Geometric relations among Voronoi diagrams
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Fast computation of generalized Voronoi diagrams using graphics hardware
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IEEE Computer Graphics and Applications
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Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
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Computer Aided Geometric Design
Precise Voronoi cell extraction of free-form rational planar closed curves
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SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
The predicates for the Voronoi diagram of ellipses
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Computational Geometry: Theory and Applications
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Computational Geometry: Algorithms and Applications
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Computer-Aided Design
Convex hull and voronoi diagram of additively weighted points
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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Computing medial axes of generic 3D regions bounded by B-spline surfaces
Computer-Aided Design
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We present an algorithm for computing the Voronoi cell for a set of planes, spheres and cylinders in R^3. 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.