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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 [Hel90, Mid93], which is popular in the geographic information... (Update)
Context of citations to this paper: More
...that must be added or deleted to minimally achieve a userspecified screen space deviation. It maintains a Delaunay triangulation [5, 8, 23, 10, 11] of the (two dimensional) domain samples, incrementally adding and deleting the desired samples. The triangles generated by...
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BibTeX entry: (Update)
Olivier Devillers. On Deletion in Delaunay Triangulations. Proceedings of the Fifteenth Annual Symposium on Computational Geometry. Association for Computing Machinery, June 1999. http://citeseer.ist.psu.edu/article/devillers99deletion.html More
@inproceedings{ devillers99deletion,
author = "Olivier Devillers",
title = "On Deletion in Delaunay Triangulations",
booktitle = "Symposium on Computational Geometry",
pages = "181-188",
year = "1999",
url = "citeseer.ist.psu.edu/article/devillers99deletion.html" }
Citations (may not include all citations):159 Spatial Tessellations: Concepts and Applications of Voronoi .. (context) - Okabe, Boots et al. - 1992
81 A linear-time algorithm for computing the Voronoi diagram of.. (context) - Aggarwal, Guibas et al. - 1989
58 Incremental topological flipping works for regular triangula.. (context) - Edelsbrunner, Shah - 1996
56 Constructing higher-dimensional convex hulls at logarithmic .. (context) - Seidel - 1986
40 Computing Dirichlet tessellations in the plane (context) - Green, Sibson - 1978
34 Shellable decompositions of cells and spheres (context) - Bruggesser, Mani - 1971
33 The nature and meaning of perturbations in geometric computi.. (context) - Seidel - 1998
29 algorithms and applications (context) - Aurenhammer, properties - 1987
27 Building Voronoi diagrams for convex polygons in linear expe.. (context) - Chew - 1986
21 Improved incremental randomized Delaunay triangulation - Devillers - 1998
16 Triangulation algorithms for adaptive terrain modeling (context) - Heller - 1990
14 Intersections with random geometric objects (context) - Bose, Devroye - 1995
14 A probabilistic analysis of the power of arithmetic filters - Devillers, Preparata - 1998
7 Fast randomized point location without preprocessing in two-.. - Mcke, Saias et al. - 1996
7 a comprehensive course (context) - Pedoe - 1970
5 Removing degeneracies by perturbing the problem or the world - Alliez, Devillers et al. - 1997
5 a geometric tool to unify duality results on Voronoi diagram.. (context) - Devillers, Meiser et al. - 1992
4 Triangulation de Delaunay et arbres multidimensionnels (context) - Lemaire - 1997
4 Further results on arithmetic filters for geometric predicat.. - Devillers, Preparata - 1999
4 Spatial Modelling by Delaunay Networks of Two and Three Dime.. (context) - Midtb - 1993
2 Non redundant flip for point deletion in delaunay triangulat.. (context) - Snoeyink - 1998
2 Interval arithmetic yields efficient dynamic filters for com.. (context) - Brnnimann, Burnikel et al. - 1998
1 a fast point location procedure in 2d Delaunay triangulation.. (context) - Devroye, Lemaire et al. - 1998
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