Isotopic meshing of a real algebraic surface

Bernard Mourrain 1 Jean-Pierre Técourt 1
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We present a new algorithm for computing the topology of a real algebraic surface $S$, even in singular cases. We use previous algorithms for 2D and 3D algebraic curves and show how properties of the polar variety of $S$ yield a topological complex equivalent to $S$, or even a simplicial complex isotopic to $S$. The proof of correctness of the algorithm is detailed. It is based on tools from stratification theory. We construct an explicit Whitney stratification of $S$, by resultant computation. Using Thom's isotopy lemma, we show how to deduce the topology of $S$ from a finite number of characteristic points on the surface. An analysis of the complexity of the algorithm and effectivity issues conclude the paper.
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Submitted on : Friday, May 19, 2006 - 8:40:06 PM
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  • HAL Id : inria-00070499, version 1

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Bernard Mourrain, Jean-Pierre Técourt. Isotopic meshing of a real algebraic surface. [Research Report] RR-5508, INRIA. 2006, pp.21. 〈inria-00070499〉

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