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Reporting intersecting pairs of convex polytopes in two and three dimensions

2002
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Computational geometry
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Let P = {P 1 , . . . , P m } be a set of m convex polytopes in R d , for d = 2, 3, with a total of n vertices. We present output-sensitive algorithms for reporting all k pairs of indices (i, j ) such that P i intersects P j . For the planar case we describe a simple algorithm with running time O(n 4/3 log 2+ε n + k), for any constant ε > 0, and an improved randomized algorithm with expected running time O((n log m + k)α(n) log n) (which is faster for small values of k). For d = 3, we present an

doi:10.1016/s0925-7721(02)00049-4
fatcat:wl2swhgeubdfrnh3oyg7gm6kr4