On-line randomized construction of the upper envelope of triangles and surface patches in R3 - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 1993

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

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.

Domains

Other [cs.OH]
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Dates and versions

inria-00074795 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00074795 , version 1

Cite

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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