Expansive Motions and the Polytope of Pointed Pseudo-Triangulations
TLDR
In this paper, the authors introduce the polytope of pointed pseudo-triangulations of a point set in the plane, which is defined as the polytoope of infinitesimal expansive motions of the points subject to certain constraints on the increase of their distances.Abstract:
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.read more
Citations
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Proceedings ArticleDOI
Straightening polygonal arcs and convexifying polygonal cycles
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Geometric Graphs and Arrangements
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Many non-equivalent realizations of the associahedron
TL;DR: It is shown that two Hohlweg-Lange associahedra have linearly equivalent normal fans if and only if they are isometric, as a consequence of the classification of these constructions modulo linear equivalence of their normal fans.
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Planar Minimally Rigid Graphs and Pseudo-Triangulations
Ruth Haas,David Orden,Günter Rote,Francisco Santos,Brigitte Servatius,Herman Servatius,Diane L. Souvaine,Ileana Streinu,Walter Whiteley +8 more
TL;DR: Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than 180 degrees) as mentioned in this paper, which admit pointed embeddings, even under certain natural topological and combinatorial constraints.
References
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