pax_global_header00006660000000000000000000000064141342520500014506gustar00rootroot0000000000000052 comment=0f907a014f2caf517f8eaeb3067f136d9afb6ee1 dmsh-0.2.18/000077500000000000000000000000001413425205000125315ustar00rootroot00000000000000dmsh-0.2.18/.codecov.yml000066400000000000000000000000141413425205000147470ustar00rootroot00000000000000comment: no dmsh-0.2.18/.flake8000066400000000000000000000001531413425205000137030ustar00rootroot00000000000000[flake8] ignore = E203, E266, E501, W503 max-line-length = 80 max-complexity = 18 select = B,C,E,F,W,T4,B9 dmsh-0.2.18/.github/000077500000000000000000000000001413425205000140715ustar00rootroot00000000000000dmsh-0.2.18/.github/workflows/000077500000000000000000000000001413425205000161265ustar00rootroot00000000000000dmsh-0.2.18/.github/workflows/ci.yml000066400000000000000000000015031413425205000172430ustar00rootroot00000000000000name: 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 dmsh --cov-report xml --cov-report term - uses: codecov/codecov-action@v1 if: ${{ matrix.python-version == '3.9' }} dmsh-0.2.18/.gitignore000066400000000000000000000001641413425205000145220ustar00rootroot00000000000000*.pyc *.swp *.prof MANIFEST README.rst dist/ build/ .coverage .cache/ *.egg-info/ .pytest_cache/ .tox/ coverage.xml dmsh-0.2.18/.pre-commit-config.yaml000066400000000000000000000004531413425205000170140ustar00rootroot00000000000000repos: - repo: https://github.com/PyCQA/isort rev: 5.9.3 hooks: - id: isort - repo: https://github.com/psf/black rev: 21.8b0 hooks: - id: black language_version: python3 - repo: https://github.com/PyCQA/flake8 rev: 3.9.2 hooks: - id: flake8 dmsh-0.2.18/LICENSE000066400000000000000000001045161413425205000135450ustar00rootroot00000000000000 GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The GNU General Public License is a free, copyleft license for software and other kinds of works. The licenses for most software and other practical works are designed to take away your freedom to share and change the works. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program--to make sure it remains free software for all its users. We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors. You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for them if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs, and that you know you can do these things. To protect your rights, we need to prevent others from denying you these rights or asking you to surrender the rights. Therefore, you have certain responsibilities if you distribute copies of the software, or if you modify it: responsibilities to respect the freedom of others. For example, if you distribute copies of such a program, whether gratis or for a fee, you must pass on to the recipients the same freedoms that you received. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights. Developers that use the GNU GPL protect your rights with two steps: (1) assert copyright on the software, and (2) offer you this License giving you legal permission to copy, distribute and/or modify it. For the developers' and authors' protection, the GPL clearly explains that there is no warranty for this free software. For both users' and authors' sake, the GPL requires that modified versions be marked as changed, so that their problems will not be attributed erroneously to authors of previous versions. Some devices are designed to deny users access to install or run modified versions of the software inside them, although the manufacturer can do so. This is fundamentally incompatible with the aim of protecting users' freedom to change the software. The systematic pattern of such abuse occurs in the area of products for individuals to use, which is precisely where it is most unacceptable. Therefore, we have designed this version of the GPL to prohibit the practice for those products. If such problems arise substantially in other domains, we stand ready to extend this provision to those domains in future versions of the GPL, as needed to protect the freedom of users. Finally, every program is threatened constantly by software patents. States should not allow patents to restrict development and use of software on general-purpose computers, but in those that do, we wish to avoid the special danger that patents applied to a free program could make it effectively proprietary. To prevent this, the GPL assures that patents cannot be used to render the program non-free. The precise terms and conditions for copying, distribution and modification follow. TERMS AND CONDITIONS 0. Definitions. "This License" refers to version 3 of the GNU General Public License. "Copyright" also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. "The Program" refers to any copyrightable work licensed under this License. Each licensee is addressed as "you". "Licensees" and "recipients" may be individuals or organizations. To "modify" a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a "modified version" of the earlier work or a work "based on" the earlier work. A "covered work" means either the unmodified Program or a work based on the Program. To "propagate" a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To "convey" a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays "Appropriate Legal Notices" to the extent that it includes a convenient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the interface presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion. 1. Source Code. The "source code" for a work means the preferred form of the work for making modifications to it. "Object code" means any non-source form of a work. A "Standard Interface" means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The "System Libraries" of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A "Major Component", in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The "Corresponding Source" for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work's System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynamically linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work. 2. Basic Permissions. All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited permission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sublicensing is not allowed; section 10 makes it unnecessary. 3. Protecting Users' Legal Rights From Anti-Circumvention Law. No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technological measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the work's users, your or third parties' legal rights to forbid circumvention of technological measures. 4. Conveying Verbatim Copies. You may convey verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with section 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee. 5. Conveying Modified Source Versions. You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: a) The work must carry prominent notices stating that you modified it, and giving a relevant date. b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to "keep intact all notices". c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 additional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; however, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an "aggregate" if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation's users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate. 6. Conveying Non-Source Forms. You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: a) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A "User Product" is either (1) a "consumer product", which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, "normally used" refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. "Installation Information" for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying. 7. Additional Terms. "Additional permissions" are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own removal in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or b) Requiring preservation of specified reasonable legal notices or author attributions in that material or in the Appropriate Legal Notices displayed by works containing it; or c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or d) Limiting the use for publicity purposes of names of licensors or authors of the material; or e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered "further restrictions" within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way. 8. Termination. You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, you do not qualify to receive new licenses for the same material under section 10. 9. Acceptance Not Required for Having Copies. You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so. 10. Automatic Licensing of Downstream Recipients. Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An "entity transaction" is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party's predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it. 11. Patents. A "contributor" is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor's "contributor version". A contributor's "essential patent claims" are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, "control" includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contributor's essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a "patent license" is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To "grant" such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. "Knowingly relying" means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient's use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is "discriminatory" if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law. 12. No Surrender of Others' Freedom. If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program. 13. Use with the GNU Affero General Public License. Notwithstanding any other provision of this License, you have permission to link or combine any covered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such. 14. Revised Versions of this License. The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License "or any later version" applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy's public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obligations are imposed on any author or copyright holder as a result of your choosing to follow a later version. 15. Disclaimer of Warranty. THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 16. Limitation of Liability. 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. Copyright (C) This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 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 General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Also add information on how to contact you by electronic and paper mail. If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode: Copyright (C) This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, your program's commands might be different; for a GUI interface, you would use an "about box". You should also get your employer (if you work as a programmer) or school, if any, to sign a "copyright disclaimer" for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see . The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read . dmsh-0.2.18/README.md000066400000000000000000000233561413425205000140210ustar00rootroot00000000000000

dmsh

The worst mesh generator you'll ever use.

[![PyPi Version](https://img.shields.io/pypi/v/dmsh.svg?style=flat-square)](https://pypi.org/project/dmsh/) [![Packaging status](https://repology.org/badge/tiny-repos/python:dmsh.svg)](https://repology.org/project/python:dmsh/versions) [![PyPI pyversions](https://img.shields.io/pypi/pyversions/dmsh.svg?style=flat-square)](https://pypi.org/project/dmsh/) [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.4728039.svg?style=flat-square)](https://doi.org/10.5281/zenodo.4728039) [![GitHub stars](https://img.shields.io/github/stars/nschloe/dmsh.svg?style=flat-square&logo=github&label=Stars&logoColor=white)](https://github.com/nschloe/dmsh) [![PyPi downloads](https://img.shields.io/pypi/dm/dmsh.svg?style=flat-square)](https://pypistats.org/packages/dmsh) [![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/dmsh/ci?style=flat-square)](https://github.com/nschloe/dmsh/actions?query=workflow%3Aci) [![codecov](https://img.shields.io/codecov/c/github/nschloe/dmsh.svg?style=flat-square)](https://app.codecov.io/gh/nschloe/dmsh) [![LGTM](https://img.shields.io/lgtm/grade/python/github/nschloe/dmsh.svg?style=flat-square)](https://lgtm.com/projects/g/nschloe/dmsh) [![Code style: black](https://img.shields.io/badge/code%20style-black-000000.svg?style=flat-square)](https://github.com/psf/black) Inspired by [distmesh](http://persson.berkeley.edu/distmesh/), dmsh can be slow, requires a lot of memory, and isn't terribly robust either. On the plus side, - it's got a user-friendly interface, - is pure Python (and hence easily installable on any system), and - it produces pretty high-quality meshes. Combined with [optimesh](https://github.com/nschloe/optimesh), dmsh produces the highest-quality 2D meshes in the west. ### Examples #### Primitives | circle | circle | circle | | :-----------------------------------------------------------------------------: | :--------------------------------------------------------------------------------: | :------------------------------------------------------------------------------: | ```python import dmsh import meshio import optimesh geo = dmsh.Circle([0.0, 0.0], 1.0) X, cells = dmsh.generate(geo, 0.1) # optionally optimize the mesh X, cells = optimesh.optimize_points_cells(X, cells, "CVT (full)", 1.0e-10, 100) # visualize the mesh dmsh.helpers.show(X, cells, geo) # and write it to a file meshio.Mesh(X, {"triangle": cells}).write("circle.vtk") ``` ```python import dmsh geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0) X, cells = dmsh.generate(geo, 0.1) ``` ```python import dmsh geo = dmsh.Polygon( [ [0.0, 0.0], [1.1, 0.0], [1.2, 0.5], [0.7, 0.6], [2.0, 1.0], [1.0, 2.0], [0.5, 1.5], ] ) X, cells = dmsh.generate(geo, 0.1) ``` #### Combinations ##### Difference | | | | | :--------------------------------------------------------------: | :----------------------------------------------------------------: | :-----------------------------------------------------------------------------------: | ```python import dmsh geo = dmsh.Circle([-0.5, 0.0], 1.0) - dmsh.Circle([+0.5, 0.0], 1.0) X, cells = dmsh.generate(geo, 0.1) ``` ```python import dmsh geo = dmsh.Circle([0.0, 0.0], 1.0) - dmsh.Polygon([[0.0, 0.0], [1.5, 0.4], [1.5, -0.4]]) X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10) ``` The following example uses a nonconstant edge length; it depends on the distance to the circle `c`. ```python import dmsh import numpy as np r = dmsh.Rectangle(-1.0, +1.0, -1.0, +1.0) c = dmsh.Circle([0.0, 0.0], 0.3) geo = r - c X, cells = dmsh.generate(geo, lambda pts: np.abs(c.dist(pts)) / 5 + 0.05, tol=1.0e-10) ``` ##### Union | | | | | :-----------------------------------------------------------------------: | :--------------------------------------------------------------------------: | :-----------------------------------------------------------------------------: | ```python import dmsh geo = dmsh.Circle([-0.5, 0.0], 1.0) + dmsh.Circle([+0.5, 0.0], 1.0) X, cells = dmsh.generate(geo, 0.15) ``` ```python import dmsh geo = dmsh.Rectangle(-1.0, +0.5, -1.0, +0.5) + dmsh.Rectangle(-0.5, +1.0, -0.5, +1.0) X, cells = dmsh.generate(geo, 0.15) ``` ```python import dmsh import numpy as np angles = np.pi * np.array([3.0 / 6.0, 7.0 / 6.0, 11.0 / 6.0]) geo = dmsh.Union( [ dmsh.Circle([np.cos(angles[0]), np.sin(angles[0])], 1.0), dmsh.Circle([np.cos(angles[1]), np.sin(angles[1])], 1.0), dmsh.Circle([np.cos(angles[2]), np.sin(angles[2])], 1.0), ] ) X, cells = dmsh.generate(geo, 0.15) ``` #### Intersection | | | | | :------------------------------------------------------------------------------: | :------------------------------------------------------------------------------------: | :---------------------------------------------------------------------------------------: | ```python import dmsh geo = dmsh.Circle([0.0, -0.5], 1.0) & dmsh.Circle([0.0, +0.5], 1.0) X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10) ``` ```python import dmsh import numpy as np angles = np.pi * np.array([3.0 / 6.0, 7.0 / 6.0, 11.0 / 6.0]) geo = dmsh.Intersection( [ dmsh.Circle([np.cos(angles[0]), np.sin(angles[0])], 1.5), dmsh.Circle([np.cos(angles[1]), np.sin(angles[1])], 1.5), dmsh.Circle([np.cos(angles[2]), np.sin(angles[2])], 1.5), ] ) X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10) ``` The following uses the `HalfSpace` primtive for cutting off a circle. ```python import dmsh geo = dmsh.HalfSpace([1.0, 1.0]) & dmsh.Circle([0.0, 0.0], 1.0) X, cells = dmsh.generate(geo, 0.1) ``` ### Rotation, translation, scaling | | | | :------------------------------------------------------------------: | :-----------------------------------------------------------------: | ```python import dmsh import numpy as np geo = dmsh.Rotation(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), 0.1 * np.pi) X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10) ``` ```python import dmsh geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0) + [1.0, 1.0] X, cells = dmsh.generate(geo, 0.1) ``` ```python import dmsh geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0) * 2.0 X, cells = dmsh.generate(geo, 0.1, tol=1.0e-5) ``` ### Local refinement local-refinement All objects can be used to refine the mesh according to the distance to the object; e.g. a `Path`: ```python import dmsh geo = dmsh.Rectangle(0.0, 1.0, 0.0, 1.0) p1 = dmsh.Path([[0.4, 0.6], [0.6, 0.4]]) def edge_size(x): return 0.03 + 0.1 * p1.dist(x) X, cells = dmsh.generate(geo, edge_size, tol=1.0e-10) ``` ### Custom shapes It is also possible to define your own geometry. Simply create a class derived from `dmsh.Geometry` that contains a `dist` method and a method to project points onto the boundary. ```python import dmsh import numpy as np class MyDisk(dmsh.Geometry): def __init__(self): self.r = 1.0 self.x0 = [0.0, 0.0] bounding_box = [-1.0, 1.0, -1.0, 1.0] feature_points = np.array([[], []]).T super().__init__(bounding_box, feature_points) def dist(self, x): assert x.shape[0] == 2 y = (x.T - self.x0).T return np.sqrt(np.einsum("i...,i...->...", y, y)) - self.r def boundary_step(self, x): # project onto the circle y = (x.T - self.x0).T r = np.sqrt(np.einsum("ij,ij->j", y, y)) return ((y / r * self.r).T + self.x0).T geo = MyDisk() X, cells = dmsh.generate(geo, 0.1) ``` ### Debugging | ![level-set-poly](https://nschloe.github.io/dmsh/levelset-polygon.png) | ![level-set-rect-hole](https://nschloe.github.io/dmsh/levelset-rect-hole.png) | | :--------------------------------------------------------------------: | :---------------------------------------------------------------------------: | dmsh is rather fragile, but sometimes the break-downs are due to an incorrectly defined geometry. Use ``` geo.show() ``` to inspect the level set function of your domain. (It must be negative inside the domain and positive outside. The 0-level set forms the domain boundary.) ### Installation dmsh is [available from the Python Package Index](https://pypi.org/project/dmsh/), so simply type ``` pip install dmsh ``` to install. ### Testing To run the dmsh unit tests, check out this repository and type ``` tox ``` ### License This software is published under the [MIT license](https://en.wikipedia.org/wiki/MIT_License). dmsh-0.2.18/justfile000066400000000000000000000014551413425205000143060ustar00rootroot00000000000000version := `python3 -c "from configparser import ConfigParser; p = ConfigParser(); p.read('setup.cfg'); print(p['metadata']['version'])"` default: @echo "\"just publish\"?" tag: @if [ "$(git rev-parse --abbrev-ref HEAD)" != "main" ]; then exit 1; fi curl -H "Authorization: token `cat ~/.github-access-token`" -d '{"tag_name": "v{{version}}"}' https://api.github.com/repos/nschloe/dmsh/releases upload: clean @if [ "$(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 . dmsh-0.2.18/pyproject.toml000066400000000000000000000001761413425205000154510ustar00rootroot00000000000000[build-system] requires = ["setuptools>=42", "wheel"] build-backend = "setuptools.build_meta" [tool.isort] profile = "black" dmsh-0.2.18/setup.cfg000066400000000000000000000024261413425205000143560ustar00rootroot00000000000000[metadata] name = dmsh version = 0.2.18 author = Nico Schlömer author_email = nico.schloemer@gmail.com description = High-quality 2D mesh generator based on distmesh url = https://github.com/nschloe/dmsh project_urls = Code=https://github.com/nschloe/dmsh Issues=https://github.com/nschloe/dmsh/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 :: 4 - Beta 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 = importlib_metadata;python_version<"3.8" meshplex >= 0.16.0, < 0.17.0 npx numpy scipy python_requires = >=3.7 [options.packages.find] where=src [options.extras_require] all = matplotlib plot = matplotlib dmsh-0.2.18/src/000077500000000000000000000000001413425205000133205ustar00rootroot00000000000000dmsh-0.2.18/src/dmsh/000077500000000000000000000000001413425205000142535ustar00rootroot00000000000000dmsh-0.2.18/src/dmsh/__about__.py000066400000000000000000000003261413425205000165340ustar00rootroot00000000000000try: # Python 3.8 from importlib import metadata except ImportError: import importlib_metadata as metadata try: __version__ = metadata.version("dmsh") except Exception: __version__ = "unknown" dmsh-0.2.18/src/dmsh/__init__.py000066400000000000000000000010521413425205000163620ustar00rootroot00000000000000from .__about__ import __version__ from .geometry import ( Circle, Difference, Ellipse, Geometry, HalfSpace, Intersection, Path, Polygon, Rectangle, Rotation, Scaling, Stretch, Translation, Union, ) from .main import generate __all__ = [ "__version__", "generate", "Circle", "Difference", "Ellipse", "Geometry", "HalfSpace", "Intersection", "Path", "Polygon", "Rectangle", "Rotation", "Stretch", "Scaling", "Translation", "Union", ] dmsh-0.2.18/src/dmsh/geometry/000077500000000000000000000000001413425205000161065ustar00rootroot00000000000000dmsh-0.2.18/src/dmsh/geometry/__init__.py000066400000000000000000000010721413425205000202170ustar00rootroot00000000000000from .circle import Circle from .ellipse import Ellipse from .geometry import ( Difference, Geometry, Intersection, Scaling, Stretch, Translation, Union, ) from .halfspace import HalfSpace from .path import Path from .polygon import Polygon from .rectangle import Rectangle from .rotation import Rotation __all__ = [ "Circle", "Difference", "Ellipse", "Geometry", "HalfSpace", "Intersection", "Path", "Polygon", "Rectangle", "Rotation", "Scaling", "Stretch", "Translation", "Union", ] dmsh-0.2.18/src/dmsh/geometry/circle.py000066400000000000000000000031571413425205000177270ustar00rootroot00000000000000from typing import Tuple import numpy as np from .geometry import Geometry class CirclePath: def __init__(self, x0: Tuple[float, float], r: float): self.x0 = x0 self.r = r def p(self, t): v = np.array([np.cos(2 * np.pi * t), np.sin(2 * np.pi * t)]) return ((self.r * v).T + self.x0).T def dp_dt(self, t): return ( self.r * 2 * np.pi * np.array([-np.sin(2 * np.pi * t), np.cos(2 * np.pi * t)]) ) class Circle(Geometry): def __init__(self, x0, r): self.x0 = x0 self.r = r bounding_box = [x0[0] - r, x0[0] + r, x0[1] - r, x0[1] + r] self.paths = [CirclePath(x0, r)] feature_points = np.array([[], []]).T super().__init__(bounding_box, feature_points) def dist(self, x): assert x.shape[0] == 2 y = (x.T - self.x0).T return np.sqrt(np.einsum("i...,i...->...", y, y)) - self.r def boundary_step(self, x): # simply project onto the circle y = (x.T - self.x0).T r = np.sqrt(np.einsum("ij,ij->j", y, y)) return ((y / r * self.r).T + self.x0).T def plot(self, level_set=True): import matplotlib.pyplot as plt if level_set: X, Y, Z = self._get_xyz() alpha = np.max(np.abs(Z)) cf = plt.contourf( X, Y, Z, levels=20, cmap=plt.cm.coolwarm, vmin=-alpha, vmax=alpha ) plt.colorbar(cf) circle1 = plt.Circle(self.x0, self.r, color="k", fill=False) plt.gca().add_patch(circle1) plt.gca().set_aspect("equal") dmsh-0.2.18/src/dmsh/geometry/ellipse.py000066400000000000000000000027021413425205000201160ustar00rootroot00000000000000import numpy as np from ..helpers import multi_newton from .geometry import Geometry class Ellipse(Geometry): def __init__(self, x0, a, b): super().__init__() self.x0 = x0 self.a = a self.b = b self.bounding_box = [x0[0] - a, x0[0] + a, x0[1] - b, x0[1] + b] self.feature_points = np.array([]) def dist(self, x): assert x.shape[0] == 2 return ( ((x[0] - self.x0[0]) / self.a) ** 2 + ((x[1] - self.x0[1]) / self.b) ** 2 - 1.0 ) def _boundary_step(self, x): ax = (x[0] - self.x0[0]) / self.a ay = (x[1] - self.x0[1]) / self.b alpha = ax ** 2 + ay ** 2 - 1.0 jac = np.array([4 * alpha * ax / self.a, 4 * alpha * ay / self.b]) dalpha_dx = 2 * ax / self.a dalpha_dy = 2 * ay / self.b hess = np.array( [ [ 4 * dalpha_dx * ax / self.a + 4 * alpha / self.a ** 2, 4 * dalpha_dy * ax / self.a, ], [ 4 * dalpha_dx * ay / self.b, 4 * dalpha_dy * ay / self.b + 4 * alpha / self.b ** 2, ], ] ) p = -np.linalg.solve(np.moveaxis(hess, -1, 0), jac.T) return x + p.T def boundary_step(self, x): return multi_newton( x.T, self.dist, self._boundary_step, 1.0e-10, max_num_steps=10 ).T dmsh-0.2.18/src/dmsh/geometry/geometry.py000066400000000000000000000254271413425205000203250ustar00rootroot00000000000000import numpy as np from ..helpers import find_feature_points class Geometry: def __init__(self, bounding_box, feature_points): self.bounding_box = bounding_box self.feature_points = feature_points def _get_xyz(self, nx=101, ny=101): x0, x1, y0, y1 = self.bounding_box w = x1 - x0 h = x1 - x0 x = np.linspace(x0 - w * 0.1, x1 + w * 0.1, nx) y = np.linspace(y0 - h * 0.1, y1 + h * 0.1, ny) X, Y = np.meshgrid(x, y) Z = self.dist(np.array([X, Y])) return X, Y, Z def dist(self, _): raise NotImplementedError("dist() not implemented") def _plot_level_set(self): import matplotlib.pyplot as plt X, Y, Z = self._get_xyz() alpha = np.max(np.abs(Z)) cf = plt.contourf( X, Y, Z, levels=20, cmap=plt.cm.coolwarm, vmin=-alpha, vmax=alpha ) plt.colorbar(cf) def plot(self, level_set=True): import matplotlib.pyplot as plt X, Y, Z = self._get_xyz() if level_set: alpha = np.max(np.abs(Z)) cf = plt.contourf( X, Y, Z, levels=20, cmap=plt.cm.coolwarm, vmin=-alpha, vmax=alpha ) plt.colorbar(cf) # mark the 0-level (the domain boundary) plt.contour(X, Y, Z, levels=[0.0], colors="k") plt.gca().set_aspect("equal") def show(self, *args, **kwargs): import matplotlib.pyplot as plt self.plot(*args, **kwargs) plt.show() def __add__(self, obj): if isinstance(obj, Geometry): return Union([self, obj]) return Translation(self, obj) def __radd__(self, obj): return self.__add__(obj) def __sub__(self, obj): if isinstance(obj, Geometry): return Difference(self, obj) return Translation(self, -obj) def __and__(self, obj): return Intersection([self, obj]) def __or__(self, obj): return Union([self, obj]) def __mul__(self, alpha: float): return Scaling(self, alpha) def __rmul__(self, alpha: float): return self.__mul__(alpha) def stretch(self, obj): return Stretch(self, obj) class Union(Geometry): def __init__(self, geometries): self.geometries = geometries bounding_box = [ np.min([geo.bounding_box[0] for geo in geometries]), np.max([geo.bounding_box[1] for geo in geometries]), np.min([geo.bounding_box[2] for geo in geometries]), np.max([geo.bounding_box[3] for geo in geometries]), ] fp = [geo.feature_points for geo in geometries] fp.append(find_feature_points(geometries)) feature_points = np.concatenate(fp) # Only keep the feature points on the outer boundary alpha = np.array([geo.dist(feature_points.T) for geo in geometries]) tol = 1.0e-5 is_on_boundary = np.all(alpha > -tol, axis=0) feature_points = feature_points[is_on_boundary] self.paths = [path for geo in self.geometries for path in geo.paths] super().__init__(bounding_box, feature_points) def dist(self, x): return np.min([geo.dist(x) for geo in self.geometries], axis=0) def boundary_step(self, x, tol=1.0e-12, max_steps=100): # step for the is_inside with the smallest value x = np.asarray(x) alpha = np.array([geo.dist(x) for geo in self.geometries]) step = 0 while np.any(np.abs(np.min(alpha, axis=0)) > tol): assert step <= max_steps, "Exceeded maximum number of boundary steps." step += 1 # If the point has a positive geo distance, it is outside of the domain. In # this case, move it to the geo boundary with the smallest distance. # If the point is strictly inside all geometries, move it to the furthest # geometry boundary. mask = np.all(alpha > tol, axis=0) | np.any(alpha < -tol, axis=0) x_tmp = x[:, mask] idx = np.argmin(alpha[:, mask], axis=0) for k, geo in enumerate(self.geometries): if np.any(idx == k): x_tmp[:, idx == k] = geo.boundary_step(x_tmp[:, idx == k]) x[:, mask] = x_tmp alpha = np.array([geo.dist(x) for geo in self.geometries]) return x class Stretch(Geometry): def __init__(self, geometry, v): self.geometry = geometry self.alpha = np.sqrt(np.dot(v, v)) self.v = v / self.alpha # bounding box bb = geometry.bounding_box corners = np.array( [[bb[0], bb[2]], [bb[1], bb[2]], [bb[1], bb[3]], [bb[0], bb[3]]] ) vx = np.multiply.outer(np.dot(self.v, corners.T), self.v) stretched_corners = (vx * self.alpha + (corners - vx)).T bounding_box = [ np.min(stretched_corners[0]), np.max(stretched_corners[0]), np.min(stretched_corners[1]), np.max(stretched_corners[1]), ] super().__init__(bounding_box, feature_points=[]) def dist(self, x): # scale the component of x in direction v by 1/alpha x_shape = x.shape assert x.shape[0] == 2 x = x.reshape(2, -1) vx = np.multiply.outer(np.dot(self.v, x), self.v) y = vx / self.alpha + (x.T - vx) y = y.T.reshape(x_shape) return self.geometry.dist(y) def boundary_step(self, x): vx = np.multiply.outer(np.dot(self.v, x), self.v) y = vx / self.alpha + (x.T - vx) y2 = self.geometry.boundary_step(y.T) vy2 = np.multiply.outer(np.dot(self.v, y2), self.v) return (vy2 * self.alpha + (y2.T - vy2)).T class Difference(Geometry): def __init__(self, geo0, geo1): self.geo0 = geo0 self.geo1 = geo1 fp = [geo0.feature_points, geo1.feature_points] fp.append(find_feature_points([geo0, geo1])) feature_points = np.concatenate(fp) # Only keep the feature points on the outer boundary alpha = self.dist(feature_points.T) tol = 1.0e-5 is_on_boundary = (-tol < alpha) & (alpha < tol) feature_points = feature_points[is_on_boundary] self.paths = [path for geo in [geo0, geo1] for path in geo.paths] super().__init__(geo0.bounding_box, feature_points) def dist(self, x): return np.max([self.geo0.dist(x), -self.geo1.dist(x)], axis=0) # Choose tolerance above sqrt(machine_eps). This is necessary as the polygon # dist() is only accurate to that precision. def boundary_step(self, x, tol=1.0e-12, max_steps=100): # Scale the tolerance with the domain diameter. This is necessary at least for # polygons where the distance calculation is flawed with round-off proportional # to the edge lengths. try: tol *= self.geo0.diameter except AttributeError: pass alpha = np.array([self.geo0.dist(x), -self.geo1.dist(x)]) mask = np.any(alpha > tol, axis=0) | np.all(alpha < -tol, axis=0) step = 0 while np.any(mask): assert step <= max_steps, "Exceeded maximum number of boundary steps." step += 1 x_tmp = x[:, mask] idx = np.argmax(alpha[:, mask], axis=0) if np.any(idx == 0): x_tmp[:, idx == 0] = self.geo0.boundary_step(x_tmp[:, idx == 0]) if np.any(idx == 1): x_tmp[:, idx == 1] = self.geo1.boundary_step(x_tmp[:, idx == 1]) x[:, mask] = x_tmp alpha = np.array([self.geo0.dist(x), -self.geo1.dist(x)]) mask = np.any(alpha > tol, axis=0) | np.all(alpha < -tol, axis=0) return x class Translation(Geometry): def __init__(self, geometry, v): self.geometry = geometry self.v = v bounding_box = [ geometry.bounding_box[0] + v[0], geometry.bounding_box[1] + v[0], geometry.bounding_box[2] + v[1], geometry.bounding_box[3] + v[1], ] super().__init__(bounding_box, feature_points=[]) def dist(self, x): return self.geometry.dist((x.T - self.v).T) def boundary_step(self, x): return (self.geometry.boundary_step((x.T - self.v).T).T + self.v).T class Intersection(Geometry): def __init__(self, geometries): self.geometries = geometries bounding_box = [ np.max([geo.bounding_box[0] for geo in geometries]), np.min([geo.bounding_box[1] for geo in geometries]), np.max([geo.bounding_box[2] for geo in geometries]), np.min([geo.bounding_box[3] for geo in geometries]), ] feature_points = find_feature_points(geometries) # filter out the feature points outside the intersection feature_points = feature_points[ np.all( [geo.dist(feature_points.T) < 1.0e-10 for geo in geometries], axis=0, ) ] self.paths = [path for geo in self.geometries for path in geo.paths] super().__init__(bounding_box, feature_points) def dist(self, x): return np.max([geo.dist(x) for geo in self.geometries], axis=0) def boundary_step(self, x, tol=1.0e-12, max_steps=100): # step for the is_inside with the smallest value x = np.asarray(x) alpha = np.array([geo.dist(x) for geo in self.geometries]) step = 0 while np.any(np.abs(np.max(alpha, axis=0)) > tol): assert step <= max_steps, "Exceeded maximum number of boundary steps." step += 1 # If the point has a positive geo distance, it is outside of the domain. In # this case, move it to the geo boundary with the largest distance. # If the point is strictly inside all geometries, move it to the closest # geometry boundary. # Both of these cases correspond to finding the domain with the max dist # value. mask = np.any(alpha > tol, axis=0) | np.all(alpha < -tol, axis=0) x_tmp = x[:, mask] alpha_pos = alpha[:, mask] idx = np.argmax(alpha_pos, axis=0) for k, geo in enumerate(self.geometries): if np.any(idx == k): x_tmp[:, idx == k] = geo.boundary_step(x_tmp[:, idx == k]) x[:, mask] = x_tmp alpha = np.array([geo.dist(x) for geo in self.geometries]) return x class Scaling(Geometry): def __init__(self, geometry: Geometry, alpha: float): self.geometry = geometry self.alpha = alpha bounding_box = alpha * np.array(geometry.bounding_box) super().__init__(bounding_box, feature_points=[]) def dist(self, x): return self.geometry.dist(x / self.alpha) def boundary_step(self, x): return self.geometry.boundary_step(x / self.alpha) * self.alpha dmsh-0.2.18/src/dmsh/geometry/halfspace.py000066400000000000000000000026461413425205000204160ustar00rootroot00000000000000import numpy as np from .geometry import Geometry class LinePath: def __init__(self, v, tangent): self.v = v self.tangent = tangent def p(self, t): """This parametrization of the line is (inf, inf) for t=0 and t=1.""" # Don't warn on division by 0 with np.errstate(divide="ignore"): out = ( np.multiply.outer(self.tangent, (2 * t - 1) / t / (1 - t)).T + self.v ).T return out def dp_dt(self, t): with np.errstate(divide="ignore"): dt = 1 / t ** 2 + 1 / (1 - t) ** 2 return np.multiply.outer(self.tangent, dt) class HalfSpace(Geometry): def __init__(self, normal, alpha=0.0): self.normal = normal self.alpha = alpha bounding_box = [-np.inf, +np.inf, -np.inf, +np.inf] # One point on the line: v = self.normal / np.dot(self.normal, self.normal) * self.alpha tangent = np.array([-self.normal[1], self.normal[0]]) self.paths = [LinePath(v, tangent)] super().__init__(bounding_box, feature_points=[]) def dist(self, x): assert x.shape[0] == 2 out = self.alpha - np.dot(self.normal, x.reshape(x.shape[0], -1)) return out.reshape(x.shape[1:]) def boundary_step(self, x): beta = self.alpha - np.dot(self.normal, x) / np.dot(self.normal, self.normal) return x + np.multiply.outer(self.normal, beta) dmsh-0.2.18/src/dmsh/geometry/path.py000066400000000000000000000017601413425205000174200ustar00rootroot00000000000000import numpy as np from . import pypathlib class LineSegmentPath: def __init__(self, x0, x1): self.x0 = x0 self.x1 = x1 return def p(self, t): return np.multiply.outer(self.x0, 1 - t) + np.multiply.outer(self.x1, t) def dp_dt(self, t): ones = np.ones(t.shape) return np.multiply.outer(self.x0, -ones) + np.multiply.outer(self.x1, ones) class Path: def __init__(self, points): points = np.array(points) self.path = pypathlib.Path(points) self.bounding_box = [ np.min(points[:, 0]), np.max(points[:, 0]), np.min(points[:, 1]), np.max(points[:, 1]), ] self.feature_points = points self.paths = [ LineSegmentPath(p0, p1) for p0, p1 in zip(points[:-1], points[1:]) ] return def dist(self, x): return self.path.distance(x.T) def boundary_step(self, x): return self.path.closest_points(x.T).T dmsh-0.2.18/src/dmsh/geometry/polygon.py000066400000000000000000000027501413425205000201530ustar00rootroot00000000000000import numpy as np from . import pypathlib from .geometry import Geometry class LineSegmentPath: def __init__(self, x0, x1): self.x0 = x0 self.x1 = x1 def p(self, t): return np.multiply.outer(self.x0, 1 - t) + np.multiply.outer(self.x1, t) def dp_dt(self, t): ones = np.ones(t.shape) return np.multiply.outer(self.x0, -ones) + np.multiply.outer(self.x1, ones) class Polygon(Geometry): def __init__(self, points): points = np.asarray(points) bounding_box = [ np.min(points[:, 0]), np.max(points[:, 0]), np.min(points[:, 1]), np.max(points[:, 1]), ] self.polygon = pypathlib.ClosedPath(points) self.paths = [ LineSegmentPath(p0, p1) for p0, p1 in zip(points, np.roll(points, -1, axis=0)) ] self.diameter = self.polygon.diameter super().__init__(bounding_box, feature_points=points) def dist(self, x): assert x.shape[0] == 2 X = x.reshape(2, -1) out = self.polygon.signed_distance(X.T) return out.reshape(x.shape[1:]) def boundary_step(self, x): return self.polygon.closest_points(x.T).T def plot(self, level_set=True): import matplotlib.pyplot as plt if level_set: self._plot_level_set() obj = plt.Polygon(self.feature_points, color="k", fill=False) plt.gca().add_patch(obj) plt.gca().set_aspect("equal") dmsh-0.2.18/src/dmsh/geometry/pypathlib/000077500000000000000000000000001413425205000201025ustar00rootroot00000000000000dmsh-0.2.18/src/dmsh/geometry/pypathlib/__init__.py000066400000000000000000000001501413425205000222070ustar00rootroot00000000000000from .closed_path import ClosedPath from .path import Path __all__ = [ "ClosedPath", "Path", ] dmsh-0.2.18/src/dmsh/geometry/pypathlib/closed_path.py000066400000000000000000000054521413425205000227470ustar00rootroot00000000000000import numpy as np from .helpers import shoelace from .path import Path class ClosedPath(Path): def __init__(self, points): closed_points = np.concatenate([points, [points[0]]]) super().__init__(closed_points) assert self.points.shape[0] > 2 assert self.points.shape[1] == 2 self.area = 0.5 * shoelace(self.points) self.positive_orientation = self.area >= 0 if self.area < 0: self.area = -self.area self._is_convex_node = None return def signed_squared_distance(self, x): """Negative inside the polygon.""" x = np.array(x) assert x.shape[1] == 2 t, dist2, idx = self._all_distances(x) contains_points = self._contains_points(t, x, idx) dist2[contains_points] *= -1 return dist2 def signed_distance(self, x): """Negative inside the polygon.""" x = np.array(x) assert x.shape[1] == 2 t, dist2, idx = self._all_distances(x) dist = np.sqrt(dist2) contains_points = self._contains_points(t, x, idx) dist[contains_points] *= -1 return dist def _contains_points(self, t, x, idx): r = np.arange(idx.shape[0]) contains_points = np.zeros(x.shape[0], dtype=bool) pts0 = self.points pts1 = np.roll(self.points, -1, axis=0) # If the point is closest to a polygon edge, check which which side of the edge # it is on. is_closest_to_side = (0.0 < t[r, idx]) & (t[r, idx] < 1.0) tri = np.array( [ x[is_closest_to_side], pts0[idx[is_closest_to_side]], pts1[idx[is_closest_to_side]], ] ) contains_points[is_closest_to_side] = ( shoelace(tri) > 0.0 ) == self.positive_orientation # If the point is closest to a polygon node, check if the node is convex or # concave. is_closest_to_pt0 = t[r, idx] <= 0.0 contains_points[is_closest_to_pt0] = ~self.is_convex_node[ idx[is_closest_to_pt0] ] is_closest_to_pt1 = 1.0 <= t[r, idx] n = self.points.shape[0] - 1 contains_points[is_closest_to_pt1] = ~self.is_convex_node[ (idx[is_closest_to_pt1] + 1) % n ] return contains_points def contains_points(self, x, tol=1.0e-15): return self.signed_distance(x) < tol @property def is_convex_node(self): points = self.points[:-1] if self._is_convex_node is None: tri = np.array( [np.roll(points, +1, axis=0), points, np.roll(points, -1, axis=0)] ) self._is_convex_node = np.equal( shoelace(tri) >= 0, self.positive_orientation ) return self._is_convex_node dmsh-0.2.18/src/dmsh/geometry/pypathlib/helpers.py000066400000000000000000000002421413425205000221140ustar00rootroot00000000000000import numpy as np def shoelace(x): previous = np.roll(x, 1, axis=0) return np.sum(x[..., 1] * previous[..., 0] - x[..., 0] * previous[..., 1], axis=0) dmsh-0.2.18/src/dmsh/geometry/pypathlib/path.py000066400000000000000000000066761413425205000214270ustar00rootroot00000000000000import numpy as np class Path: def __init__(self, points): self.points = np.asarray(points) assert self.points.shape[1] == 2 self.edges = self.points[1:] - self.points[:-1] self.e_dot_e = np.einsum("ij,ij->i", self.edges, self.edges) assert np.all( self.e_dot_e > 1.0e-12 ), f"Edges of 0 length are not permitted (squared edge lengths: {self.e_dot_e})" def _all_distances(self, x): x = np.asarray(x) assert x.shape[1] == 2 if self.points.shape[0] == 1: # In case there is only one point, i.e., no sides. diff = x[:, None] - self.points[None, :] dist2_points = np.einsum("ijk,ijk->ij", diff, diff) idx = np.zeros(dist2_points.shape[0], dtype=int) t = 0.0 return t, dist2_points.T, idx # Find closest point for each side segment # diff = x[:, None] - self.points[None, :-1] t = np.einsum("ijk,jk->ij", diff, self.edges) / self.e_dot_e t[t < 0.0] = 0.0 t[t > 1.0] = 1.0 # The squared distance from the point x to the infinite line defined by the # points x0, x1 (e = x1 - x0) is , where proj is the # projection of x onto the line. The expression can be simplified to # # ( - **2) / # # but this expression is numerically disadvantageous. (For example, the # expression can become negative due to round-off.) Simply compute the # projection and the dot product. x_min_proj = diff - t[:, :, None] * self.edges[None, :, :] dist2_sides = np.einsum("ijk,ijk->ij", x_min_proj, x_min_proj) idx = np.argmin(dist2_sides, axis=1) dist2_sides = dist2_sides[np.arange(idx.shape[0]), idx] # t-parameter for each side, the squared min distance, and the index of the # closest side return t, dist2_sides, idx @property def diameter(self): # compute distance from all points to each other diff = self.points[:, None] - self.points[None, :] dist2 = np.einsum("ijk,ijk->ij", diff, diff) return np.sqrt(np.max(dist2)) def squared_distance(self, x): """Get the squared distance of all points x to the polygon.""" x = np.asarray(x) assert x.shape[1] == 2 _, dist2_sides, _ = self._all_distances(x) return dist2_sides def distance(self, x): """Get the distance of all points x to the polygon.""" return np.sqrt(self.squared_distance(x)) def closest_points(self, x): """Get the closest points on the polygon.""" x = np.asarray(x) assert x.shape[1] == 2 t, _, idx = self._all_distances(x) pts0 = self.points[idx] pts1 = np.roll(self.points, -1, axis=0)[idx] r = np.arange(t.shape[0]) t0 = t[r, idx] closest_points = (pts0.T * (1 - t0)).T + (pts1.T * t0).T return closest_points def plot(self, color="#1f77b4"): import matplotlib.pyplot as plt x = np.concatenate([self.points[:, 0], [self.points[0, 0]]]) y = np.concatenate([self.points[:, 1], [self.points[0, 1]]]) plt.plot(x, y, "-", color=color) plt.axis("square") def show(self, *args, **kwargs): import matplotlib.pyplot as plt self.plot(*args, **kwargs) plt.show() dmsh-0.2.18/src/dmsh/geometry/rectangle.py000066400000000000000000000053141413425205000204270ustar00rootroot00000000000000import numpy as np from .geometry import Geometry from .polygon import LineSegmentPath class Rectangle(Geometry): # One could simply make Rectangle a child class of Polygon. However, boundary steps # can be inaccurate for polygons (there is some computation involved). def __init__(self, x0, x1, y0, y1): assert x0 < x1 assert y0 < y1 self.x0 = x0 self.x1 = x1 self.y0 = y0 self.y1 = y1 self.points = np.array([[x0, y0], [x1, y0], [x1, y1], [x0, y1]]) bounding_box = [ np.min(self.points[:, 0]), np.max(self.points[:, 0]), np.min(self.points[:, 1]), np.max(self.points[:, 1]), ] self.paths = [ LineSegmentPath(p0, p1) for p0, p1 in zip(self.points, np.roll(self.points, -1, axis=0)) ] super().__init__(bounding_box, feature_points=self.points) def dist(self, x): # outside dist # https://gamedev.stackexchange.com/a/44496 x = np.asarray(x) w = self.x1 - self.x0 h = self.y1 - self.y0 cx = (self.x0 + self.x1) / 2 cy = (self.y0 + self.y1) / 2 dx = np.abs(x[0] - cx) - w / 2 dy = np.abs(x[1] - cy) - h / 2 is_inside = (dx <= 0) & (dy <= 0) dx[dx < 0.0] = 0.0 dy[dy < 0.0] = 0.0 dist = np.sqrt(dx ** 2 + dy ** 2) # inside dist a = np.array( [ x[0, is_inside] - self.x0, self.x1 - x[0, is_inside], x[1, is_inside] - self.y0, self.y1 - x[1, is_inside], ] ) dist[is_inside] = -np.min(a, axis=0) return dist def boundary_step(self, x): x = np.asarray(x) assert x.shape[0] == 2 is_one_dimensional = False if len(x.shape) == 1: is_one_dimensional = True x = x.reshape(-1, 1) cx = (self.x0 + self.x1) / 2 cy = (self.y0 + self.y1) / 2 w = self.x1 - self.x0 h = self.y1 - self.y0 X = x[0] - cx Y = x[1] - cy # Take care of the outside points X[X < -w / 2] = -w / 2 X[X > +w / 2] = +w / 2 Y[Y < -h / 2] = -h / 2 Y[Y > +h / 2] = +h / 2 # Interior points is_interior = (-w / 2 < X) & (X < w / 2) & (-h / 2 < Y) & (Y < h / 2) a = h * X < w * Y b = -h * X < w * Y Y[is_interior & a & b] = h / 2 Y[is_interior & ~a & ~b] = -h / 2 X[is_interior & ~a & b] = w / 2 X[is_interior & a & ~b] = -w / 2 X += cx Y += cy out = np.array([X, Y]) if is_one_dimensional: out = out.reshape(-1) return out dmsh-0.2.18/src/dmsh/geometry/rotation.py000066400000000000000000000022511413425205000203170ustar00rootroot00000000000000import numpy as np from .geometry import Geometry class Rotation(Geometry): def __init__(self, geometry, angle): self.geometry = geometry self.R = np.array( [ [+np.cos(angle), -np.sin(angle)], [+np.sin(angle), +np.cos(angle)], ] ) self.R_inv = np.array( [ [+np.cos(angle), +np.sin(angle)], [-np.sin(angle), +np.cos(angle)], ] ) # bounding box bb = geometry.bounding_box corners = np.array( [[bb[0], bb[2]], [bb[1], bb[2]], [bb[1], bb[3]], [bb[0], bb[3]]] ) rotated_corners = np.dot(self.R, corners.T) bounding_box = [ np.min(rotated_corners[0]), np.max(rotated_corners[0]), np.min(rotated_corners[1]), np.max(rotated_corners[1]), ] super().__init__(bounding_box, feature_points=[]) def dist(self, x): return self.geometry.dist(np.dot(self.R_inv, x)) def boundary_step(self, x): y = np.dot(self.R_inv, x) y2 = self.geometry.boundary_step(y) return np.dot(self.R, y2) dmsh-0.2.18/src/dmsh/helpers.py000066400000000000000000000126571413425205000163020ustar00rootroot00000000000000from __future__ import annotations from typing import Callable import numpy as np def multi_newton( x0: np.ndarray, is_inside: Callable, boundary_step: Callable, tol: float, max_num_steps: int = 10, ) -> np.ndarray: """Newton's minimization method for multiple starting points.""" x = x0.copy() fx = is_inside(x.T) k = 0 mask = np.abs(fx) > tol while np.any(mask): x[mask] = boundary_step(x[mask].T).T fx = is_inside(x.T) mask = np.abs(fx) > tol k += 1 if k >= max_num_steps: break return x def show(pts, cells, geo, title: str | None = None, full_screen: bool = True): import matplotlib.pyplot as plt eps = 1.0e-10 # highlight outside points in C3, and points which aren't part of any cell in C4 is_part_of_cell = np.zeros(len(pts), dtype=bool) is_part_of_cell[cells.flat] = True is_inside = geo.dist(pts.T) < eps sp = pts[is_inside & is_part_of_cell] plt.plot(sp[:, 0], sp[:, 1], ".", color="C0") sp = pts[~is_inside] plt.plot(sp[:, 0], sp[:, 1], ".", color="C3") sp = pts[~is_part_of_cell] plt.plot(sp[:, 0], sp[:, 1], ".", color="k") # plt.plot(pts[~is_inside, 0], pts[~is_part_of_cell, 1], ".", color="k") plt.triplot(pts[:, 0], pts[:, 1], cells) plt.axis("square") # show cells indices # for idx, barycenter in enumerate(np.sum(pts[cells], axis=1) / 3): # plt.plot(*barycenter, "xk") # plt.text( # *barycenter, idx, horizontalalignment="center", verticalalignment="center" # ) # show node indices # for idx, pt in enumerate(pts): # plt.text( # *pt, idx, horizontalalignment="center", verticalalignment="center" # ) if full_screen: figManager = plt.get_current_fig_manager() try: figManager.window.showMaximized() except AttributeError: # Some backends have no window (e.g., Agg) pass if title is not None: plt.title(title) try: geo.show(level_set=False) except AttributeError: pass def find_feature_points(geometries, num_steps: int = 10): n = len(geometries) # collect path pairs path_pairs = [ [item0, item1] for i in range(n) for j in range(i + 1, n) for item0 in geometries[i].paths for item1 in geometries[j].paths ] points = np.column_stack( [ _find_feature_points_between_two_paths(path0, path1, num_steps) for path0, path1 in path_pairs ] ) if points.shape[1] > 0: points = unique_float_cols(points) return points.T def _find_feature_points_between_two_paths(path0, path1, num_steps, nx=11, ny=11): """Given two geometries with their parametrization, this methods finds feature points, i.e., points where the boundaries meet. This is done by casting a net over the parameter space and performing `num_steps` Newton steps. Found solutions are checked for uniqueness. """ # Throw a net t0, t1 = np.meshgrid(np.linspace(0.0, 1.0, nx), np.linspace(0.0, 1.0, ny)) t = np.array([t0, t1]).reshape(2, -1) # t = np.random.rand(2, 100) tol = 1.0e-20 # multi_newton(x0, is_inside, boundary_step, tol, max_num_steps=10): solutions = [] for k in range(num_steps): f_t = path0.p(t[0]) - path1.p(t[1]) # remove all inf values is_infinite = np.any(np.isinf(f_t), axis=0) if np.any(is_infinite): t = t[:, ~is_infinite] f_t = f_t[:, ~is_infinite] f_dot_f = np.einsum("ij,ij->j", f_t, f_t) is_sol = f_dot_f < tol if np.any(is_sol): solutions.append(t[:, is_sol]) # remove all converged solutions t = t[:, ~is_sol] f_t = f_t[:, ~is_sol] jac_t = np.moveaxis(np.stack([path0.dp_dt(t[0]), -path1.dp_dt(t[1])]), 0, 1) # Kick out singular matrices det = jac_t[0, 0] * jac_t[1, 1] - jac_t[0, 1] * jac_t[1, 0] is_singular = np.abs(det) < 1.0e-13 if np.any(is_singular): t = t[:, ~is_singular] f_t = f_t[:, ~is_singular] jac_t = jac_t[..., ~is_singular] # Simply make it explicitly. sols = [] for k in range(f_t.shape[-1]): try: sols.append(np.linalg.solve(jac_t[..., k], f_t[:, k])) except np.linalg.linalg.LinAlgError: # singular matrix sols.append(np.zeros(f_t[:, k].shape)) sols = np.array(sols).T # Newton step t -= sols # Kick out everything that leaves the unit square still_good = np.all((0.0 <= t) & (t <= 1.0), axis=0) t = t[:, still_good] if solutions: unique_sols = unique_float_cols(np.column_stack(solutions)) points0 = path0.p(unique_sols[0]) # points1 = path1.p(unique_sols[1]) else: points0 = np.array([[], []]) return points0 def unique_float_cols(data: np.ndarray, k: int = 0, tol: float = 1.0e-10): """In a (k, n) array `data`, find the unique columns.""" if k == data.shape[0]: return data[:, 0] idx = np.argsort(data[k]) data = data[:, idx] diff = data[k, 1:] - data[k, :-1] cut = diff > tol idx = np.where(cut)[0] chunks = np.split(data, idx + 1, axis=1) out = np.column_stack([unique_float_cols(chunk, k + 1, tol) for chunk in chunks]) return out dmsh-0.2.18/src/dmsh/main.py000066400000000000000000000267531413425205000155660ustar00rootroot00000000000000from __future__ import annotations import math from typing import Callable import meshplex import npx import numpy as np import scipy.spatial from .geometry import Geometry from .helpers import show as show_mesh def _create_cells(pts, geo: Geometry): # compute Delaunay triangulation tri = scipy.spatial.Delaunay(pts) cells = tri.simplices.copy() # kick out all cells whose barycenter is not in the geometry bc = np.sum(pts[cells], axis=1) / 3.0 cells = cells[geo.dist(bc.T) < 0.0] # # kick out all cells whose barycenter or edge midpoints are not in the geometry # btol = 1.0e-3 # bc = np.sum(pts[cells], axis=1) / 3.0 # barycenter_inside = geo.dist(bc.T) < btol # # Remove cells which are (partly) outside of the domain. Check at the midpoint of # # all edges. # mid0 = (pts[cells[:, 1]] + pts[cells[:, 2]]) / 2 # mid1 = (pts[cells[:, 2]] + pts[cells[:, 0]]) / 2 # mid2 = (pts[cells[:, 0]] + pts[cells[:, 1]]) / 2 # edge_midpoints_inside = ( # (geo.dist(mid0.T) < btol) # & (geo.dist(mid1.T) < btol) # & (geo.dist(mid2.T) < btol) # ) # cells = cells[barycenter_inside & edge_midpoints_inside] return cells def _recell_and_boundary_step(mesh, geo, flip_tol): # We could do a _create_cells() here, but inverted boundary cell removal plus Lawson # flips produce the same result and are much cheaper. This is because, most of the # time, there are no cells to be removed and no edges to be flipped. (The flip is # still a fairly expensive operation.) while True: idx = mesh.is_boundary_point points_new = mesh.points.copy() points_new[idx] = geo.boundary_step(points_new[idx].T).T mesh.points = points_new # num_removed_cells = mesh.remove_boundary_cells( lambda is_bdry_cell: mesh.compute_signed_cell_volumes(is_bdry_cell) < 1.0e-10 ) # # The flip has to come right after the boundary cell removal to prevent # "degenerate cell" errors. mesh.flip_until_delaunay(tol=flip_tol) # if num_removed_cells == 0: break # Last kick out all boundary cells whose barycenters are not in the geometry. mesh.remove_boundary_cells( lambda is_bdry_cell: geo.dist(mesh.compute_cell_centroids(is_bdry_cell).T) > 0.0 ) def create_staggered_grid(h, bounding_box): x_step = h y_step = h * np.sqrt(3) / 2 bb_width = bounding_box[1] - bounding_box[0] bb_height = bounding_box[3] - bounding_box[2] midpoint = [ (bounding_box[0] + bounding_box[1]) / 2, (bounding_box[2] + bounding_box[3]) / 2, ] num_x_steps = int(bb_width / x_step) if num_x_steps % 2 == 1: num_x_steps -= 1 num_y_steps = int(bb_height / y_step) if num_y_steps % 2 == 1: num_y_steps -= 1 # Generate initial (staggered) point list from bounding box. # Make sure that the midpoint is one point in the grid. x2 = num_x_steps // 2 y2 = num_y_steps // 2 x, y = np.meshgrid( midpoint[0] + x_step * np.arange(-x2, x2 + 1), midpoint[1] + y_step * np.arange(-y2, y2 + 1), ) # Staggered, such that the midpoint is not moved. # Unconditionally move to the right, then add more points to the left. offset = (y2 + 1) % 2 x[offset::2] += h / 2 out = np.column_stack([x.reshape(-1), y.reshape(-1)]) # add points in the staggered lines to preserve symmetry n = 2 * (-(-y2 // 2)) extra = np.empty((n, 2)) extra[:, 0] = midpoint[0] - x_step * x2 - h / 2 extra[:, 1] = midpoint[1] + y_step * np.arange(-y2 + offset, y2 + 1, 2) out = np.concatenate([out, extra]) return out # def get_max_step(mesh): # # Some methods are stable (CPT), others can break down if the mesh isn't very # # smooth. A break-down manifests, for example, in a step size that lets triangles # # become fully flat or even "overshoot". After that, anything can happen. To prevent # # this, restrict the maximum step size to half of the minimum the incircle radius of # # all adjacent cells. This makes sure that triangles cannot "flip". # # # max_step = np.full(mesh.points.shape[0], np.inf) # np.minimum.at( # max_step, mesh.cells("points").reshape(-1), np.repeat(mesh.cell_inradius, 3), # ) # max_step *= 0.5 # return max_step def generate( geo: Geometry, target_edge_size: float | Callable, # smoothing_method="distmesh", tol: float = 1.0e-5, random_seed: int = 0, show: bool = False, max_steps: int = 10000, verbose: bool = False, flip_tol: float = 0.0, ): target_edge_size_function = ( target_edge_size if callable(target_edge_size) else lambda pts: np.full(pts.shape[1], target_edge_size) ) # Find h0 from edge_size (function) if callable(target_edge_size): # Find h0 by sampling h00 = (geo.bounding_box[1] - geo.bounding_box[0]) / 100 pts = create_staggered_grid(h00, geo.bounding_box) sizes = target_edge_size_function(pts.T) assert np.all( sizes > 0.0 ), "target_edge_size_function must be strictly positive." h0 = np.min(sizes) else: h0 = target_edge_size pts = create_staggered_grid(h0, geo.bounding_box) eps = 1.0e-10 # remove points outside of the region pts = pts[geo.dist(pts.T) < eps] # evaluate the element size function, remove points according to it alpha = 1.0 / target_edge_size_function(pts.T) ** 2 rng = np.random.default_rng(random_seed) pts = pts[rng.random(pts.shape[0]) < alpha / np.max(alpha)] num_feature_points = len(geo.feature_points) if num_feature_points > 0: # remove all points which are equal to a feature point diff = np.array([[pt - fp for fp in geo.feature_points] for pt in pts]) dist = np.einsum("...k,...k->...", diff, diff) ftol = h0 / 10 equals_feature_point = np.any(dist < ftol ** 2, axis=1) pts = pts[~equals_feature_point] # Add feature points pts = np.concatenate([geo.feature_points, pts]) cells = _create_cells(pts, geo) mesh = meshplex.MeshTri(pts, cells) # When creating a mesh for the staggered grid, degenerate cells can very well occur # at the boundary, where points sit in a straight line. Remove those cells. mesh.remove_cells(mesh.q_radius_ratio < 1.0e-10) # # move boundary points to the boundary exactly # is_boundary_point = mesh.is_boundary_point.copy() # mesh.points[is_boundary_point] = geo.boundary_step( # mesh.points[is_boundary_point].T # ).T # print(sum(is_boundary_point)) # show_mesh(pts, cells, geo) # exit(1) # if smoothing_method == "odt": # points, cells = optimesh.odt.fixed_point_uniform( # mesh.points, # mesh.cells("points"), # max_num_steps=max_steps, # verbose=verbose, # boundary_step=geo.boundary_step, # ) # else: # assert smoothing_method == "distmesh" dim = 2 mesh = distmesh_smoothing( mesh, geo, num_feature_points, target_edge_size_function, max_steps, tol, verbose, show, delta_t=0.2, f_scale=1 + 0.4 / 2 ** (dim - 1), # from the original article flip_tol=flip_tol, ) points = mesh.points cells = mesh.cells("points") return points, cells def distmesh_smoothing( mesh, geo, num_feature_points, target_edge_size_function, max_steps, tol, verbose, show, delta_t, f_scale, flip_tol=0.0, ): mesh.create_edges() k = 0 move2 = [0.0] while True: # print() # print(f"step {k}") if verbose: print(f"step {k}") if k > max_steps: if verbose: print(f"Exceeded max_steps ({max_steps}).") break k += 1 if show: print(f"max move: {math.sqrt(max(move2)):.3e}") show_mesh(mesh.points, mesh.cells("points"), geo) edges = mesh.edges["points"] edges_vec_normalized = mesh.points[edges[:, 1]] - mesh.points[edges[:, 0]] edge_lengths = np.sqrt( np.einsum("ij,ij->i", edges_vec_normalized, edges_vec_normalized) ) edges_vec_normalized /= edge_lengths[..., None] # Evaluate element sizes at edge midpoints edge_midpoints = (mesh.points[edges[:, 1]] + mesh.points[edges[:, 0]]) / 2 p = target_edge_size_function(edge_midpoints.T) target_lengths = ( f_scale * p * np.sqrt(np.dot(edge_lengths, edge_lengths) / np.dot(p, p)) ) force_abs = target_lengths - edge_lengths # only consider repulsive forces force_abs[force_abs < 0.0] = 0.0 # In , there's a suggestion for a # better forcing function. The below doesn't seem to work too well though. # # Need to set delta_t to 1.0e-2 or smaller to accommodate for the missing factor # `target_lengths`. # force_type = "persson" # relative_length = edge_lengths / target_lengths # if force_type.lower() == "persson": # force_abs = 1.0 - relative_length # # only consider repulsive forces # force_abs[relative_length > 1.0] = 0.0 # else: # assert force_type.lower() == "bossens" # force_abs = (1 - relative_length ** 4) * np.exp(-(relative_length ** 4)) # force vectors force = edges_vec_normalized * force_abs[..., None] n = mesh.points.shape[0] force_per_point = npx.sum_at(-force, edges[:, 0], minlength=n) + npx.sum_at( +force, edges[:, 1], minlength=n ) update = delta_t * force_per_point # # Limit the max step size to avoid overshoots # TODO this doesn't work for distmesh smoothing. hm. # mesh = meshplex.MeshTri(pts, cells) # max_step = get_max_step(mesh) # step_lengths = np.sqrt(np.einsum("ij,ij->i", update, update)) # idx = step_lengths > max_step # update[idx] *= (max_step / step_lengths)[idx, None] # # alpha = np.min(max_step / step_lengths) # # update *= alpha points_old = mesh.points.copy() # update coordinates points_new = mesh.points + update # leave feature points untouched points_new[:num_feature_points] = mesh.points[:num_feature_points] mesh.points = points_new # Some mesh boundary points may have been moved off of the domain boundary, # either because they were pushed outside or because they just became boundary # points by way of cell removal. Move them all (back) onto the domain boundary. # is_outside = geo.dist(points_new.T) > 0.0 # idx = is_outside # Alternative: Push all boundary points (the ones _inside_ the geometry as well) # back to the boundary. # idx = is_outside | is_boundary_point _recell_and_boundary_step(mesh, geo, flip_tol) diff = points_new - points_old move2 = np.einsum("ij,ij->i", diff, diff) if verbose: print(f"max_move: {np.sqrt(np.max(move2)):.6e}") if np.all(move2 < tol ** 2): break # The cell removal steps in _recell_and_boundary_step() might create points which # aren't part of any cell (dangling points). Remove them now. mesh.remove_dangling_points() return mesh dmsh-0.2.18/tests/000077500000000000000000000000001413425205000136735ustar00rootroot00000000000000dmsh-0.2.18/tests/compare-speed.py000066400000000000000000000062641413425205000170010ustar00rootroot00000000000000import time import matplotlib.pyplot as plt import meshplex import numpy as np import pygmsh import dmsh def _compute_num_boundary_points(total_num_points): # The number of boundary points, the total number of points, and the number of cells # are connected by two equations (the second of which is approximate). # # Euler: # 2 * num_points - num_boundary_edges - 2 = num_cells # # edge_length = 2 * np.pi / num_boundary_points # tri_area = np.sqrt(3) / 4 * edge_length ** 2 # num_cells = int(np.pi / tri_area) # # num_boundary_points = num_boundary_edges # # Hence: # 2 * num_points = # num_boundary_points + 2 + np.pi / (np.sqrt(3) / 4 * (2 * np.pi / num_boundary_points) ** 2) # # We need to solve # # + num_boundary_points ** 2 # + (sqrt(3) * pi) * num_boundary_points # + (2 - 2 * num_points) * (sqrt(3) * pi) # = 0 # # for the number of boundary points. sqrt3_pi = np.sqrt(3) * np.pi num_boundary_points = -sqrt3_pi / 2 + np.sqrt( 3 / 4 * np.pi ** 2 - (2 - 2 * total_num_points) * sqrt3_pi ) return num_boundary_points def dmsh_circle(num_points): target_edge_length = 2 * np.pi / _compute_num_boundary_points(num_points) geo = dmsh.Circle([0.0, 0.0], 1.0) X, cells = dmsh.generate(geo, target_edge_length) return X, cells def gmsh_circle(num_points): geom = pygmsh.built_in.Geometry() target_edge_length = 2 * np.pi / _compute_num_boundary_points(num_points) geom.add_circle( [0.0, 0.0, 0.0], 1.0, lcar=target_edge_length, num_sections=4, compound=True ) mesh = pygmsh.generate_mesh(geom, remove_lower_dim_cells=True, verbose=False) return mesh.points[:, :2], mesh.cells[0].data data = { "dmsh": {"n": [], "time": [], "q": [], "version": dmsh.__version__}, "gmsh": {"n": [], "time": [], "q": [], "version": pygmsh.get_gmsh_version()}, } for num_points in range(1000, 10000, 1000): print(num_points) # dmsh t = time.time() pts, cells = dmsh_circle(num_points) t = time.time() - t mesh = meshplex.MeshTri(pts, cells) avg_q = np.sum(mesh.cell_quality) / len(mesh.cell_quality) data["dmsh"]["n"].append(len(pts)) data["dmsh"]["time"].append(t) data["dmsh"]["q"].append(avg_q) # gmsh t = time.time() pts, cells = gmsh_circle(num_points) t = time.time() - t mesh = meshplex.MeshTri(pts, cells) avg_q = np.sum(mesh.cell_quality) / len(mesh.cell_quality) data["gmsh"]["n"].append(len(pts)) data["gmsh"]["time"].append(t) data["gmsh"]["q"].append(avg_q) # plot condition number for key, value in data.items(): plt.plot(value["n"], value["time"], "-x", label=key + " " + value["version"]) plt.xlabel("num points") plt.title("generation time [s]") plt.grid() plt.legend() plt.show() # plt.savefig("time.svg", transparent=True, bbox_inches="tight") plt.close() # plot CG iterations number for key, value in data.items(): plt.plot(value["n"], value["q"], "-x", label=key + " " + value["version"]) plt.xlabel("num points") plt.title("average cell quality") plt.grid() plt.legend() plt.show() # plt.savefig("average-cell-quality.svg", transparent=True, bbox_inches="tight") plt.close() dmsh-0.2.18/tests/generate-readme-plots.py000066400000000000000000000064601413425205000204370ustar00rootroot00000000000000import meshio import numpy as np import optimesh import dmsh def save(X, cells, filename): meshio.Mesh(X, {"triangle": cells}).write( filename, image_width=100, stroke_width=0.5 ) geo = dmsh.Circle([0.0, 0.0], 1.0) X, cells = dmsh.generate(geo, 0.1) # optionally optimize the mesh X, cells = optimesh.optimize_points_cells(X, cells, "CVT (full)", 1.0e-10, 100) save(X, cells, "circle.svg") geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0) X, cells = dmsh.generate(geo, 0.1) save(X, cells, "rectangle.svg") geo = dmsh.Polygon( [ [0.0, 0.0], [1.1, 0.0], [1.2, 0.5], [0.7, 0.6], [2.0, 1.0], [1.0, 2.0], [0.5, 1.5], ] ) X, cells = dmsh.generate(geo, 0.1) save(X, cells, "polygon.svg") geo = dmsh.Difference(dmsh.Circle([-0.5, 0.0], 1.0), dmsh.Circle([+0.5, 0.0], 1.0)) X, cells = dmsh.generate(geo, 0.1) save(X, cells, "moon.svg") geo = dmsh.Difference( dmsh.Circle([0.0, 0.0], 1.0), dmsh.Polygon([[0.0, 0.0], [1.5, 0.4], [1.5, -0.4]]), ) X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10) save(X, cells, "pacman.svg") r = dmsh.Rectangle(-1.0, +1.0, -1.0, +1.0) c = dmsh.Circle([0.0, 0.0], 0.3) geo = dmsh.Difference(r, c) X, cells = dmsh.generate(geo, lambda pts: np.abs(c.dist(pts)) / 5 + 0.05, tol=1.0e-10) save(X, cells, "rectangle-hole-refinement.svg") geo = dmsh.Union([dmsh.Circle([-0.5, 0.0], 1.0), dmsh.Circle([+0.5, 0.0], 1.0)]) X, cells = dmsh.generate(geo, 0.15) save(X, cells, "union-circles.svg") geo = dmsh.Union( [dmsh.Rectangle(-1.0, +0.5, -1.0, +0.5), dmsh.Rectangle(-0.5, +1.0, -0.5, +1.0)] ) X, cells = dmsh.generate(geo, 0.15) save(X, cells, "union-rectangles.svg") angles = np.pi * np.array([3.0 / 6.0, 7.0 / 6.0, 11.0 / 6.0]) geo = dmsh.Union( [ dmsh.Circle([np.cos(angles[0]), np.sin(angles[0])], 1.0), dmsh.Circle([np.cos(angles[1]), np.sin(angles[1])], 1.0), dmsh.Circle([np.cos(angles[2]), np.sin(angles[2])], 1.0), ] ) X, cells = dmsh.generate(geo, 0.15) save(X, cells, "union-three-circles.svg") geo = dmsh.Intersection([dmsh.Circle([0.0, -0.5], 1.0), dmsh.Circle([0.0, +0.5], 1.0)]) X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10) save(X, cells, "intersection-circles.svg") angles = np.pi * np.array([3.0 / 6.0, 7.0 / 6.0, 11.0 / 6.0]) geo = dmsh.Intersection( [ dmsh.Circle([np.cos(angles[0]), np.sin(angles[0])], 1.5), dmsh.Circle([np.cos(angles[1]), np.sin(angles[1])], 1.5), dmsh.Circle([np.cos(angles[2]), np.sin(angles[2])], 1.5), ] ) X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10) save(X, cells, "intersection-three-circles.svg") geo = dmsh.Intersection( [ dmsh.HalfSpace(np.sqrt(0.5) * np.array([1.0, 1.0]), 0.0), dmsh.Circle([0.0, 0.0], 1.0), ] ) X, cells = dmsh.generate(geo, 0.1) save(X, cells, "intersection-circle-halfspace.svg") geo = dmsh.Rotation(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), 0.1 * np.pi) X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10) save(X, cells, "rotation.svg") geo = dmsh.Scaling(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), 2.0) X, cells = dmsh.generate(geo, 0.1, tol=1.0e-5) save(X, cells, "scaling.svg") geo = dmsh.Rectangle(0.0, 1.0, 0.0, 1.0) p1 = dmsh.Path([[0.4, 0.6], [0.6, 0.4]]) X, cells = dmsh.generate(geo, edge_size=lambda x: 0.03 + 0.1 * p1.dist(x), tol=1.0e-10) save(X, cells, "local-refinement.svg") dmsh-0.2.18/tests/helpers.py000066400000000000000000000016341413425205000157130ustar00rootroot00000000000000import numpy as np def assert_equality(a, b, tol): a = np.asarray(a) b = np.asarray(b) fmt_a = ", ".join(["{:.16e}"] * len(a)) fmt_b = ", ".join(["{:.16e}"] * len(b)) assert np.all(np.abs(a - b) < tol), f"[{fmt_a}]\n[{fmt_b}]".format(*a, *b) def assert_norm_equality(X, ref_norm, tol): ref_norm = np.asarray(ref_norm) vals = np.array( [ np.linalg.norm(X, ord=1), np.linalg.norm(X, ord=2), np.linalg.norm(X, ord=np.inf), ] ) assert np.all( np.abs(vals - ref_norm) < tol * ref_norm ), "Expected: [{:.16e}, {:.16e}, {:.16e}]\nComputed: [{:.16e}, {:.16e}, {:.16e}]".format( *ref_norm, *vals ) def save(filename, X, cells): import meshplex mesh = meshplex.MeshTri(X, cells) mesh.save( filename, show_coedges=False, show_axes=False, nondelaunay_edge_color="k", ) dmsh-0.2.18/tests/justfile000066400000000000000000000003141413425205000154410ustar00rootroot00000000000000default: @echo `just png`? png: for file in test_*.py; do \ python3 $$file; \ done for file in *.png; do convert $$file -trim -resize x200 $$file; done for file in *.png; do optipng $$file; done dmsh-0.2.18/tests/logo.py000066400000000000000000000002051413425205000152020ustar00rootroot00000000000000import meshio import meshzoo points, cells = meshzoo.triangle(2) meshio.write_points_cells("logo.svg", points, {"triangle": cells}) dmsh-0.2.18/tests/test_circle.py000066400000000000000000000027241413425205000165520ustar00rootroot00000000000000import meshplex import numpy as np import pytest from helpers import assert_norm_equality import dmsh @pytest.mark.parametrize( "radius,ref_norms", [ (0.1, [3.2592107070061820e02, 1.4190745248684369e01, 1.0000000000000000e00]), (0.4, [18.899253166, 3.70111746, 1.0]), ], ) def test_circle(radius, ref_norms, show=False): geo = dmsh.Circle([0.0, 0.0], 1.0) X, cells = dmsh.generate(geo, radius, show=show, max_steps=100) meshplex.MeshTri(X, cells).show() # make sure the origin is part of the mesh assert np.sum(np.einsum("ij,ij->i", X, X) < 1.0e-6) == 1 assert_norm_equality(X.flatten(), ref_norms, 1.0e-5) return X, cells # with these target edge lengths, dmsh once produced weird results near the boundary @pytest.mark.parametrize( "target_edge_length", [0.07273, 0.07272, 0.07271, 0.0711, 0.03591] ) def test_degenerate_circle(target_edge_length): geo = dmsh.Circle([0.0, 0.0], 1.0) X, cells = dmsh.generate( geo, target_edge_length, show=False, max_steps=200, verbose=True ) mesh = meshplex.MeshTri(X, cells) min_q = np.min(mesh.q_radius_ratio) assert min_q > 0.5, f"min cell quality: {min_q:.3f}" def test_boundary_step(): geo = dmsh.Circle([0.1, 0.2], 1.0) np.random.seed(0) pts = np.random.uniform(-1.0, 1.0, (2, 100)) pts = geo.boundary_step(pts) tol = 1.0e-12 assert np.all(np.abs(geo.dist(pts)) < tol) if __name__ == "__main__": test_boundary_step() dmsh-0.2.18/tests/test_closed_path.py000066400000000000000000000122211413425205000175670ustar00rootroot00000000000000import numpy as np from dmsh.geometry import pypathlib def test_show(): path = pypathlib.ClosedPath([[0.0, 0.0], [1.0, 0.0], [1.1, 1.1], [0.1, 1.0]]) path.show() def test_convex(): path = pypathlib.ClosedPath([[0.0, 0.0], [1.0, 0.0], [1.1, 1.1], [0.1, 1.0]]) ref = 1.045 assert abs(path.area - ref) < 1.0e-12 * ref assert path.positive_orientation assert all(path.is_convex_node) def test_orientation(): path = pypathlib.ClosedPath([[0.1, 1.0], [1.1, 1.1], [1.0, 0.0], [0.0, 0.0]]) ref = 1.045 assert abs(path.area - ref) < 1.0e-12 * ref assert not path.positive_orientation assert all(path.is_convex_node) def test_concave(): path = pypathlib.ClosedPath( [[0.0, 0.0], [1.0, 0.0], [0.9, 0.5], [1.1, 1.1], [0.1, 1.0]] ) ref = 0.965 assert abs(path.area - ref) < 1.0e-12 * ref assert path.positive_orientation assert np.array_equal(path.is_convex_node, [True, True, False, True, True]) def test_concave_counterclock(): path = pypathlib.ClosedPath( [[0.1, 1.0], [1.1, 1.1], [0.9, 0.5], [1.0, 0.0], [0.0, 0.0]] ) ref = 0.965 assert abs(path.area - ref) < 1.0e-12 * ref assert not path.positive_orientation assert np.array_equal(path.is_convex_node, [True, True, False, True, True]) def test_squared_distance(): path = pypathlib.ClosedPath( [[0.0, 0.0], [1.0, 0.0], [0.9, 0.5], [1.0, 1.0], [0.0, 1.0]] ) dist = path.squared_distance( [[0.2, 0.1], [0.5, 0.5], [1.0, 0.5], [0.0, 1.1], [-0.1, 1.1], [1.0, 1.0]] ) ref = np.array([0.01, 0.16, 1.0 / 104.0, 0.01, 0.02, 0.0]) assert np.all(np.abs(dist - ref) < 1.0e-12) def test_distance(): path = pypathlib.ClosedPath( [[0.0, 0.0], [1.0, 0.0], [0.9, 0.5], [1.0, 1.0], [0.0, 1.0]] ) dist = path.distance( [[0.2, 0.1], [0.5, 0.5], [1.0, 0.5], [0.0, 1.1], [-0.1, 1.1], [1.0, 1.0]] ) ref = np.array([0.1, 0.4, np.sqrt(1.0 / 104.0), 0.1, np.sqrt(2) / 10, 0.0]) assert np.all(np.abs(dist - ref) < 1.0e-12) def test_signed_distance(): path = pypathlib.ClosedPath( [[0.0, 0.0], [1.0, 0.0], [0.9, 0.5], [1.0, 1.0], [0.0, 1.0]] ) dist = path.signed_distance( [[0.2, 0.1], [0.5, 0.5], [1.0, 0.5], [0.0, 1.1], [-0.1, 1.1], [1.0, 1.0]] ) print(dist) ref = np.array([-0.1, -0.4, np.sqrt(1.0 / 104.0), 0.1, np.sqrt(2) / 10, 0.0]) assert np.all(np.abs(dist - ref) < 1.0e-12) def test_inside(): path = pypathlib.ClosedPath( [[0.0, 0.0], [1.0, 0.0], [0.9, 0.5], [1.0, 1.0], [0.0, 1.0]] ) contains_points = path.contains_points( [[0.2, 0.1], [0.5, 0.5], [1.0, 0.5], [0.0, 1.1], [-0.1, 1.1], [1.0, 1.0]] ) assert np.array_equal(contains_points, [True, True, False, False, False, True]) def test_closest_points(): path = pypathlib.ClosedPath( [[0.0, 0.0], [1.0, 0.0], [0.9, 0.5], [1.0, 1.0], [0.0, 1.0]] ) closest_points = path.closest_points( [ [0.2, 0.1], [0.5, 0.5], [1.0, 0.5 + 1.0e-12], [0.0, 1.1], [-0.1, 1.1], [1.0, 1.0], ] ) ref = np.array( [ [0.2, 0.0], [0.9, 0.5], [9.0384615384615385e-01, 5.1923076923076927e-01], [0.0, 1.0], [0.0, 1.0], [1.0, 1.0], ] ) assert np.all(np.abs(closest_points - ref) < 1.0e-12) def test_signed_squared_distance(): path = pypathlib.ClosedPath( [[0.0, 0.0], [1.0, 0.0], [0.9, 0.5], [1.0, 1.0], [0.0, 1.0]] ) dist = path.signed_squared_distance( [[0.2, 0.1], [0.5, 0.5], [1.0, 0.5], [0.0, 1.1], [-0.1, 1.1], [1.0, 1.0]] ) ref = np.array([-0.01, -0.16, 1.0 / 104.0, 0.01, 0.02, 0.0]) assert np.all(np.abs(dist - ref) < 1.0e-12) def test_sharp_angle(): path = pypathlib.ClosedPath( [ [0.0, 0.0], [1.0, 0.0], [1.0, 0.45], [0.6, 0.5], [1.0, 0.55], [1.0, 1.0], [0.0, 1.0], ] ) contains_points = path.contains_points([[0.5, 0.4], [0.5, 0.6]]) assert np.all(contains_points) dist = path.signed_squared_distance([[0.5, 0.4], [0.5, 0.6]]) ref = np.array([-0.02, -0.02]) assert np.all(np.abs(dist - ref) < 1.0e-12) def test_project_distance(): path = pypathlib.ClosedPath( [ [0.0, 0.0], [1.5, 0.4], [1.0, 1.0], ] ) closest_points = path.closest_points( [ [0.5, 0.1], [0.5, 0.2], [0.5, 0.3], [0.5, 0.4], [0.5, 0.5], ] ) # closest_points = np.array([4.9170124481327798e-01, 1.3112033195020747e-01]) # closest_points = np.array([4.9170124481327804e-01, 1.3112033195020747e-01]) # the projected point should be _on_ the polygon dist = path.distance(closest_points) assert np.all(dist < 1.0e-12) # def test_two_points(): # path = pypathlib.ClosedPath([[-0.5, 1.0], [+0.5, 1.0]]) # contains_points = path.contains_points([[0.0, 0.0], [0.0, 2.0]]) # assert np.array_equal(contains_points, [False, False]) if __name__ == "__main__": test_closest_points() dmsh-0.2.18/tests/test_difference.py000066400000000000000000000041441413425205000174010ustar00rootroot00000000000000import numpy as np from helpers import assert_norm_equality import dmsh def test_difference(show=False): geo = dmsh.Circle([-0.5, 0.0], 1.0) - dmsh.Circle([+0.5, 0.0], 1.0) X, cells = dmsh.generate(geo, 0.1, show=show, max_steps=100) geo.plot() ref_norms = [2.9409044729708609e02, 1.5855488859739937e01, 1.5000000000000000e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-6) return X, cells def test_boundary_step(): geo = dmsh.Difference(dmsh.Circle([-0.5, 0.0], 1.0), dmsh.Circle([+0.5, 0.0], 1.0)) pts = np.array( [ [-2.1, 0.0], [0.1, 0.0], [-1.4, 0.0], [-0.6, 0.0], ] ) pts = geo.boundary_step(pts.T).T ref = np.array([[-1.5, 0.0], [-0.5, 0.0], [-1.5, 0.0], [-0.5, 0.0]]) assert np.all(np.abs(pts - ref) < 1.0e-10) def test_boundary_step2(): geo = dmsh.Difference(dmsh.Circle([-0.5, 0.0], 1.0), dmsh.Circle([+0.5, 0.0], 1.0)) np.random.seed(0) pts = np.random.uniform(-2.0, 2.0, (2, 100)) pts = geo.boundary_step(pts) # geo.plot() # import matplotlib.pyplot as plt # plt.plot(pts[0], pts[1], "xk") # plt.show() assert np.all(np.abs(geo.dist(pts)) < 1.0e-12) def test_boundary_step_pacman(): geo = dmsh.Difference( dmsh.Circle([0.0, 0.0], 1.0), dmsh.Polygon([[0.0, 0.0], [1.5, 0.4], [1.5, -0.4]]), ) # np.random.seed(0) # pts = np.random.uniform(-2.0, 2.0, (2, 100)) # pts = np.array([[-2.0, 0.0]]) # pts = np.array([[-0.1, 0.0]]) # pts = np.array([[0.0, 2.0]]) # pts = np.array([[0.0, 0.9]]) # pts = np.array([[2.0, 0.1]]) # pts = np.array([[0.1, 0.1]]) # pts = np.array([[0.7, 0.1]]) pts = np.array([[0.5, 0.1]]) pts = pts.T print(pts.T.shape) pts = geo.boundary_step(pts) geo.plot() import matplotlib.pyplot as plt plt.plot(pts[0], pts[1], "xk") plt.show() # assert np.all(np.abs(geo.dist(pts)) < 1.0e-12) if __name__ == "__main__": # from helpers import save X, cells = test_difference(show=True) # save("difference.png", X, cells) # test_boundary_step_pacman() dmsh-0.2.18/tests/test_ellipse.py000066400000000000000000000007651413425205000167510ustar00rootroot00000000000000import pytest from helpers import assert_norm_equality, save import dmsh @pytest.mark.skip def test_ellipse(show=False): geo = dmsh.Ellipse([0.0, 0.0], 2.0, 1.0) X, cells = dmsh.generate(geo, 0.2, show=show) geo.plot() ref_norms = [2.5108941453435716e02, 1.5652963447587933e01, 1.9890264390440919e00] assert_norm_equality(X.flatten(), ref_norms, 2.0e-2) return X, cells if __name__ == "__main__": X, cells = test_ellipse(show=True) save("ellipse.png", X, cells) dmsh-0.2.18/tests/test_halfspace.py000066400000000000000000000011431413425205000172310ustar00rootroot00000000000000import numpy as np from helpers import assert_norm_equality, save import dmsh def test_halfspace(show=False): geo = dmsh.Intersection( [ dmsh.HalfSpace(np.sqrt(0.5) * np.array([1.0, 1.0])), dmsh.Circle([0.0, 0.0], 1.0), ] ) X, cells = dmsh.generate(geo, 0.1, show=show, max_steps=100) ref_norms = [1.6399670188761661e02, 1.0011048291798387e01, 9.9959986881486440e-01] assert_norm_equality(X.flatten(), ref_norms, 1.0e-6) return X, cells if __name__ == "__main__": X, cells = test_halfspace(show=True) save("halfspace.png", X, cells) dmsh-0.2.18/tests/test_intersection.py000066400000000000000000000037531413425205000200220ustar00rootroot00000000000000import numpy as np from helpers import assert_norm_equality, save import dmsh def test_intersection(show=False): geo = dmsh.Circle([0.0, -0.5], 1.0) & dmsh.Circle([0.0, +0.5], 1.0) X, cells = dmsh.generate(geo, 0.1, show=show, tol=1.0e-10, max_steps=100) geo.plot() ref_norms = [8.6491736892894920e01, 6.1568624411912278e00, 8.6602540378466342e-01] assert_norm_equality(X.flatten(), ref_norms, 1.0e-10) return X, cells def test_intersection_circles(show=False): angles = np.pi * np.array([3.0 / 6.0, 7.0 / 6.0, 11.0 / 6.0]) geo = dmsh.Intersection( [ dmsh.Circle([np.cos(angles[0]), np.sin(angles[0])], 1.5), dmsh.Circle([np.cos(angles[1]), np.sin(angles[1])], 1.5), dmsh.Circle([np.cos(angles[2]), np.sin(angles[2])], 1.5), ] ) X, cells = dmsh.generate(geo, 0.1, show=show, tol=1.0e-10, max_steps=100) ref_norms = [6.7661318585210836e01, 5.0568863746561723e00, 7.2474487138537913e-01] assert_norm_equality(X.flatten(), ref_norms, 1.0e-10) return X, cells def test_boundary_step(): geo = dmsh.Circle([0.0, -0.5], 1.0) & dmsh.Circle([0.0, +0.5], 1.0) pts = np.array([[0.0, -5.0], [0.0, 4.1]]) pts = geo.boundary_step(pts.T).T ref = np.array([[0.0, -0.5], [0.0, 0.5]]) assert np.all(np.abs(pts - ref) < 1.0e-10) pts = np.array([[0.0, -0.1], [0.0, 0.1]]) pts = geo.boundary_step(pts.T).T ref = np.array([[0.0, -0.5], [0.0, 0.5]]) assert np.all(np.abs(pts - ref) < 1.0e-10) def test_boundary_step2(): geo = dmsh.Circle([0.0, -0.5], 1.0) & dmsh.Circle([0.0, +0.5], 1.0) np.random.seed(0) pts = np.random.uniform(-1.0, 1.0, (2, 100)) pts = geo.boundary_step(pts) # geo.plot() # import matplotlib.pyplot as plt # plt.plot(pts[0], pts[1], "xk") # plt.show() assert np.all(np.abs(geo.dist(pts)) < 1.0e-7) if __name__ == "__main__": X, cells = test_intersection(show=True) save("intersection.png", X, cells) # test_boundary_step2() dmsh-0.2.18/tests/test_large.py000066400000000000000000000010171413425205000163750ustar00rootroot00000000000000from helpers import assert_norm_equality import dmsh def test_large(show=False): # https://github.com/nschloe/dmsh/issues/11 r = dmsh.Rectangle(-10.0, +20.0, -10.0, +20.0) c = dmsh.Circle([0.0, 0.0], 3) geo = dmsh.Difference(r, c) X, cells = dmsh.generate(geo, 2.0, tol=1.0e-5, max_steps=100, show=show) ref_norms = [4.6292581642363657e03, 2.4187329297982635e02, 2.0000000000000000e01] assert_norm_equality(X.flatten(), ref_norms, 1.0e-4) if __name__ == "__main__": test_large(show=True) dmsh-0.2.18/tests/test_pacman.py000066400000000000000000000011211413425205000165360ustar00rootroot00000000000000from helpers import assert_norm_equality import dmsh def test_pacman(show=False): geo = dmsh.Difference( dmsh.Circle([0.0, 0.0], 1.0), dmsh.Polygon([[0.0, 0.0], [1.5, 0.4], [1.5, -0.4]]), ) X, cells = dmsh.generate(geo, 0.1, show=show, tol=1.0e-5, max_steps=100) ref_norms = [3.0173012692535394e02, 1.3565685453257570e01, 9.9999999999884770e-01] assert_norm_equality(X.flatten(), ref_norms, 1.0e-10) return X, cells if __name__ == "__main__": X, cells = test_pacman(show=True) # from helpers import save # save("pacman.png", X, cells) dmsh-0.2.18/tests/test_path.py000066400000000000000000000014121413425205000162360ustar00rootroot00000000000000import numpy as np from dmsh.geometry import pypathlib def test_squared_distance(): path = pypathlib.Path([[0.0, 0.0], [1.0, 0.0], [0.9, 0.5], [1.0, 1.0], [0.0, 1.0]]) dist = path.squared_distance( [[0.2, 0.1], [0.5, 0.5], [1.0, 0.5], [0.0, 1.1], [-0.1, 1.1], [1.0, 1.0]] ) ref = np.array([0.01, 0.16, 1.0 / 104.0, 0.01, 0.02, 0.0]) assert np.all(np.abs(dist - ref) < 1.0e-12) return def test_one_point(): path = pypathlib.Path([[0.0, 0.0]]) dist = path.squared_distance( [[0.2, 0.1], [0.5, 0.5], [1.0, 0.5], [0.0, 1.1], [-0.1, 1.1], [1.0, 1.0]] ) ref = np.array([0.05, 0.5, 1.25, 1.21, 1.22, 2.0]) assert np.all(np.abs(dist - ref) < 1.0e-12) return if __name__ == "__main__": test_squared_distance() dmsh-0.2.18/tests/test_polygon.py000066400000000000000000000024051413425205000167740ustar00rootroot00000000000000import numpy as np from helpers import assert_norm_equality import dmsh def test(show=False): geo = dmsh.Polygon( [ [0.0, 0.0], [1.1, 0.0], [1.2, 0.5], [0.7, 0.6], [2.0, 1.0], [1.0, 2.0], [0.5, 1.5], ] ) # geo.show() X, cells = dmsh.generate(geo, 0.1, show=show, max_steps=100) ref_norms = [4.1426056822140765e02, 2.1830112296142847e01, 2.0000000000000000e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-5) return X, cells def test_boundary_step2(plot=False): geo = dmsh.Polygon( [ [0.0, 0.0], [1.1, 0.0], [1.2, 0.5], [0.7, 0.6], [2.0, 1.0], [1.0, 2.0], [0.5, 1.5], ] ) np.random.seed(0) pts = np.random.uniform(-2.0, 2.0, (2, 100)) pts = geo.boundary_step(pts) if plot: geo.plot() import matplotlib.pyplot as plt plt.plot(pts[0], pts[1], "xk") plt.show() dist = geo.dist(pts) assert np.all(np.abs(dist) < 1.0e-12) if __name__ == "__main__": # from helpers import save # X, cells = test(show=False) # save("polygon.svg", X, cells) test_boundary_step2(plot=True) dmsh-0.2.18/tests/test_quarter_annulus.py000066400000000000000000000014611413425205000205360ustar00rootroot00000000000000import numpy as np from helpers import assert_norm_equality import dmsh def test_quarter_annulus(): h = 0.05 disk0 = dmsh.Circle([0.0, 0.0], 0.25) disk1 = dmsh.Circle([0.0, 0.0], 1.0) diff0 = dmsh.Difference(disk1, disk0) rect = dmsh.Rectangle(0.0, 1.0, 0.0, 1.0) quarter = dmsh.Intersection([diff0, rect]) points, cells = dmsh.generate( quarter, lambda x: h + 0.1 * np.abs(disk0.dist(x)), tol=1.0e-10, max_steps=100, ) ref_norms = [7.7455372708027483e01, 6.5770003813066431e00, 1.0000000000000000e00] assert_norm_equality(points.flatten(), ref_norms, 1.0e-10) return points, cells if __name__ == "__main__": import meshio points, cells = test_quarter_annulus() meshio.Mesh(points, {"triangle": cells}).write("out.vtk") dmsh-0.2.18/tests/test_rectangle.py000066400000000000000000000045441413425205000172570ustar00rootroot00000000000000import numpy as np from helpers import assert_norm_equality, save import dmsh def test_boundary_step(): geo = dmsh.Rectangle(-2.0, +2.0, -1.0, +1.0) # Check boundary steps out = geo.boundary_step([0.1, 0.0]) assert np.all(np.abs(out - [2.0, 0.0]) < 1.0e-10) out = geo.boundary_step([0.0, 0.1]) assert np.all(np.abs(out - [0.0, 1.0]) < 1.0e-10) out = geo.boundary_step([-0.1, 0.0]) assert np.all(np.abs(out - [-2.0, 0.0]) < 1.0e-10) out = geo.boundary_step([0.0, -0.1]) assert np.all(np.abs(out - [0.0, -1.0]) < 1.0e-10) out = geo.boundary_step([2.1, 0.037]) assert np.all(np.abs(out - [2.0, 0.037]) < 1.0e-10) out = geo.boundary_step([0.037, 1.1]) assert np.all(np.abs(out - [0.037, 1.0]) < 1.0e-10) out = geo.boundary_step([-2.1, 0.037]) assert np.all(np.abs(out - [-2.0, 0.037]) < 1.0e-10) out = geo.boundary_step([0.037, -1.1]) assert np.all(np.abs(out - [0.037, -1.0]) < 1.0e-10) out = geo.boundary_step([2.1, 1.1]) assert np.all(np.abs(out - [2.0, 1.0]) < 1.0e-10) out = geo.boundary_step([-2.1, 1.1]) assert np.all(np.abs(out - [-2.0, 1.0]) < 1.0e-10) out = geo.boundary_step([2.1, -1.1]) assert np.all(np.abs(out - [2.0, -1.0]) < 1.0e-10) out = geo.boundary_step([-2.1, -1.1]) assert np.all(np.abs(out - [-2.0, -1.0]) < 1.0e-10) def test_rectangle(show=False): geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0) X, cells = dmsh.generate(geo, 0.1, show=show, max_steps=100) ref_norms = [9.7172325705673779e02, 3.1615286239175994e01, 2.0000000000000000e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-10) return X, cells def test_duplicate_points(show=False): # https://github.com/nschloe/dmsh/issues/66 # geo = dmsh.Rectangle(0.0, 1.8, 0.0, 0.41) # points, cells = dmsh.generate(geo, 0.2, tol=2e-2, show=show) # is_part_of_cell = np.zeros(len(points), dtype=bool) # is_part_of_cell[cells.flat] = True # assert np.all(is_part_of_cell) geo = dmsh.Rectangle(0.0, 1.4, 0.0, 0.41) points, cells = dmsh.generate(geo, 0.025, tol=1e-5, show=show, max_steps=1) is_part_of_cell = np.zeros(len(points), dtype=bool) is_part_of_cell[cells.flat] = True assert np.all(is_part_of_cell) if __name__ == "__main__": # test_duplicate_points(show=True) X, cells = test_rectangle(show=False) save("rectangle.png", X, cells) dmsh-0.2.18/tests/test_rectangle_hole.py000066400000000000000000000016251413425205000202630ustar00rootroot00000000000000from helpers import assert_norm_equality import dmsh def test_rectangle_hole(show=False): geo = dmsh.Difference( dmsh.Rectangle(60, 330, 380, 650), dmsh.Rectangle(143, 245, 440, 543) ) X, cells = dmsh.generate( geo, 20, tol=1.0e-5, show=show, flip_tol=1.0e-10, max_steps=100 ) ref_norms = [1.2931633675576400e05, 7.6377328985582844e03, 6.5000000000000000e02] assert_norm_equality(X.flatten(), ref_norms, 1.0e-10) def test_rectangle_hole2(show=False): geo = dmsh.Difference( dmsh.Rectangle(0.0, 5.0, 0.0, 5.0), dmsh.Polygon([[1, 1], [4, 1], [4, 4], [1, 4]]), ) X, cells = dmsh.generate(geo, 1.0, show=show, tol=1.0e-3, max_steps=100) ref_norms = [1.3990406144096474e02, 2.2917592510234346e01, 5.0000000000000000e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-2) if __name__ == "__main__": test_rectangle_hole2(show=True) dmsh-0.2.18/tests/test_refinement_point_line.py000066400000000000000000000011601413425205000216560ustar00rootroot00000000000000from helpers import assert_norm_equality, save import dmsh def test(show=False): geo = dmsh.Rectangle(0.0, 1.0, 0.0, 1.0) # p0 = dmsh.Path([[0.0, 0.0]]) p1 = dmsh.Path([[0.4, 0.6], [0.6, 0.4]]) def edge_size(x): return 0.03 + 0.1 * p1.dist(x) X, cells = dmsh.generate(geo, edge_size, show=show, tol=1.0e-10, max_steps=100) ref_norms = [3.7918105331047593e02, 1.5473837427489348e01, 1.0000000000000000e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-3) return X, cells if __name__ == "__main__": X, cells = test(show=False) save("refinement_line.png", X, cells) dmsh-0.2.18/tests/test_rotation.py000066400000000000000000000010071413425205000171410ustar00rootroot00000000000000import numpy as np from helpers import assert_norm_equality, save import dmsh def test(show=False): geo = dmsh.Rotation(dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0), 0.1 * np.pi) X, cells = dmsh.generate(geo, 0.1, show=show, tol=1.0e-10, max_steps=100) ref_norms = [9.4730152857365385e02, 3.1160562530932285e01, 2.2111300269652543e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-10) return X, cells if __name__ == "__main__": X, cells = test(show=False) save("rotation.png", X, cells) dmsh-0.2.18/tests/test_scaling.py000066400000000000000000000010521413425205000167220ustar00rootroot00000000000000from helpers import assert_norm_equality, save import dmsh def test(show=False): # should both work geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0) * 2.0 geo = 2.0 * dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0) X, cells = dmsh.generate(geo, 0.1, show=show, tol=1.0e-5, max_steps=100) ref_norms = [7.6829959173892494e03, 1.2466061090733828e02, 4.0000000000000000e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-7) return X, cells if __name__ == "__main__": X, cells = test(show=False) save("scaling.png", X, cells) dmsh-0.2.18/tests/test_show_level_set.py000066400000000000000000000002651413425205000203310ustar00rootroot00000000000000import dmsh def test_show(): # geo = dmsh.Circle([0.0, 0.0], 1.0) geo = dmsh.Rectangle(-1.0, +1.0, -1.0, +1.0) geo.show() if __name__ == "__main__": test_show() dmsh-0.2.18/tests/test_speed.py000066400000000000000000000020471413425205000164070ustar00rootroot00000000000000import numpy as np import perfplot import pytest from matplotlib import path from dmsh.geometry import pypathlib @pytest.mark.skip(reason="fails on gh-actions for some reason") def test_speed(n=3): path_pts = [[0, 0], [0, 1], [1, 1], [1, 0]] path0 = path.Path(path_pts) path1 = pypathlib.ClosedPath(path_pts) def _mpl_path(pts): return path0.contains_points(pts) def _pypathlib_contains_points(pts): return path1.contains_points(pts) np.random.seed(0) perfplot.show( setup=lambda n: np.random.rand(n, 2), kernels=[_mpl_path, _pypathlib_contains_points], n_range=[2 ** k for k in range(n)], labels=["matplotlib.path.contains_points", "pypathlib.contains_points"], logx=True, logy=True, xlabel="num points", ) def benchmark(): path_pts = [[0, 0], [0, 1], [1, 1], [1, 0]] path1 = pypathlib.ClosedPath(path_pts) pts = np.random.rand(5000000, 2) path1.contains_points(pts) if __name__ == "__main__": # test_speed(20) benchmark() dmsh-0.2.18/tests/test_square_hole_refined.py000066400000000000000000000012161413425205000213070ustar00rootroot00000000000000import numpy as np from helpers import assert_norm_equality, save import dmsh def test(show=False): r = dmsh.Rectangle(-1.0, +1.0, -1.0, +1.0) c = dmsh.Circle([0.0, 0.0], 0.3) geo = dmsh.Difference(r, c) X, cells = dmsh.generate( geo, lambda pts: np.abs(c.dist(pts)) / 5 + 0.05, show=show, tol=1.0e-10, max_steps=100, ) ref_norms = [2.3686099753024831e02, 1.1750558136202198e01, 1.0000000000000000e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-2) return X, cells if __name__ == "__main__": X, cells = test(show=True) save("square_hole_refined.png", X, cells) dmsh-0.2.18/tests/test_stretch.py000066400000000000000000000007511413425205000167630ustar00rootroot00000000000000from helpers import assert_norm_equality, save import dmsh def test(show=False): geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0).stretch([1.0, 1.0]) X, cells = dmsh.generate(geo, 0.3, show=show, tol=1.0e-3, max_steps=100) ref_norms = [1.9006907971528796e02, 1.5666202908904914e01, 2.6213203435596428e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-2) return X, cells if __name__ == "__main__": X, cells = test(show=False) save("stretch.png", X, cells) dmsh-0.2.18/tests/test_translation.py000066400000000000000000000007411413425205000176440ustar00rootroot00000000000000from helpers import assert_norm_equality import dmsh def test(show=False): # should both work geo = [1.0, 1.0] + dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0) geo = dmsh.Rectangle(-1.0, +2.0, -1.0, +1.0) + [1.0, 1.0] X, _ = dmsh.generate(geo, 0.1, show=show, max_steps=100) ref_norms = [1.7524999999999998e03, 5.5612899955332637e01, 3.0000000000000000e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-7) if __name__ == "__main__": test(show=False) dmsh-0.2.18/tests/test_union.py000066400000000000000000000053041413425205000164360ustar00rootroot00000000000000import numpy as np from helpers import assert_equality, assert_norm_equality import dmsh def test_union_circles(show=False): geo = dmsh.Circle([-0.5, 0.0], 1.0) + dmsh.Circle([+0.5, 0.0], 1.0) X, cells = dmsh.generate(geo, 0.15, show=show, tol=1.0e-5, max_steps=100) geo.plot() ref_norms = [3.0080546580519666e02, 1.5775854476745508e01, 1.5000000000000000e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-10) return X, cells def test_union_rectangles(show=False): geo = dmsh.Rectangle(-1.0, +0.5, -1.0, +0.5) | dmsh.Rectangle( -0.5, +1.0, -0.5, +1.0 ) X, cells = dmsh.generate(geo, 0.15, show=show, tol=1.0e-5, max_steps=100) ref_norms = [1.8417796811774514e02, 1.1277323166424049e01, 1.0000000000000000e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-10) return X, cells def test_union_three_circles(show=False): angles = np.pi * np.array([3.0 / 6.0, 7.0 / 6.0, 11.0 / 6.0]) geo = dmsh.Union( [ dmsh.Circle([np.cos(angles[0]), np.sin(angles[0])], 1.0), dmsh.Circle([np.cos(angles[1]), np.sin(angles[1])], 1.0), dmsh.Circle([np.cos(angles[2]), np.sin(angles[2])], 1.0), ] ) X, cells = dmsh.generate(geo, 0.2, show=show, tol=1.0e-5, max_steps=100) ref_norms = [4.0359760255235619e02, 2.1162741423521961e01, 2.0000000000000000e00] assert_norm_equality(X.flatten(), ref_norms, 1.0e-10) return X, cells def test_boundary_step(): geo = dmsh.Union([dmsh.Circle([-0.5, 0.0], 1.0), dmsh.Circle([+0.5, 0.0], 1.0)]) a = geo.boundary_step([-0.5, 0.9]) assert np.array_equal(a, [-0.5, 1.0]) a = geo.boundary_step([-0.5, 0.6]) assert np.array_equal(a, [-0.5, 1.0]) a = geo.boundary_step([0.05, 0.05]) assert_equality(a, [-4.4469961425821203e-01, 9.9846976285554556e-01], 1.0e-10) pts = np.array([[-5.0, 0.0], [4.1, 0.0]]) pts = geo.boundary_step(pts.T).T ref = np.array([[-1.5, 0.0], [1.5, 0.0]]) assert np.all(np.abs(pts - ref) < 1.0e-10) pts = np.array([[-0.9, 0.0], [1.1, 0.0]]) pts = geo.boundary_step(pts.T).T ref = np.array([[-1.5, 0.0], [1.5, 0.0]]) assert np.all(np.abs(pts - ref) < 1.0e-10) def test_boundary_step2(): geo = dmsh.Union([dmsh.Circle([-0.5, 0.0], 1.0), dmsh.Circle([+0.5, 0.0], 1.0)]) np.random.seed(0) pts = np.random.uniform(-2.0, 2.0, (2, 100)) pts = geo.boundary_step(pts) # geo.plot() # import matplotlib.pyplot as plt # plt.plot(pts[0], pts[1], "xk") # plt.show() assert np.all(np.abs(geo.dist(pts)) < 1.0e-12) if __name__ == "__main__": # from helpers import save X, cells = test_union_circles(show=True) # save("union.png", X, cells) # test_boundary_step2() dmsh-0.2.18/tox.ini000066400000000000000000000002661413425205000140500ustar00rootroot00000000000000[tox] envlist = py3 isolated_build = True [testenv] deps = optimesh perfplot pytest pytest-codeblocks pytest-cov extras = all commands = pytest {posargs} --codeblocks