The name of this library derives from the notion of an (abstract) simplicial complex, and is not related to complex numbers. The scope of this library is probably best captured with the term DEC (discrete exterior calculus), although the terms discrete differential geometry, discrete topology, subdivision surfaces and multigrid also apply.
This library provides useful functionality in a wide range of computational and graphical modelling contexts
- Computational modelling, such as fluid dynamics, electromagnetics or elasticity
- Surface modelling, subdivision curves, and other geometric manipulations
The examples folder contains a comprehensive set of brief but illustrative use cases. This includes simple problems illustrating concepts in computational geometry or discrete exterior calculus, to the implementation of some landmarks papers in these fields.
Aside from serving my own projects and curiosity, it is my aim that the coding this in this package should be sufficiently clean and generic that it may serve the dissemination of ideas between novices and people working out new ideas alike.
- All functionality is vectorized and efficiently implemented, so useful for real-world problem sizes
- (almost all) functionality is agnostic to the number of dimensions used
- Complete separation of topology and geometry
- Handling of simplicial and cubical complexes
- Handling of different geometries (spherical, Euclidian, and potentially others)
- Handling of boundary topology, geometry and boundary conditions in a unified manner
- Hierarchical subdivision logic, for use in subdivision surfaces and multigrid solvers
- Construction of boundary dual and relation to formulation of boundary conditions
- Picking of primal/dual power diagram elements using only a single closest-point query
- Fundamental-domain interpolation of dual 0-forms; much simpler conceptually than barycentric, and can be efficiently implemented
- Semi-structured multigrid transfer operator
The discrete exterior calculus components of this package provide a lot of overlapping functionality with pydec, although the vectorized implementations provided here will scale a lot better
Many of the algorithms implemented here are generalized variants of those initially implemented in Escheresque, which was intended to become the first real use-cases of this package.
- Stencil-based cochain complexes on regular nd-grids; possibly with efficient gpu kernels
- Add 3d electrodynamics example; preferably also by means of implementing a complex with spacetime-metric
- Multigrid support
- Black box multigrid on simplicial and regular meshes, for all k-forms
- Replace ugly casting system with some more automagic dynamic dispatch
- Cylindrical coordinates and corresponding metric calculations
- Hybrid triangle-quad meshes
- Try to implement something along the lines of these references https://pdfs.semanticscholar.org/f3b2/532c517e1e6efaff90e7fe69d2b9e8ff75bc.pdf https://arxiv.org/pdf/0804.0279.pdf
Pycomplex currently targets python 3 primarily. The source is mostly python 2 compliant and would be easy to make so if the need arose, but compatibility is currently not actively maintained for convenience reasons. Pycomplex has been successfully (but not systematically) tested on all major platforms
To invoke the tests from the command line, run pytest --show_plot=False Many tests have a visual component that will be suppressed by using this flag
The intent of the licenses offered is to make this work easily accessible for all uses, while incentivising contributions to it.
- CC BY-NC-SA 4.0 OSL3/ ASL academic public license
- AGPLv3
- Proprietary
For educational and research use, the CC BY-NC-SA 4.0 license is probably most relevant. All educational and research use is considered non-commercial use for the purposes of this license, so it works like any open-access paper; you are free to use it, with attribution. With one exception; this is a share-alike license, and it obliges you to distribute your code. Of course since you are a scientist and strive to do work that is reproducible in a meaningfull sense of the word, you do always publish your code. But as for those other wannabe-scientists out there who feel putting their code out is too much trouble; sorry, you cant use this code either.
Proprietary licensing can be arranged. Considering that this package is only of modest size, there is only so much stopping you from absorbing the ideas contained therein, and making a good faith effort at writing your own independent implementation thereof. However, reimbursing me for my spent is probably a more efficient solution.
An AGPL license is also offered.
Note, that is AGPL, not LGPL. If you use this software, id like you to contribute back in some way or another,
and technically obsolete details like linking or distributing have no bearing on that logic as far as I am concerned.
Note that these considerations pertain to the pycomplex python package.
All code in the sister-module examples is free-as-in-beer.
What I particularly hope to see is people implementing research in the field of computational geometry or computational physics using this package.
This can be in the form of you adding this package as a dependency to your project,
but from the perspective of this project, adding a submodule to the examples module would be even better.
Such contributions would be happily merged into the examples module, and I feel it is natural you should retain authorship thereof.
When it comes to bugfixes or minor contributions to the core of the package, I would be happy to consider them, but under CLA such as to not complicate my creative control of this project. In the unlikely event anyone is interested in making major additions relative to the existing project, it would be best to discuss that in advance and work out something mutually agreeable.