Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations

Abstract

I discuss algorithms for constructing constrained Delaunay triangulations (CDTs) in dimensions higher than two. If the CDT of a set of vertices and constraining simplices exists, it can be constructed in O(nvns) time, where nv is the number of input vertices and ns is the number of output d-simplices. In practice, the running time is likely to be O(nv2+ns log nv) in all but the most pathological cases. The CDT of a star-shaped polytope can be constructed in O(ns log nv) time, yielding an efficient way to delete a vertex from a CDT.