Constrained higher order Delaunay triangulations

Authors:
Joachim Gudmundsson;Herman J. Haverkort;Marc van Kreveld
Affiliations:
Department of Mathematics and Computing Science, TU Eindhoven, 5600 MB Eindhoven, The Netherlands;Institute of Information and Computing Sciences, Utrecht University, PO Box 80.089, 3508 TB Utrecht, The Netherlands;Institute of Information and Computing Sciences, Utrecht University, PO Box 80.089, 3508 TB Utrecht, The Netherlands
Venue:
Computational Geometry: Theory and Applications
Year:
2005

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Abstract

We extend the notion of higher-order Delaunay triangulations to constrained higher-order Delaunay triangulations and provide various results. We can determine the order k of a given triangulation in O(min(nk log n log k, n3/2logO(1) n)) time. We show that the completion of a set of useful order-k Delaunay edges may have order 2k - 2, which is worst-case optimal. We give an algorithm for the lowest-order completion for a set of useful order-k Delaunay edges when k ≤ 3. For higher orders the problem is open.