LaPy is a package to compute spectral features (Laplace-Beltrami operator) on tetrahedral and triangle meshes. It is written purely in python 3 without sacrificing speed as almost all loops are vectorized, drawing upon efficient and sparse mesh data structures. It is basically a port of the C++ ShapeDNA project with extended differential geometry capabilities.
- TriaMesh: a class for triangle meshes offering various operations, such as fixing orientation, smoothing, curvature, boundary, quality, normals, and various efficient mesh datastructure (edges, adjacency matrices)
- TetMesh: a class for tetrahedral meshes (orientation, boundary ...)
- TriaIO, TetIO: for both tets and trias from off, vtk, etc. formats
- FuncIO: import/export vertex functions and eigenvector files
- Solver: a class for linear FEM computation (Laplace stiffness and mass matrix, fast and sparse eigenvalue solver, anisotropic Laplace, Poisson)
- DiffGeo: compute gradients, divergence, mean curvature flow, etc.
- Heat: for heat kernel and diffusion
- ShapeDNA: compute the ShapeDNA descriptor of surfaces and solids
- Plot: functions for interactive visualization (wrapping plotly)
- Add unit tests and automated testing (e.g. travis)
- Add command line scripts for various functions
The LaPy package is a comprehensive collection of scripts, so we refer to the 'help' function and docstring of each module / function / class for usage info. For example:
import lapy as lp
help(lp.TriaMesh)
help(lp.Solver)
In the examples subdirectory, we provide several Jupyter notebooks that
illustrate prototypical use cases of the toolbox.
Use the following code to download, build and install a package from this repository into your local Python package directory:
pip3 install --user git+https://github.com/Deep-MI/LaPy.git#egg=lapy
Use the following code to install the package in editable mode to a location of your choice:
pip3 install --user --src /my/preferred/location --editable git+https://github.com/Deep-MI/Lapy.git#egg=lapy
Several functions, e.g. the Solver, require a sparse matrix decomposition, for which either the LU decomposition (from scipy sparse) or the faster Cholesky decomposition (from scikit-sparse cholmod) can be used. If the parameter flag use_cholmod is True, the code will try to import cholmod from the scikit-sparse package and will fall back to LU if the import fails. If you would like to use cholmod, you need to install scikit-sparse separately. It cannot be listed among LaPy's dependencies (e.g. in setup.py or requirements.txt) as that causes errors with pip. scikit-sparse requires numpy and scipy to be installed separately beforehand.
If you use this software for a publication please cite both these papers:
[1] Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids. Reuter M, Wolter F-E, Peinecke N Computer-Aided Design. 2006;38(4):342-366. http://dx.doi.org/10.1016/j.cad.2005.10.011
[2] BrainPrint: a discriminative characterization of brain morphology. Wachinger C, Golland P, Kremen W, Fischl B, Reuter M Neuroimage. 2015;109:232-48. http://dx.doi.org/10.1016/j.neuroimage.2015.01.032 http://www.ncbi.nlm.nih.gov/pubmed/25613439
[1] introduces the FEM methods and the Laplace spectra for shape analysis, while [2] focusses on medical applications.
For Geodesics please cite:
[3] Crane K, Weischedel C, Wardetzky M. Geodesics in heat: A new approach to computing distance based on heat flow. ACM Transactions on Graphics. https://doi.org/10.1145/2516971.2516977
For non-singular mean curvature flow please cite:
[4] Kazhdan M, Solomon J, Ben-Chen M. 2012. Can Mean-Curvature Flow be Modified to be Non-singular? Comput. Graph. Forum 31, 5, 1745–1754. https://doi.org/10.1111/j.1467-8659.2012.03179.x
We also invite you to check out our lab webpage at https://deep-mi.org
Martin Reuter