Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.cad.2010.04.005 | Computer-Aided Design |
Keywords | Field | DocType |
riemannian metric,computational geometry,hyperbolic voronoi diagram,different notion,introductory result,useful application,geodesic,fundamental concept,incremental algorithm,geometric space,3d hyperbolic upper half-space,voronoi diagram,hyperbolic upper half-space,hyperbolic manifold | Power diagram,Combinatorics,Mathematical optimization,Bowyer–Watson algorithm,Centroidal Voronoi tessellation,Hyperbolic tree,Mathematical diagram,Pure mathematics,Lloyd's algorithm,Voronoi diagram,Weighted Voronoi diagram,Mathematics | Journal |
Volume | Issue | ISSN |
42 | 9 | Computer-Aided Design |
Citations | PageRank | References |
2 | 0.43 | 7 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Z. Nilforoushan | 1 | 2 | 0.43 |
| Ali Mohades | 2 | 140 | 26.04 |
| M. M. Rezaii | 3 | 9 | 0.96 |
| A. Laleh | 4 | 2 | 0.43 |