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Title: On the proofs of two lemmas describing the intersections of spheres with the boundary of a convex polytope
Authors: Golin, Mordecai J.
Na, Hyeon-Suk
Keywords: Convex polytope
2-Dimensional Poisson distribution
3-Dimensional Voronoi Diagram
Two lemmas
Issue Date: 9-Jul-2001
Series/Report no.: HKUST Theoretical Computer Science Center Research Report ; HKUST-TCSC-2001-09
Abstract: Let P be the boundary of a convex polytope and Sn be a set of points drawn from the 2-dimensional Poisson distribution with rate n over P. In a companion paper [1] the authors show that the expected complexity of the 3-dimensional Voronoi Diagram of Sn is O(n). In the derivation of that fact [1] used two lemmas describing the geometric structure of the intersection of various types of spheres with P. In this note we provide the proofs of those two lemmas.
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