article

Regular triangulations of dynamic sets of points

Authors:

Josep CotrinaAuthors Info & Claims

Computer Aided Geometric Design, Volume 19, Issue 2

Pages 127 - 149

https://doi.org/10.1016/S0167-8396(01)00082-6

Published: 11 February 2002 Publication History

Abstract

The Delaunay triangulations of a set of points are a class of triangulations which play an important role in a variety of different disciplines of science. Regular triangulations are a generalization of Delaunay triangulations that maintain both their relationship with convex hulls and with Voronoi diagrams. In regular triangulations, a real value, its weight, is assigned to each point.In this paper a simple data structure is presented that allows regular triangulations of sets of points to be dynamically updated, that is, new points can be incrementally inserted in the set and old points can be deleted from it. The algorithms we propose for insertion and deletion are based on a geometric interpretation of the history data structure in one more dimension and use lifted flips as the unique topological operation. This results in rather simple and efficient algorithms. The algorithms have been implemented and experimental results are given.

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Cited By

Silva LScheidegger LEtiene TComba JNonato LSilva C(2014)A Weighted Delaunay Triangulation Framework for Merging Triangulations in a Connectivity Oblivious FashionComputer Graphics Forum10.1111/cgf.1227433:6(18-30)Online publication date: 1-Sep-2014
https://dl.acm.org/doi/10.1111/cgf.12274
Yan DWonka P(2013)Gap processing for adaptive maximal poisson-disk samplingACM Transactions on Graphics10.1145/2516971.251697332:5(1-15)Online publication date: 8-Oct-2013
https://dl.acm.org/doi/10.1145/2516971.2516973
Beyer TMeyer-Hermann M(2006)Recover from non-flippable configurations in parallel approaches to three dimensional kinetic regular triangulationsProceedings of the 8th WSEAS international conference on Automatic control, modeling & simulation10.5555/1973458.1973532(399-404)Online publication date: 12-Mar-2006
https://dl.acm.org/doi/10.5555/1973458.1973532

Index Terms

Regular triangulations of dynamic sets of points
1. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image Computer Aided Geometric Design

Computer Aided Geometric Design Volume 19, Issue 2

February 2002

78 pages

ISSN:0167-8396

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 11 February 2002

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Cited By

Silva LScheidegger LEtiene TComba JNonato LSilva C(2014)A Weighted Delaunay Triangulation Framework for Merging Triangulations in a Connectivity Oblivious FashionComputer Graphics Forum10.1111/cgf.1227433:6(18-30)Online publication date: 1-Sep-2014
https://dl.acm.org/doi/10.1111/cgf.12274
Yan DWonka P(2013)Gap processing for adaptive maximal poisson-disk samplingACM Transactions on Graphics10.1145/2516971.251697332:5(1-15)Online publication date: 8-Oct-2013
https://dl.acm.org/doi/10.1145/2516971.2516973
Beyer TMeyer-Hermann M(2006)Recover from non-flippable configurations in parallel approaches to three dimensional kinetic regular triangulationsProceedings of the 8th WSEAS international conference on Automatic control, modeling & simulation10.5555/1973458.1973532(399-404)Online publication date: 12-Mar-2006
https://dl.acm.org/doi/10.5555/1973458.1973532

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