MongeAmpere++

This library is designed to solve large instance of semi-discrete optimal transport problems, also known as the constrained least-square assignment problem. More precisely, MongeAmpere++ can be used to solve the quadratic optimal transport problem between a piecewise linear density on a 2D triangulation and a finite sum of Dirac masses.

Other features that might be useful for other numerical applications include :

• the robust computation of the intersections between a Voronoi diagram (or more generally a power/Laguerre diagram) and a triangulation ;
• the computation of the discrete Monge-Ampère operator, and its first and second derivatives with respect to the values of the function ;
• an implementation of Lloyd's algorithm for a piecewise linear density with exact integrals.

The documentation is currently (very) scarse, but you can look at the test/ directory to have a taste of what can be done with this MA++.

Dependencies

This software depends on recent versions of CGAL, Boost, SparseSuite (optional), CImg and CMake. It also requires a C++14 compatible compiler.

Tests have been performed with these versions of the following librairies:

• Gcc 4.9.1 (C++14 compatibility is required)

• CMake 2.8.12.2
• CImg 1.5.7
• Eigen 3.2.1
• Suitesparse 4.4.1 (optionnal)
• Boost 1.55
• Cgal 4.11