Shape reconstruction from planar cross sections
Computer Vision, Graphics, and Image Processing
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Efficient exact arithmetic for computational geometry
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Rounding arrangements dynamically
Proceedings of the eleventh annual symposium on Computational geometry
Towards exact geometric computation
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Snap rounding line segments efficiently in two and three dimensions
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Vertex-rounding a three-dimensional polyhedral subdivision
Proceedings of the fourteenth annual symposium on Computational geometry
Computational geometry and discrete computations
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Robust Proximity Queries in Implicit Voronoi Diagrams
Robust Proximity Queries in Implicit Voronoi Diagrams
| Hi-index | 5.23 |
Computational geometry classically assumes real-number arithmetic which does not exist in actual computers. A solution consists in using integer coordinates for data and exact arithmetic for computations. This approach implies that if the results of an algorithm are the input of another, these results must be rounded to match this hypothesis of integer coordinates. In this paper, we treat the case of two-dimensional Voronoi diagrams and are interested in rounding the Voronoi vertices to grid points while interesting properties of the Voronoi diagram are preserved. These properties are the planarity of the embedding and the convexity of the cells. We give a condition on the grid size to ensure that rounding to the nearest grid point preserves the properties. We also present heuristics to round vertices (not to the nearest grid point) and preserve these properties.