Efficient Observer-Dependent Simplification in Polygonal Domains

Abstract

In this paper, we consider a special version of the well-known linesimplification problem for simplifying the boundary of a region illuminated by a point light source q, or its visibility polygon VP(q). In this simplification approach, we should take the position of q as an essential factor into account to determine the quality of the resulting simplification. For this purpose, we redefine the known distanceand area-distortion error criteria as the main simplification criteria to take into account the distance between the observer q and the boundary of VP(q). Based on this, we propose algorithms for simplifying VP(q). More precisely, we propose simplification algorithms of O(n 2 ) and O(n 4/3+δ ) running time for observer-dependent distance-distortion simplification criterion and an O(n 3 ) simplification algorithm for observer-dependent area-distortion criterion where n is the number of vertices in VP(q). Moreover, we consider the observer-dependent distance-distortion simplification problem in the data streaming model where the vertices of VP(q) are given as a stream and only a constant amount of memory is available.