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PseudoTriangulations  a Survey
 CONTEMPORARY MATHEMATICS
"... A pseudotriangle is a simple polygon with exactly three convex vertices, and a pseudotriangulation is a facetoface tiling of a planar region into pseudotriangles. Pseudotriangulations appear as data structures in computational geometry, as planar barandjoint frameworks in rigidity theory an ..."
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Cited by 25 (5 self)
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A pseudotriangle is a simple polygon with exactly three convex vertices, and a pseudotriangulation is a facetoface tiling of a planar region into pseudotriangles. Pseudotriangulations appear as data structures in computational geometry, as planar barandjoint frameworks in rigidity theory
Enumerating PseudoTriangulations in the Plane
 In Proc. 14th Canad. Conf. Comp. Geom
, 2002
"... A pseudotriangle is a simple polygon with exactly three convex vertices. A minimum pseudotriangulation of a set S is a partition of the convex hull of S into the least number of interior disjoint pseudotriangles whose vertices are the points of S. The graph of pseudotriangulations G_pse has pseu ..."
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Cited by 8 (0 self)
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A pseudotriangle is a simple polygon with exactly three convex vertices. A minimum pseudotriangulation of a set S is a partition of the convex hull of S into the least number of interior disjoint pseudotriangles whose vertices are the points of S. The graph of pseudotriangulations G_pse has
Enumerating pseudotriangulations in the plane
 COMPUT. GEOM. THEORY APPL
, 2005
"... A pseudotriangle is a simple polygon with exactly three convex vertices. A pseudotriangulation of a finite point set S in the plane is a partition of the convex hull of S into interior disjoint pseudotriangles whose vertices are points of S. A pointed pseudotriangulation is one which has the le ..."
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Cited by 10 (0 self)
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A pseudotriangle is a simple polygon with exactly three convex vertices. A pseudotriangulation of a finite point set S in the plane is a partition of the convex hull of S into interior disjoint pseudotriangles whose vertices are points of S. A pointed pseudotriangulation is one which has
Pseudotriangulations, rigidity and motion planning
 Discrete and Computational Geometry
, 2005
"... Abstract We propose a combinatorial approach to planning noncolliding trajectories for a polygonal barandjoint framework with n vertices. It is based on a new class of simple motionsinduced by expansive onedegreeoffreedom mechanisms, which guarantee noncollisions by moving all points away fr ..."
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Cited by 7 (0 self)
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that convexify both configurations with expansive motions (which never bring two points closer together) and then taking one path in reverse. All of the constructions are elementary and are based on a novel class of planar embedded graphs called pointed pseudotriangulations, for which we prove a variety
Contemporary Mathematics PseudoTriangulations  Survey
"... A pseudotriangle is a simple polygon with exactly three convex vertices, and a pseudotriangulation is a facetoface tiling of a planar region into pseudotriangles. Pseudotriangulations appear as data structures in computational geometry, as planar barandjoint frameworks in rigidity theory a ..."
Abstract
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A pseudotriangle is a simple polygon with exactly three convex vertices, and a pseudotriangulation is a facetoface tiling of a planar region into pseudotriangles. Pseudotriangulations appear as data structures in computational geometry, as planar barandjoint frameworks in rigidity theory
Pseudotriangulations: Theory and Applications
 In Proc. 12th Annu. ACM Sympos. Comput. Geom
, 1996
"... this paper is (1) to give three new applications of these concepts to 2dimensional visibility problems, and (2) to study realizability questions suggested by the pseudotrianglepseudoline duality; see Figure 1. Our first application is related to the rayshooting problem in the plane: preprocess a ..."
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Cited by 29 (5 self)
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this paper is (1) to give three new applications of these concepts to 2dimensional visibility problems, and (2) to study realizability questions suggested by the pseudotrianglepseudoline duality; see Figure 1. Our first application is related to the rayshooting problem in the plane: preprocess a set of objects into a data structure such that the first object hit by a query ray can be computed efficiently. In section 3 we show that for a scene of n objects, where the objects are pairwise disjoint convex sets with m 'simple' arcs in total, one can obtain O(log m) query time using
A Comment on PseudoTriangulation in Three Dimensions
, 2002
"... Pseudotriangulations in two dimensions had attracted attention in computational geometry in recent years [CEG + 94, PV96, Str00, ABG + 01]. We present one possible extension of this concept to three dimensions. Our construction has several desirable properties, among them having the same number pse ..."
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Pseudotriangulations in two dimensions had attracted attention in computational geometry in recent years [CEG + 94, PV96, Str00, ABG + 01]. We present one possible extension of this concept to three dimensions. Our construction has several desirable properties, among them having the same number
On Numbers of PseudoTriangulations∗
, 2014
"... We study the maximum numbers of pseudotriangulations and pointed pseudotriangulations that can be embedded over a specific set of points in the plane or contained in a specific triangulation. We derive the bounds O(5.45N) and Ω(2.41N) for the maximum number of pointed pseudotriangulations that c ..."
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We study the maximum numbers of pseudotriangulations and pointed pseudotriangulations that can be embedded over a specific set of points in the plane or contained in a specific triangulation. We derive the bounds O(5.45N) and Ω(2.41N) for the maximum number of pointed pseudotriangulations
COMBINATORIAL PSEUDOTRIANGULATIONS
, 2005
"... Abstract. We prove that a planar graph is generically rigid in the plane if and only if it can be embedded as a pseudotriangulation. This generalizes the main result of [4] which treats the minimally generically rigid case. The proof uses the concept of combinatorial pseudotriangulation, CPT, in t ..."
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Abstract. We prove that a planar graph is generically rigid in the plane if and only if it can be embedded as a pseudotriangulation. This generalizes the main result of [4] which treats the minimally generically rigid case. The proof uses the concept of combinatorial pseudotriangulation, CPT
Results 1  10
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171,750