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LibMAT

LibMAT is a C++ library, with an optional CUDA part and Python bindings, for computing the 3D medial axis transform (MAT) of a shape given as a triangle or tetrahedral mesh.

  • Python

    Every function takes and returns numpy arrays, in the style of gpytoolbox.

    Python API

  • C++

    The same functions in namespace libmat with Eigen matrices, plus the low-level modules they are built on, as CMake targets.

    C++ library

  • CPU and CUDA

    The CPU library builds everywhere. Build with LIBMAT_WITH_CUDA=ON to add the GPU restricted power diagram and GPU distance queries.

    Installation

  • Examples

    Python scripts covering every function, with polyscope visualizations.

    Examples

Quick example

import numpy as np
import libmat

# a closed triangle mesh with sharp and concave edges
V, F = libmat.read_surface_mesh("data/mesh_69058.obj")

# its sharp and concave features
E, E_type, E_line, corners, corner_type = libmat.detect_sharp_features(V, F)

# medial spheres with the ball-shrinking algorithm (at most one per triangle)
C, R, types = libmat.shrink_spheres(V, F)

# their neighbors in the power diagram
T, E_rt, valid = libmat.regular_triangulation(C, R)

# how well does a medial mesh approximate a surface?
SV, SF = libmat.read_surface_mesh("data/bug.obj")
MV, MR, ME, MF = libmat.read_ma("data/bug.ma")
D, prim_type, prim_id = libmat.distance_to_medial_mesh(SV, MV, MR, ME, MF)
print("one-sided Hausdorff distance:", np.abs(D).max())

Credit

If LibMAT is helpful in your research, please cite us!

@misc{libmat,
  title = {{LibMAT}: A C++ Library for Medial Axis Transform},
  author = {Ningna Wang and others},
  howpublished = "\url{https://github.com/ningnawang/libmat}",
  year = {2024}
}

LibMAT is built upon the following papers:

  • Ningna Wang, Rui Xu, Yibo Yin, Zichun Zhong, Taku Komura, Wenping Wang, Xiaohu Guo. MATStruct: High-quality Medial Mesh Computation via Structure-aware Variational Optimization. SIGGRAPH Asia 2025 Conference Papers. Project · arXiv · Code
  • Ningna Wang, Hui Huang, Shibo Song, Bin Wang, Wenping Wang, Xiaohu Guo. MATTopo: Topology-preserving Medial Axis Transform with Restricted Power Diagram. ACM Transactions on Graphics (SIGGRAPH Asia 2024). Paper · Project · arXiv · Code
  • Ningna Wang, Bin Wang, Wenping Wang, Xiaohu Guo. Computing Medial Axis Transform with Feature Preservation via Restricted Power Diagram. ACM Transactions on Graphics (SIGGRAPH Asia 2022). Project · arXiv · Code
  • Jaehwan Ma, Sang Won Bae, Sunghee Choi. 3D medial axis point approximation using nearest neighbors and the normal field. The Visual Computer, 2012. Paper

LibMAT is released under the GPL-3.0 license.

Contribute

We hope LibMAT is useful for your work, and we would love your help to make it better.

LibMAT is a young library, and we want contributing to it to be as easy as possible. You can add a new function, improve an existing one, or fix a bug, and open a pull request on GitHub. A new function usually consists of a header and a source file (include/libmat/<name>.h, src/api/<name>.cpp), a binding (python/bindings/), a Python wrapper with its docstring (python/libmat/<name>.py) and a test (tests/).

Please don't let that list stop you: we will gladly review your code with you and adapt it to the conventions of the library, and the tests will tell us if anything breaks. If you have code from a past project that is related to the medial axis or to geometry processing and is not in LibMAT yet, we encourage you to submit it as it is. Contributors are credited in the documentation of the functions they write and on this page.

Contributors

None yet: be the first!