Geometric relations among Voronoi diagrams
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Fast computation of generalized Voronoi diagrams using graphics hardware
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On the design of CGAL a computational geometry algorithms library
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IEEE Computer Graphics and Applications
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Computer Aided Geometric Design
Precise Voronoi cell extraction of free-form rational planar closed curves
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The predicates for the Voronoi diagram of ellipses
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ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
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ESA'05 Proceedings of the 13th annual European conference on Algorithms
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We present an algorithm for computing the Voronoi cell for a set of planes, spheres and cylinders in R3. The algorithm is based on a lower envelope computation of the bisector surfaces between these primitives, and the projection of the trisector curves onto planes bounding the object for which the Voronoi cell is computed, denoted the base object. We analyze the different bisectors and trisectors that can occur in the computation. Our analysis shows that most of the bisector surfaces are quadric surfaces and five of the ten possible trisectors are conic section curves. We have implemented our algorithm using the IRIT library and the CGAL 3D lower envelope package. All presented results are from our implementation.