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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
Issue Date 2001-07-09
Summary Let P be the boundary of a convex polytope and S<sub>n</sub> 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 S<sub>n</sub> 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.
Language English
Format Technical report
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