We introduce anisotropic Voronoi diagrams, a generalization of multiplicatively weighted Voronoi diagrams suitable for generating guaranteed-quality meshes of domains in which lon...
I discuss algorithms based on bistellar flips for inserting and deleting constraining (d − 1)-facets in d-dimensional constrained Delaunay triangulations (CDTs) and weighted CD...
Inference of topological and geometric attributes of a hidden manifold from its point data is a fundamental problem arising in many scientific studies and engineering application...
We present two new fundamental lower bounds on the worst-case combinatorial complexity of sets of free lines and sets of maximal free line segments in the presence of balls in thr...
Sampling conditions for recovering the homology of a set using topological persistence are much weaker than sampling conditions required by any known algorithm for producing a top...