Polygonization of implicit surfaces
Computer Aided Geometric Design
An efficient method for analyzing the topology of plane real algebraic curves
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Algorithms to compute the topology of orientable real algebraic surfaces
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Rational quadratic approximation to real algebraic curves
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
Algorithmical determination of the topology of a real algebraic surface
Journal of Symbolic Computation
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Determining the topology of an algebraic surface is not only an interesting mathematical problem, but also a key issue in computer graphics and CAGD. An algorithm is proposed to determine the intrinsic topology of an implicit real algebraic surface f(x,y,z) = 0 in R3, where f(x,y,z) ∈ Q[x,y,z] and Q is the field of rational numbers. There exist algorithms to determine the topology for algebraic surfaces of special type [2, 3, 4, 7]. The CAD method proposed by Collins [1] can divide the space into cylindrical parts. But it does not give the connection information neither the intrinsic representation.