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Conference Papers Year : 1999

On deletion in Delaunay triangulations

Olivier Devillers

Abstract

This paper presents how the space of spheres and shelling may be used to delete a point from a d-dimensional triangu- lation efficiently. In dimension two, if k is the degree of the deleted vertex, the complexity is O( k log k), but we notice that this number only applies to low cost operations, while time consuming computations are only done a linear number of times. This algorithm may be viewed as a variation of Heller’s algorithm [He190, Mid93], which is popular in the geographic information system community. Unfortunately, Heller algorithm is false, as explained in this paper.

Dates and versions

hal-01179435 , version 1 (22-07-2015)

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Olivier Devillers. On deletion in Delaunay triangulations. Proceedings of the 15th Annual Symposium on Computational Geometry, 1999, Miami, United States. pp.181-189, ⟨10.1145/304893.304969⟩. ⟨hal-01179435⟩
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