LaPy is an open-source Python package for differential geometry on triangle and tetrahedra meshes. It includes an FEM solver to estimate the Laplace, Poisson or Heat equations, also the computations of gradients, divergence, mean-curvature flow, conformal mappings, geodesics, ShapeDNA and more.
LaPy is an open-source Python library for differential geometry and finite-element computations on triangle and tetrahedral meshes. It provides mesh data structures and fast, vectorized algorithms to compute differential operators, curvature flows, spectral descriptors and to solve PDEs such as Laplace, Poisson and Heat equations on surfaces and volumes.
Key design goals:
TriaMesh: triangle mesh class with orientation checking, boundary handling, normals, smoothing and quality metrics; efficient edge and adjacency representations; IO for OFF, VTK and related formats.TetMesh: tetrahedral mesh utilities, boundary handling and IO.Solver: FEM routines producing stiffness and mass matrices, sparse eigenvalue solvers, Poisson and heat equation solvers, and support for anisotropic operators.diffgeo: gradient, divergence, mean-curvature flow and related differential operators.heat: heat kernel and diffusion utilities, geodesics via heat method.shapedna: compute ShapeDNA (Laplace spectra) for shape descriptors.conformal: conformal mapping methods for genus-0 surfaces.io: read/write vertex functions and eigenvector files.plot: lightweight Plotly wrappers for interactive visualization.Install the released package:
python3 -m pip install lapy
Import and inspect main classes:
import lapy as lp
help(lp.TriaMesh)
help(lp.Solver)
A minimal example (compute eigenpairs of a triangular mesh):
import lapy as lp
mesh = lp.TriaMesh.from_off('examples/data/sample.off') # or other supported reader
solver = lp.Solver(mesh)
vals, vecs = solver.eigensystem(k=20) # compute 20 smallest nontrivial eigenpairs
Install the development version to a chosen source location:
python3 -m pip install --user --src /my/preferred/location --editable git+https://github.com/Deep-MI/Lapy.git#egg=lapy
pip on all platforms; use conda when possible. If use_cholmod=True is requested, LaPy attempts to import CHOLMOD and will raise if it is unavailable. Install ordering: install numpy and scipy first, then scikit-sparse.use_cholmod=True when constructing Solver.examples directory demonstrating common workflows (mesh IO, curvature, diffusion, ShapeDNA, geodesics).pytest).If you use LaPy in publications, please cite:
Reuter M, Wolter F-E, Peinecke N. "Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids." Computer-Aided Design. 2006;38(4):342–366. http://dx.doi.org/10.1016/j.cad.2005.10.011
Wachinger C, Golland P, Kremen W, Fischl B, Reuter M. "BrainPrint: a discriminative characterization of brain morphology." NeuroImage. 2015;109:232–248. http://dx.doi.org/10.1016/j.neuroimage.2015.01.032 http://www.ncbi.nlm.nih.gov/pubmed/25613439
Additional algorithmic sources:
LICENSE file for license terms.
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