Degeneracy of Angular Voronoi Diagram

Details Degeneracy of Angular Voronoi Diagram Degeneracy of Angular Voronoi Diagram

2007-10-04

arxiv.org/abs/0710.0925v1

Computer Science

Computational Geometry

8 pages, 11 figures, 1 table, presented at 4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD07)

Scientific paper

Angular Voronoi diagram was introduced by Asano et al. as fundamental research for a mesh generation. In an angular Voronoi diagram, the edges are curves of degree three. From view of computational robustness we need to treat the curves carefully, because they might have a singularity. We enumerate all the possible types of curves that appear as an edge of an angular Voronoi diagram, which tells us what kind of degeneracy is possible and tells us necessity of considering a singularity for computational robustness.

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