A Predictor-Corrector Type Incremental Algorithm for Weighted Straight Skeletons

Abstract

Introduction: In classical straight skeleton problem, each edge of the polygon moves inwards with a constant unit velocity in such a way that it remains essentially parallel to itself throughout the course of the shrinking process. The regions swept by the polygon edges construct the faces of the straight skeleton structure of the underlying polygon. During the shrinking process, polygon topology might change due to edge collapse and edge split events. The edge collapse event takes place at an instance when at least one edge of the polygon collapses down to a point, whereas the edge split event comes into play as at least one of the vertices hits an edge or another vertex of the polygon. The existing algorithms for the construction of straight skeletons are based on wave propagation and they make use of the additional tools like kinetic triangulation [1] or motorcycle graph [2]. The weighted version of the straight skeleton algorithm was pioneered in [3].