Affiliation:
1. Universität Salzburg, FB Computerwissenschaften, 5020 Salzburg, Austria
Abstract
Piecewise-linear terrains (“roofs”) over simple polygons were first studied by Aichholzer et al. (J. UCS 1995) in their work on straight skeletons of polygons. We show how to construct a roof over the polygonal footprint of a building that has minimum or maximum volume among all roofs that drain water. Our algorithm for computing such a roof extends the standard plane-sweep approach known from the theory of straight skeletons by additional events. For both types of roofs our algorithm runs in [Formula: see text] time for a simple polygon with [Formula: see text] vertices.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science