On Deletion in Delaunay Triangulations

Olivier Devillers 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This paper presents how the space of spheres and shelling may be used to delete a point from a $d$-dimensional triangulation 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 [Heller, Symp. Spatial Data Handling 1990] which is popular in the geographic information system community. Unfortunately, Heller algorithm is false, as explained in this paper.
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International Journal of Computational Geometry and Applications, World Scientific Publishing, 2002, 12, pp.193-205. 〈10.1142/S0218195902000815〉
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Olivier Devillers. On Deletion in Delaunay Triangulations. International Journal of Computational Geometry and Applications, World Scientific Publishing, 2002, 12, pp.193-205. 〈10.1142/S0218195902000815〉. 〈inria-00167201〉

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