Mathematical elements for computer graphics (2nd ed.)
Mathematical elements for computer graphics (2nd ed.)
The Voronoi diagram of curved objects
Proceedings of the eleventh annual symposium on Computational geometry
Two-Dimensional Voronoi Diagrams in the Lp-Metric
Journal of the ACM (JACM)
Voronoi diagram of a circle set from Voronoi diagram of a point set: geometry
Computer Aided Geometric Design
Three dimensional euclidean Voronoi diagrams of lines with a fixed number of orientations
Proceedings of the eighteenth annual symposium on Computational geometry
Polyhedral Voronoi diagrams of polyhedra in three dimensions
Proceedings of the eighteenth annual symposium on Computational geometry
A sweepline algorithm for Euclidean Voronoi diagram of circles
Computer-Aided Design
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part V
Transactions on Computational Science XIV
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Voronoi diagrams have useful applications in various fields and are one of the most fundamental concepts in computational geometry. Although Voronoi diagrams in the plane have been studied extensively, using different notions of sites and metrics, little is known for other geometric spaces. In this paper, we are interested in the Voronoi diagram of a set of sites in the 3D hyperbolic upper half-space. We first present some introductory results in 3D hyperbolic upper half-space and then give an incremental algorithm to construct Voronoi diagram. Finally, we consider five models of 3D hyperbolic manifolds that are equivalent under isometries. By these isometries we can transform the Voronoi diagram of each model to others.