Expansive motions and the polytope of pointed pseudo-triangulations

Expansive motions and the polytope of pointed pseudo-triangulations (2003)

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by Günter Rote , Francisco Santos , Ileana Streinu

Venue:	Discrete and Computational Geometry - The Goodman-Pollack Festschrift, Algorithms and Combinatorics
Citations:	39 - 15 self

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Datum	Value	Source
TITLE	Expansive motions and the polytope of pointed pseudo-triangulations	INFERENCE
AUTHOR NAME	Günter Rote	SVM HeaderParse 0.2
AUTHOR NAME	Francisco Santos	SVM HeaderParse 0.2
AUTHOR NAME	Ileana Streinu	SVM HeaderParse 0.2
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. For points in convex position we obtain a new realization of the associahedron, i.e., a geometric representation of the set of triangulations of an n-gon, or of the set of binary trees on n vertices, or of many other combinatorial objects that are counted by the Catalan numbers. By considering the 1-dimensional version of the polytope of constrained expansive motions we obtain a second distinct realization of the associahedron as a perturbation of the positive cell in a Coxeter arrangement. Our methods produce as a by-product a new proof that every simple polygon or polygonal arc in the plane has expansive motions, a key step in the proofs of	SVM HeaderParse 0.2
YEAR	2003	INFERENCE
VENUE	Discrete and Computational Geometry - The Goodman-Pollack Festschrift, Algorithms and Combinatorics	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	699--736	INFERENCE
VOLUME	25	INFERENCE
TECH	Manuscript, FU-Berlin	INFERENCE
CITATIONS	27 found	ParsCit 1.0