Subdividing alpha complex

Abstract

Given two simplicial complexes C1 and C2 embedded in Euclidean space ℝd, C1 subdivides C2 if (i) C1 and C2 have the same underlying space, and (ii) every simplex in C1 is contained in a simplex in C2. In this paper we present a method to compute a set of weighted points whose alpha complex subdivides a given simplicial complex. Following this, we also show a simple method to approximate a given polygonal object with a set of balls via computing the subdividing alpha complex of the boundary of the object. The approximation is robust and is able to achieve a union of balls whose Hausdorff distance to the object is less than a given positive real number ε. © Springer-Verlag Berlin Heidelberg 2004.