A polynomial-time algorithm for the topological type of a real algebraic curve
Journal of Symbolic Computation
Computer Aided Geometric Design
Singular points of algebraic curves
Journal of Symbolic Computation
An improved upper complexity bound for the topology computation of a real algebraic plane curve
Journal of Complexity - Special issue for the Foundations of Computational Mathematics conference, Rio de Janeiro, Brazil, Jan. 1997
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
Elementary geometry of algebraic curves: an undergraduate introduction
Elementary geometry of algebraic curves: an undergraduate introduction
Algorithms for rational real algebraic curves
Fundamenta Informaticae - Special issue on symbolic computation and artificial intelligence
Polynomial Algorithms in Computer Algebra
Polynomial Algorithms in Computer Algebra
Irreducible decomposition of curves
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
Computing the topology of real algebraic surfaces
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Algorithmical determination of the topology of a real algebraic surface
Journal of Symbolic Computation
Exact geometric-topological analysis of algebraic surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
On the computation of the topology of a non-reduced implicit space curve
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Regularity criteria for the topology of algebraic curves and surfaces
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Topology of 2D and 3D rational curves
Computer Aided Geometric Design
An adapted version of the Bentley-Ottmann algorithm for invariants of plane curves singularities
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
On the isotopic meshing of an algebraic implicit surface
Journal of Symbolic Computation
Approximating algebraic space curves by circular arcs
Proceedings of the 7th international conference on Curves and Surfaces
Computing the shapes arising in a family of space rational curves depending on one parameter
Computer Aided Geometric Design
Certified approximation of parametric space curves with cubic B-spline curves
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
Journal of Symbolic Computation
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An algorithm for computing the topology of a real algebraic space curve C, implicitly defined as the intersection of two surfaces, is presented. Given C, the algorithm generates a space graph which is topologically equivalent to the real variety on the Euclidean space. The algorithm is based on the computation of the graphs of at most two projections of C. For this purpose, we introduce the notion of space general position for space curves, we show that any curve under the above conditions can always be linearly transformed to be in general position, and we present effective methods for checking whether space general position has been reached.