Isotopic triangulation of a real algebraic surface

Abstract: We present a new algorithm for computing the topology of a real algebraic surface in a ball , even in singular cases. We use algorithms for 2D and 3D algebraic curves and show how one can compute a topological complex equivalent to , and even a simplicial complex isotopic to by exploiting properties of the contour curve of . The correctness proof of the algorithm is based on results from stratification theory. We construct an explicit Whitney stratification of , by resultant computation. Using Thom’s isotopy lemma, we show how to deduce the topology of from a finite number of characteristic points on the surface. An analysis of the complexity of the algorithm and effectiveness issues conclude the paper. [Copyright &y& Elsevier]