Loading...
Please wait, while we are loading the content...
Similar Documents
Duals of orphan-free anisotropic voronoi diagrams are embedded meshes (2012).
| Content Provider | CiteSeerX |
|---|---|
| Author | Canas, Guillermo D. |
| Abstract | Given an anisotropic Voronoi diagram, we address the fundamental question of when its dual is embedded. We show that, by requiring only that the primal be orphan-free (have connected Voronoi regions), its dual is always guaranteed to be an embedded triangulation. Further, the primal diagram and its dual have properties that parallel those of ordinary Voronoi diagrams: the primal’s vertices, edges, and faces are connected, and the dual triangulation has a simple, closed boundary. Additionally, if the underlying metric has bounded anisotropy (ratio of eigenvalues), the dual is guaranteed to triangulate the convex hull of the sites. These results apply to the duals of anisotropic Voronoi diagrams of any set of sites, so long as their Voronoi diagram is orphan-free. By combining this general result with existing conditions for obtaining orphan-free anisotropic Voronoi diagrams, a simple and natural condition for a set of sites to form an embedded anisotropic Delaunay triangulation follows. |
| File Format | |
| Publisher Date | 2012-01-01 |
| Access Restriction | Open |
| Subject Keyword | Orphan-free Anisotropic Voronoi Diagram Anisotropic Voronoi Diagram Embedded Triangulation Primal Diagram Primal Vertex Ordinary Voronoi Diagram Voronoi Diagram Fundamental Question Embedded Anisotropic Delaunay Triangulation Voronoi Region Dual Triangulation General Result Convex Hull Natural Condition |
| Content Type | Text |
