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gptoolbox - Geometry Processing Toolbox

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This is a toolbox of useful matlab functions for geometry processing. There are also tools related to constrainted optimization and image processing. Typically these are utility functions that are not stand alone applications.

Here's an incomplete list of cool features this matlab toolbox contains:

  • wrappers for TetGen, Triangle, QSlim, meshfix
  • mesh smoothing
  • mesh clean up (remove duplicates, remove unreferenced)
  • geodesic distances on triangle and tetrahedral meshes
  • mesh quantities and queries (normals, discrete gaussian curvature, list boundary edges, topology, angles, dihedral angles etc.)
  • mesh deformation (as-rigid-as-possible (ARAP), moving least-squares, etc.)
  • mesh parameterization (harmonic, least squares conformal, ARAP, etc.)
  • automatic skinning weight computation (bounded biharmonic weights, bone heat)
  • 2D triangle mesh from binary image
  • Input/Output for many mesh formats (.obj,.off,.stl,.wrl,.ply,.mesh,.node,.ele,.poly,.smf,.bdl,.face)
  • discrete differential geometry operators for triangle and tetrahedral meshes (cotangent Laplacian, gradient, divergence)
  • quadratic programming, active set solver
  • scribble-based image colorization, diffusion curves
  • exact (un)signed distance field computation for meshes
  • constructive solid geometry operations on meshes, booleans
  • accelerated point location in triangle and tetrahedral meshes
  • image dithering
  • deep matlab function dependency

The functions have been organized into folders based on their primary application:

  • external/
  • imageprocessing/
  • images/
  • matrix/
  • mesh/
  • mex/
  • utility/
  • wrappers/


The vast majority of this code is straight MATLAB (*.m files). Thus, only installing MATLAB and adding the qptoolbox directory and its subdirectories to your MATLAB path is needed for installation. Let's assume you cloned gptoolbox at /Users/ajx/Repos/gptoolbox/, then you could issue:

addpath(strjoin(strcat(['/Users/ajx/Repos/gptoolbox/'],{'external','imageprocessing', 'images', 'matrix', 'mesh', 'mex', 'quat','utility','wrappers'}),':'))

To make this change permanent, then issue:


There are some mex files, whose documentation for installation are included in respective mex/ file.

Full installation

This strives to be full installation instructions, but will no doubt remain incomplete for some time. Begin by adding paths as above.

As stated above, most files are straight matlab and will just run if you have gptoolbox in your path.

Compile /mex

Most of our mex files will depend on libigl. Some depend on cgal and embree. We recently switched to a cmake-based build.

See mex/ for details.

Compile external/toolbox_fast_marching/

In MATLAB issue:

cd external/toolbox_fast_marching/


gptoolbox depends on MATLAB and some of its toolbox extensions. Many functions should also work with Octave, though this has not been tested.

Functions that rely on quadprog have been tested and optimized assuming that the Mosek toolbox has been installed, but should also work with the quadprog in MATLAB's Optimization Toolbox.

Mex files may have other external dependencies (e.g. CGAL, Eigen, libigl). See their respective READMEs for more information. When installing mex libraries, you may need to modify the files in wrappers/ (such as path_to_libigl.m) so gptoolbox knows where to look.


If you use gptoolbox in your academic projects, please cite the papers we implement as appropriate. To cite the library in general, you could use this BibTeX entry:

  title = {{gptoolbox}: Geometry Processing Toolbox},
  author = {Alec Jacobson and others},
  note = {},
  year = {2021},


This work is dual licensed under MIT and Apache 2.

Please take extra note that the external/ directory contains code from elsewhere with potentially more restricted licenses.

Most of the mex/ directory includes libigl and Eigen (and some include CGAL), each with their own licenses.


The Geometry Processing Toolbox grew out of Alec Jacobson's private codebase during his PhD, but has benefited a lot from various collaborators at NYU, ETH Zurich, Columbia, University of Toronto and elsewhere. Now, the Geometry Processing Toolbox is a group endeavour. If you're intersted in contributing, please contact Alec Jacobson ( or submit a pull request on github.


For now, documentation is limited to a per-function basis. For example, to find documentation for cotmatrix, in MATLAB issue:

help cotmatrix