On-line randomized construction of the upper envelope of triangles and surface patches in R3

Jean-Daniel Boissonnat 1 Katrin Dobrindt 1
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this paper we describe an on-line randomized algorithm for computing the upper envelope (i.e. poinwise maximum) of a set of n triangles in three dimensions. The main new feature of this algorithm is the combination of two layers of influence graphs, which were introduced. We can insert the n-th triangle in 0(log n 7A(n;r=1) F(f o(|r/2|) ; r2)) expected time, where fo(r) is the expected size of an intermediate result for r triangles. Since fo(r) = 0(r2 5 (r))., the expected time for the insertion of the last triangle is bounded in the worst case by 0(r2 5 (r)). This algorithm is easy to implement and works also nicely for surfaces and surface patches of fixed maximum degree.
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Rapport
[Research Report] RR-1878, INRIA. 1993
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Soumis le : mercredi 24 mai 2006 - 16:26:08
Dernière modification le : samedi 27 janvier 2018 - 01:30:56
Document(s) archivé(s) le : mardi 12 avril 2011 - 19:22:13

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Jean-Daniel Boissonnat, Katrin Dobrindt. On-line randomized construction of the upper envelope of triangles and surface patches in R3. [Research Report] RR-1878, INRIA. 1993. 〈inria-00074795〉

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