SIAM Journal on Computing
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Voronoi diagrams and Delaunay triangulations
Handbook of discrete and computational geometry
Proceedings of the twenty-second annual symposium on Computational geometry
Shortest paths on realistic polyhedra
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Improved Bounds on the Union Complexity of Fat Objects
Discrete & Computational Geometry
On the expected complexity of voronoi diagrams on terrains
Proceedings of the twenty-eighth annual symposium on Computational geometry
The complexity of geodesic Voronoi diagrams on triangulated 2-manifold surfaces
Information Processing Letters
| Hi-index | 0.00 |
We prove tight bounds on the complexity of bisectors and Voronoi diagrams on so-called realistic terrains, under the geodesic distance. In particular, if ndenotes the number of triangles in the terrain, we show the following two results.(i) If the triangles of the terrain have bounded slope and the projection of the set of triangles onto the xy-plane has low density, then the worst-case complexity of a bisector is 茂戮驴(n).(ii) If, in addition, the triangles have similar sizes and the domain of the terrain is a rectangle of bounded aspect ratio, then the worst-case complexity of the Voronoi diagram of mpoint sites is $\Theta(n+m\sqrt{n})$.