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347
Weighted triangulations for geometry processing
"... In this paper, we investigate the use of weighted triangulations as discrete, augmented approximations of surfaces for digital geometry processing. By incorporating a scalar weight per mesh vertex, we introduce a new notion of discrete metric that defines an orthogonal dual structure for arbitrary t ..."
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Cited by 3 (0 self)
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In this paper, we investigate the use of weighted triangulations as discrete, augmented approximations of surfaces for digital geometry processing. By incorporating a scalar weight per mesh vertex, we introduce a new notion of discrete metric that defines an orthogonal dual structure for arbitrary
Planar MinimumWeight Triangulations
, 1995
"... The classic problem of finding a minimumweight triangulation for a given planar straightline graph is considered in this paper. A brief overview of known methods is given in addition to some new results. A parallel greedy triangulation algorithm is presented along with experimental data that sugge ..."
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Cited by 2 (0 self)
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The classic problem of finding a minimumweight triangulation for a given planar straightline graph is considered in this paper. A brief overview of known methods is given in addition to some new results. A parallel greedy triangulation algorithm is presented along with experimental data
Approximating the Minimum Weight Triangulation
, 1991
"... We show that the length of the minimum weight Steiner triangulation (MWST) of a point set can be approximated within a constant factor by a triangulation algorithm based on quadtrees. In O(n log n) time we can compute a triangulation with O(n) new points, and no obtuse triangles, that approximat ..."
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Cited by 9 (4 self)
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We show that the length of the minimum weight Steiner triangulation (MWST) of a point set can be approximated within a constant factor by a triangulation algorithm based on quadtrees. In O(n log n) time we can compute a triangulation with O(n) new points, and no obtuse triangles
Drawing outerplanar minimum weight triangulations
, 1996
"... We consider the problem of characterizing those graphs that can be drawn as minimum weight triangulations and answer the question for maximal outerplanar graphs. We provide a complete characterization of minimum weight triangulations of regular polygons by studying the combinatorial properties of th ..."
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Cited by 3 (2 self)
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We consider the problem of characterizing those graphs that can be drawn as minimum weight triangulations and answer the question for maximal outerplanar graphs. We provide a complete characterization of minimum weight triangulations of regular polygons by studying the combinatorial properties
Minimum weight triangulation is NPhard
 IN PROC. 22ND ANNU. ACM SYMPOS. COMPUT. GEOM
, 2006
"... A triangulation of a planar point set S is a maximal plane straightline graph with vertex set S. In the minimum weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem ..."
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Cited by 42 (0 self)
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A triangulation of a planar point set S is a maximal plane straightline graph with vertex set S. In the minimum weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem
On βskeleton as a Subgraph of the Minimum Weight Triangulation
"... Given a set S of n points in the plane, a triangulation is a maximal set of nonintersecting edges connecting the points in S. The weight of the triangulation is the sum of the lengths of the edges. In this paper, we show that for fi ? 1= sin , the βskeleton of S is a subgraph of a minimum weight ..."
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Cited by 4 (0 self)
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Given a set S of n points in the plane, a triangulation is a maximal set of nonintersecting edges connecting the points in S. The weight of the triangulation is the sum of the lengths of the edges. In this paper, we show that for fi ? 1= sin , the βskeleton of S is a subgraph of a minimum
A Parallel Approximation Algorithm for Minimum Weight Triangulation
"... In this paper we show a parallel algorithm that produces a triangulation which is within a constant factor longer than the Minimum Weight Triangulation (MWT) in time O(log n) using O(n) processors and linear space in the CRCW PRAM model. This is done by proving that a relaxed version of the qu ..."
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In this paper we show a parallel algorithm that produces a triangulation which is within a constant factor longer than the Minimum Weight Triangulation (MWT) in time O(log n) using O(n) processors and linear space in the CRCW PRAM model. This is done by proving that a relaxed version
Minimum weight triangulation by cutting out triangles
 In Proceeding of the 16th Annual International Symposium on Algorithms and Computation
, 2005
"... Abstract. We describe a fixed parameter algorithm for computing the minimum weight triangulation (MWT) of a simple polygon with (n − k) vertices on the perimeter and k hole vertices in the interior, that is, for a total of n vertices. Our algorithm is based on cutting out empty triangles (that is, t ..."
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Cited by 6 (1 self)
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Abstract. We describe a fixed parameter algorithm for computing the minimum weight triangulation (MWT) of a simple polygon with (n − k) vertices on the perimeter and k hole vertices in the interior, that is, for a total of n vertices. Our algorithm is based on cutting out empty triangles (that is
The Minimum Weight Triangulation Problem With Few Inner Points
, 2006
"... We propose to look at the computational complexity of 2dimensional geometric optimization problems on a finite point set with respect to the number of inner points (that is, points in the interior of the convex hull). As a case study, we consider the minimum weight triangulation problem. Finding a ..."
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Cited by 8 (1 self)
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We propose to look at the computational complexity of 2dimensional geometric optimization problems on a finite point set with respect to the number of inner points (that is, points in the interior of the convex hull). As a case study, we consider the minimum weight triangulation problem. Finding a
Results 1  10
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347