Discrete Differential Geometry: Meshes and Duals

[bollu]

• A surface mesh data structure representing vertices (0D), edges (1D), and faces (2D) along with edge lengths that obey triangle inequality
• Treat surface mesh as simplicial complex by forgetting edge length data
• Computation of dual mesh.
• Computation of hodge dual of (k-forms) from the dual mesh.
• Computation of discrete laplacian from the mesh.
• Solutions to the heat and wave equation in terms of the discrete laplacian

References

• https://github.com/nmwsharp/geometry-central
• Keenan Crane's discrete differential geometry textbook, chapter 2: https://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf
• The vector heat method https://arxiv.org/pdf/1805.09170.pdf

CC: @slel

Component: geometry

Keywords: discrete, differential geometry

Issue created by migration from https://trac.sagemath.org/ticket/30197

[bollu]

Changed keywords from none to discrete, differential geometry

[mkoeppe]

comment:4

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.