Bisector Graphs for Min-/Max-Volume Roofs over Simple Polygons
نویسندگان
چکیده
Piecewise-linear terrains (“roofs”) over simple polygons were studied by Aichholzer et al. (1995) in their work on straight skeletons of polygons. We show how to construct a roof over a simple polygon that has minimum (or maximum) volume among all roofs that drain water. Such a maximum-volume (minimumvolume) roof can have quadratic (maybe cubic, resp.) number of facets. Our algorithm for computing such a roof extends the standard wavefront propagation known from the theory of straight skeletons by two additional events. Both the minimum-volume and the maximum-volume roof of a simple polygon with n vertices can be computed in O(n log n) time.
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