Meshing Piecewise Smooth Complexes
Years and Authors of Summarized Original Work
2006; Boissonnat, Oudot
2007; Cheng, Dey, Ramos
2007: Cheng, Dey, Levine
2012; Cheng, Dey, Shewchuk
The class of piecewise smooth complex (PSC) includes geometries that go beyond smooth surfaces. They contain polyhedra, smooth and non-smooth surfaces with or without boundaries, and more importantly non-manifolds. Thus, provable mesh generation algorithms for this domain extend the scope of mesh generation to a wide variety of domains. Just as in surface mesh generation, we are required to compute a set of points on the input complex and then connect them with a simplicial complex which is geometrically close and is topologically equivalent to the input. One challenge that makes this task harder is that the PSCs allow arbitrary small input angles, a notorious well-known hurdle for mesh generation.
A PSC is a set of cells, each being a smooth, connected manifold, possibly with boundary. The 0-cells, 1-cells, and 2-cells...
KeywordsDelaunay mesh Delaunay refinement Piecewise smooth complex Volume mesh Topology
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