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Polygon DEC

Open nzfeng opened this issue 5 months ago • 3 comments

Adds polygon Laplacian and other operators for general polygon meshes.

Summary of contributions:

  • implementation of polygon Laplacian and mass matrices (unlumped & lumped) from Polygon Laplacian Made Simple by Bunge et al. 2020.
  • implementation of polygon Laplacian, mass matrix, gradient, divergence, connection Laplacian, and DEC operators from Discrete Differential Operators on Polygonal Meshes by de Goes et al 2020.
  • A PolygonMeshHeatSolver that implements the Vector Heat Method, Unsigned Heat Method, and Signed Heat Method on polygon meshes, analogous to the PointCloudHeatSolver for point clouds.
  • Documentation & tests.

image

The only thing I'm not quite satisfied with is the naming convention for the operators from "Polygon Laplacian Made Simple": geometry.simplePolygonLaplacian, geometry.simplePolygonVertexLumpedMassMatrix, and geometry.simplePolygonVertexGalerkinMassMatrix. My concerns are

  • the names can be quite long;
  • perhaps the word "simple" will be mistaken as meaning "less sophisticated" and therefore "less accurate";
  • perhaps the operators will be mistaken as only applying to "simple polygons", which are non-self-intersecting polygons without holes, though they can indeed apply even when polygon faces are self-intersecting.

Suggestions & review are welcome!

nzfeng avatar Sep 17 '24 17:09 nzfeng