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Regular triangulations of dynamic sets of points

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Vigo Anglada, MarcMés informacióMés informacióMés informació
Pla García, NúriaMés informacióMés informacióMés informació
Document typeResearch report
Defense date2000-10
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
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 geometrical 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.
CitationVigo, M., Pla, N. "Regular triangulations of dynamic sets of points". 2000. 
Is part ofR00-64
URIhttp://hdl.handle.net/2117/96493
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  • GIE - Grup d'Informàtica en l'Enginyeria - Reports de recerca [82]
  • Departament de Ciències de la Computació - Reports de recerca [1.106]
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