Technical Report CS0657

TR#:CS0657
Class:CS
Title: AN 0{N-Hl1+£)-TIME ALGORITM TO MERGE H SIMPLE POLYGONS
Authors: R. Bar-Yehuda and R. Grinwald
PDFCS0657.pdf
Abstract: Many problems in computational geometry dealing with a single simple polygon have efficient algorithms. To apply these algorithms for a set of disjoint polygons, we suggest a merging process, which keeps many of the geometric properties of the original set, among them the triangulation and the convex hull. Given H non-intersecting simple polygons with a total number of N vertices, we present a divide∑and-conquer algorithm, whose time complexity is O(N + H 1+£). For a restricted class of polygons, including convex and monotone ones, we develop an optimal time merging algorithm.
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