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Discrete Laplacians for Polygonal/Polyhedral Meshes

This repository contains the source code for the discrete polygonal/polyhedral Laplacians proposed in these papers:

  • Bunge, Herholz, Kazhdan, Botsch, Polygon Laplacian Made Simple, Computer Graphics Forum 39(2), 2020.
  • Bunge, Botsch, Alexa, The Diamond Laplace for Polygonal and Polyhedral Meshes, Computer Graphics Forum 40(5), 2021.
  • Bunge, Bukenberger, Wagner, Alexa, Botsch, Polygon Laplacian Made Robust, Computer Graphics Forum 43(2), 2024.

In order to compare to related methods, the code also contains implementations of these methods:

  • Martin, Kaufmann, Botsch, Wicke, Gross, Polyhedral Finite Elements Using Harmonic Basis Functions, Computer Graphics Forum 27(5), 2008.
  • Alexa, Wardetzky, Discrete Laplacians on General Polygonal Meshes, ACM Transactions on Graphics 30(4), 2011.
  • de Goes, Butts, Desbrun, Discrete Differential Operators on Polygonal Meshes, ACM Transactions on Graphics 39(4), 2020.

Comparisons of the different Laplace operators on a range of example applications (also included in the source code) are provided in these papers:

  • Bunge, Botsch, A Survey on Discrete Laplacians for General Polygonal Meshes, Computer Graphics Forum 42(2), 2023.
  • Bunge, Alexa, Botsch, Discrete Laplacians for General Polygonal and Polyhedral Meshes, SIGGRAPH Asia Courses, 2023.

Installation, building, and running the demos

Since we use pmp-library as submodule, you have to clone the repository recursively:

git clone --recursive git@github.com:mbotsch/polyLaplace.git

Configure and build:

cd polyLaplace && mkdir build && cd build && cmake .. && make

This will automatically build our code and all dependencies. Finally, start the GUI apps with a polygon mesh or a polyhedral mesh:

./poly_demo ../data/fertility.obj
./surface_viewer ../data/surface_meshes/grid/quad_4.obj 
./volume_viewer ../data/volume_meshes/cubes/cube_hexahedron_3.ovm

Alternatively you can run the volume and surface convergence tests by executing:

./run_surface_tests
./run_volume_tests

Have fun!