) return np.dot(corners, bary).T def test_triangle(): bary, cells = meshzoo.triangle(4) assert len(bary.T) == 15 assert is_near_equal(np.sum(_get_points(bary), axis=0), [0.0, 0.0]) assert len(cells) == 16 # make sure the order of the nodes in each cell is counterclockwise corner_coords = np.array([[0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]) coords = np.dot(corner_coords, bary) assert np.all(signed_simplex_volumes(coords.T, cells) > 0.0) def test_plot2d(): bary, cells = meshzoo.triangle(4) meshzoo.show2d(_get_points(bary), cells) def test_edges(): _, cells = meshzoo.triangle(2) edges_nodes, edges_cells = meshzoo.create_edges(cells) assert np.all( edges_nodes == [[0, 1], [0, 3], [1, 2], [1, 3], [1, 4], [2, 4], [3, 4], [3, 5], [4, 5]] ) assert np.all(edges_cells == [[3, 1, 0], [5, 4, 2], [6, 3, 4], [8, 7, 6]]) if __name__ == "__main__": points, cells = meshzoo.triangle(5000) # import meshio # meshio.write_points_cells('triangle.vtk', points, {'triangle': cells}) meshzoo-0.9.2/tests/test_tube.py000066400000000000000000000003741415713753400167360ustar00rootroot00000000000000import numpy as np import meshzoo from .helpers import is_near_equal def test_tube(): points, cells = meshzoo.tube(n=10) assert len(points) == 20 assert is_near_equal(np.sum(points, axis=0), [0.0, 0.0, 0.0]) assert len(cells) == 20 meshzoo-0.9.2/tox.ini000066400000000000000000000002721415713753400145340ustar00rootroot00000000000000[tox] envlist = py3 isolated_build = True [testenv] deps = pytest pytest-codeblocks pytest-cov pytest-randomly extras = all commands = pytest {posargs} --codeblocks