Subdividing Alpha Complex

Abstract. Given two simplicial complexes C1 and C2 embedded in Euclidean space IRd , 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 .

• Type: Conference
• Year: 2004
• Where: FSTTCS
• Authors: Ho-Lun Cheng, Tony Tan
• Keywords: Alpha Complex, Alpha Complex Subdivides, Euclidean Space Ird, FSTTCS 2004