LaPy

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:

• Pure Python 3 implementation with heavy use of NumPy and SciPy for performance.
• Sparse, memory-efficient mesh data structures and vectorized algorithms.
• Utilities for IO, visualization, and common geometry processing tasks.

Table of contents

• Features
• Quick start
• Installation
• Solver backends
• Examples and documentation
• Development and testing
• References

Features

• TriaMesh: triangle mesh class with orientation checking, boundary handling, normals, smoothing and quality metrics; efficient edge and adjacency representations; IO for OFF, VTK; Gifti and related formats.
• TetMesh: tetrahedral mesh utilities, boundary handling and IO.
• Polygon: polygon class representing open and closed polygon curves.
• 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.
• intersect: self-intersection tests for triangle meshes, and undoing vertex moves that create intersections.
• remesh: isotropic remeshing to near-equilateral triangles that keeps the topology, and closest points on a surface.
• io: read/write vertex functions and eigenvector files.
• plot: lightweight Plotly wrappers for interactive visualization.

Quick start

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

Installation

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

Dependencies and optional backends

• Core: Python 3, NumPy, SciPy.
• Optional: cholespy (for CHOLMOD) to accelerate sparse solves with the Cholesky decomposition. Install it with pip install lapy[chol]. If use_cholmod=True is requested without cholespy, LaPy raises an ImportError.

Solver backends

• Default: SciPy sparse LU/QR routines.
• Optional: CHOLMOD (faster for symmetric positive definite systems). Toggle with use_cholmod=True when constructing Solver.

Examples and documentation

• Example Jupyter notebooks are available in the examples directory demonstrating common workflows (mesh IO, curvature, diffusion, ShapeDNA, geodesics).
• Full API documentation: https://deep-mi.org/LaPy

Development and testing

• The project includes unit tests and example notebooks. Use the development installation command above and run tests with your preferred test runner (e.g., pytest).
• Contributions and issues are welcome via the repository issue tracker.

References

If you use LaPy in publications, please cite:

1. 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

2. 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:

• Crane K, Weischedel C, Wardetzky M. "Geodesics in heat." ACM Trans. Graph. (use for heat-based geodesics) https://doi.org/10.1145/2516971.2516977
• Kazhdan M, Solomon J, Ben-Chen M. "Can Mean-Curvature Flow be Modified to be Non-singular?" Comput. Graph. Forum (2012) (for non-singular mean curvature flow) https://doi.org/10.1111/j.1467-8659.2012.03179.x
• Choi PT, Lam KC, Lui LM. "FLASH: Fast Landmark Aligned Spherical Harmonic Parameterization for Genus-0 Closed Brain Surfaces." SIAM J. Imaging Sci. (for conformal mapping methods) https://doi.org/10.1137/130950008

Website

• Lab / project page: https://deep-mi.org

License

• See the repository LICENSE file for license terms.

Contact

• Report issues or feature requests via the repository issue tracker on GitHub.