Algebraic decomposition of regular curves
Journal of Symbolic Computation
A polynomial-time algorithm for the topological type of a real algebraic curve
Journal of Symbolic Computation
Computer Aided Geometric Design
Algorithms for polynomial real root isolation
Algorithms for polynomial real root isolation
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
Spline approximations of real algebraic surfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually!
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
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
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Rational quadratic approximation to real algebraic curves
Computer Aided Geometric Design
A delineability-based method for computing critical sets of algebraic surfaces
Journal of Symbolic Computation
Complete numerical isolation of real zeros in zero-dimensional triangular systems
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Topology of real algebraic space curves
Journal of Symbolic Computation
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Exact geometric-topological analysis of algebraic surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Topology and arrangement computation of semi-algebraic planar curves
Computer Aided Geometric Design
Complete numerical isolation of real roots in zero-dimensional triangular systems
Journal of Symbolic Computation
Computer Aided Geometric Design
An efficient algorithm for the stratification and triangulation of an algebraic surface
Computational Geometry: Theory and Applications
Ambient Isotopic Meshing for Implicit Algebraic Surfaces with Singularities
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Regularity criteria for the topology of algebraic curves and surfaces
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Root isolation of zero-dimensional polynomial systems with linear univariate representation
Journal of Symbolic Computation
Local generic position for root isolation of zero-dimensional triangular polynomial systems
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Cell decomposition of almost smooth real algebraic surfaces
Numerical Algorithms
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An algorithm is proposed to determine the topology of an implicit real algebraic surface in ℝ3. The algorithm consists of three steps: surface projection, projection curve topology determination and surface patches composition. The algorithm provides a curvilinear wireframe of the surface and the surface patches of the surface determined by the curvilinear wireframe, which have the same topology as the surface. Most of the surface patches are curvilinear polygons. Some examples are used to show that our algorithm is effective.