About: Inverted Ball as Noundary-constraint for Voronoi Diagrams of 3D Spheres     Goto   Sponge   NotDistinct   Permalink

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  • We show how to avoid infinite cells in Voronoi diagrams of 3D spheres. Infinite cells are unbounded cells at the convex-hull boundary of the input set. These cells can have Voronoi edges going to infinity or contain Voronoi vertices that are very distant from the convex hull. If our interest in parts of a diagram decreases as the distance from the convex hull increases or if we do not want to handle infinity, it might be useful to introduce a boundary constraint. We propose a constraint of extending the input set by a single inverted ball. When this ball encloses the entire input set, it stops any edge that would go to infinity otherwise. This approach only approximates the convex hull of the original input set. It is suitable for tracing-algorithms used for construction of these diagrams.
  • We show how to avoid infinite cells in Voronoi diagrams of 3D spheres. Infinite cells are unbounded cells at the convex-hull boundary of the input set. These cells can have Voronoi edges going to infinity or contain Voronoi vertices that are very distant from the convex hull. If our interest in parts of a diagram decreases as the distance from the convex hull increases or if we do not want to handle infinity, it might be useful to introduce a boundary constraint. We propose a constraint of extending the input set by a single inverted ball. When this ball encloses the entire input set, it stops any edge that would go to infinity otherwise. This approach only approximates the convex hull of the original input set. It is suitable for tracing-algorithms used for construction of these diagrams. (en)
Title
  • Inverted Ball as Noundary-constraint for Voronoi Diagrams of 3D Spheres
  • Inverted Ball as Noundary-constraint for Voronoi Diagrams of 3D Spheres (en)
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  • Inverted Ball as Noundary-constraint for Voronoi Diagrams of 3D Spheres
  • Inverted Ball as Noundary-constraint for Voronoi Diagrams of 3D Spheres (en)
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  • RIV/49777513:23520/09:00502677!RIV10-GA0-23520___
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  • P(GA201/09/0097)
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  • RIV/49777513:23520/09:00502677
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  • Voronoi diagram; inverted ball (en)
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  • [61BCBE8A75C8]
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  • Kolingerová, Ivana
  • Maňák, Martin
http://localhost/t...ganizacniJednotka
  • 23520
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