Mathematica already packs some nice and strong functionality to handle meshes and it is probably an area that will be expanding in the upcoming versions. I am quite curious to know from the computational geometry development team whether there are any plans to incorporate the tools/functionality for handling discrete differential geometry in the future version 13.
There are extensive libraries which can be integrated with Mathematica to expand its computational geometry based functionality: https://www.cgal.org/ and https://www.cs.cmu.edu/~kmcrane/index.html#code and https://www.cs.cmu.edu/~kmcrane/Projects/DDG/
Some features that will be indispensable to have would be:
- Computing discrete gradients of volume and surfaces at the mesh vertices
- determining Gaussian and Mean curvatures of a mesh
- implementing Half-edge structures
- Curvature Flow
- represent vector fields on meshes
It would be great if someone from the development team can engage here or provide some kind of a roadmap for the functionality in sight for discrete differential geometry.
