2 Expansive Motions and the Polytope of Pointed Pseudo
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Expansive Motions and the Polytope of Pointed Pseudo-Triangulations
We introduce the polytope of pointed pseudo-triangulations of a point set in the plane, defined as the polytope of infinitesimal expansive motions of the points subject to certain constraints on the increase of their distances. Its 1-skeleton is the graph whose vertices are the pointed pseudo-triangulations of the point set and whose edges are flips of interior pseudo-triangulation edges. For p...
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The polytope of pointed pseudo triangulations was described in [RSS01]. This polytope is a combinatorial tool to observe all possible pseudo triangulations of a certain point set. Each point of the polytope refers to one possible pseudo triangulation of the point set. To polytope vertices are connected by an edge if their pseudo triangulations just differ in one edge-flip. Once we have a PPT-po...
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We present a definition of a pointed Delaunay pseudotriangulation of a simple polygon. We discuss why our definition is reasonable. Our approach will be motivated from maximal locally convex functions, and extends the work of Aichholzer et al.[1]. Connections between the polytope of the pointed pseudotriangulations and the Delaunay pseudo-triangulation will be given.
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تاریخ انتشار 2001