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2,420
Hyperbolic Delaunay triangulations and Voronoi diagrams made practical
, 2012
"... We study Delaunay complexes and Voronoi diagrams in the Poincaré ball, a confomal model of the hyperbolic space, in any dimension. We elaborate on our earlier work on the space of spheres [15], giving a detailed description of algorithms, and presenting a static and a dynamic variants. All proofs ..."
Abstract
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Cited by 1 (0 self)
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We study Delaunay complexes and Voronoi diagrams in the Poincaré ball, a confomal model of the hyperbolic space, in any dimension. We elaborate on our earlier work on the space of spheres [15], giving a detailed description of algorithms, and presenting a static and a dynamic variants. All proofs
Vector Weighted Voronoi Diagrams and Delaunay Triangulations
- CCCG
, 2007
"... We introduce a weighting scheme for Voronoi diagrams that has preferred directions. This generalizes the concept of weighted Delaunay triangulations and overcomes some of the difficulties of using multiplicative anisotropic weight systems. We discuss properties that make these weighting schemes attr ..."
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We introduce a weighting scheme for Voronoi diagrams that has preferred directions. This generalizes the concept of weighted Delaunay triangulations and overcomes some of the difficulties of using multiplicative anisotropic weight systems. We discuss properties that make these weighting schemes
Voronoi Diagrams and Delaunay Triangulations: Ubiquitous Siamese Twins
- DOCUMENTA MATH.
, 2012
"... ..."
Coverage Problems in Wireless Ad-hoc Sensor Networks
- in IEEE INFOCOM
, 2001
"... Wireless ad-hoc sensor networks have recently emerged as a premier research topic. They have great longterm economic potential, ability to transform our lives, and pose many new system-building challenges. Sensor networks also pose a number of new conceptual and optimization problems. Some, such as ..."
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Cited by 434 (9 self)
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by a particular sensor network. We first define the coverage problem from several points of view including deterministic, statistical, worst and best case, and present examples in each domain. By combining computational geometry and graph theoretic techniques, specifically the Voronoi diagram and graph
Visualizing the Connection Among Convex Hull, Voronoi Diagram and Delaunay Triangulation
"... The convex hull, Voronoi diagram and Delaunay triangulation are all essential concepts in computational geometry. Algorithms for solving the convex hull problem are commonly taught in an algorithms course, but the important relationship between convex hulls and the Voronoi diagram/Delaunay triangula ..."
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Cited by 2 (0 self)
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The convex hull, Voronoi diagram and Delaunay triangulation are all essential concepts in computational geometry. Algorithms for solving the convex hull problem are commonly taught in an algorithms course, but the important relationship between convex hulls and the Voronoi diagram/Delaunay
The Voronoi Diagram
"... We present a graphics hardware implementation of the tangent-plane algorithm for computing the kth-order Voronoi diagram of a set of point sites in image space. Correct and efficient implementation of this algorithm using graphics hardware is possible only with the use of an appropriate shader progr ..."
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We present a graphics hardware implementation of the tangent-plane algorithm for computing the kth-order Voronoi diagram of a set of point sites in image space. Correct and efficient implementation of this algorithm using graphics hardware is possible only with the use of an appropriate shader
Notes on Convex Sets, Polytopes, Polyhedra Combinatorial Topology, Voronoi Diagrams and Delaunay Triangulations
, 2008
"... Some basic mathematical tools such as convex sets, polytopes and combinatorial topology, are used quite heavily in applied fields such as geometric modeling, meshing, computer vision, medical imaging and robotics. This report may be viewed as a tutorial and a set of notes on convex sets, polytopes, ..."
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Cited by 4 (0 self)
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, polyhedra, combinatorial topology, Voronoi Diagrams and Delaunay Triangulations. It is intended for a broad audience of mathematically inclined readers. One of my (selfish!) motivations in writing these notes was to understand the concept of shelling and how it is used to prove the famous Euler
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