We consider the approximation of convex polygons by simpler figures such as rectangles, circles, or polygons with fewer edges. As distance measures for figures A, B we use either the area of the symmetric difference δS(A, B) or the Hausdorff-distance δH(A, B). It is shown that the optimal δS-approximation of an n-gon P by an axes-parallel rectangle can be found in time O(log3n) by a nested binary search algorithm. With respect to δH pseudo-optimal algorithms are given, i.e. algorithms producing a solution whose distance to P differs from the optimum only by a constant factor. We obtain algorithms of runtimes O(n) for approximation by rectangles and O(n3log2n) for approximation by k-gons (k
CITATION STYLE
Alt, H., Blömer, J., & Wagener, H. (1990). Approximation of convex polygons. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 443 LNCS, pp. 703–716). Springer Verlag. https://doi.org/10.1007/bfb0032068
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