Name
Abstract | ||
|---|---|---|
Voronoi diagram for a set of geometric objects is a partition of the plane (or space in higher dimensions) into disjoint regions each dominated by some given object under a predetermined criterion. In this paper we are interested in various measures associated with criteria on goodness of an input line segment with respect to each point in the plane as the "point of view". These measures basically show how the segment or information displayed on the segment can be seen from the point. Mathematically, the measures are defined in terms of the shape of the triangle determined by the point and the line segment. Given any such measure, we can define a Voronoi diagram for a set of line segments. In this paper we are interested in investigating their common combinatorial and structural properties. We investigate conditions for those measures to define regular Voronoi diagrams and also conditions that local optima on the measures lie only on Voronoi edges, not in the proper interior of Voronoi regions. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/BF03167517 | Japan Journal of Industrial and Applied Mathematics |
Keywords | Field | DocType |
computational geometry,voronoi diagram,visual angle,measure on triangles,aspect ratio,optimization,finite set,finite system,well-known conjecture,euclidean space,fundamental geometric problem,triangle,vision information,algorithms,minimal height,optimization problem | Power diagram,Line segment,Mathematical optimization,Centroidal Voronoi tessellation,Disjoint sets,Mathematical analysis,Computational geometry,Voronoi diagram,Weighted Voronoi diagram,Optimization problem,Mathematics | Conference |
Volume | Issue | ISSN |
25 | 2 | 1868-937X |
ISBN | Citations | PageRank |
0-7695-2869-4 | 3 | 0.41 |
References | Authors | |
10 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tetsuo Asano | 1 | 1448 | 229.35 |
| naoki katoh | 2 | 1101 | 187.43 |
| Hisao Tamaki | 3 | 3 | 0.41 |
| Takeshi Tokuyama | 4 | 1179 | 417.31 |