Polygonization of implicit surfaces
Computer Aided Geometric Design
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Simplicial pivoting for mesh generation of implicitly defined surfaces
Computer Aided Geometric Design
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
An implicit surface polygonizer
Graphics gems IV
Algorithms for trigonometric curves (simplification, implicitization, parameterization)
Journal of Symbolic Computation
Numerical Differentiation of Analytic Functions
ACM Transactions on Mathematical Software (TOMS)
Implicit linear interval estimations
SCCG '02 Proceedings of the 18th spring conference on Computer graphics
A Tracking Algorithm for Implicitly Defined Curves
IEEE Computer Graphics and Applications
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
Robust Adaptive Approximation of Implicit Curves
SIBGRAPI '01 Proceedings of the 14th Brazilian Symposium on Computer Graphics and Image Processing
On the exact computation of the topology of real algebraic curves
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Fast and exact geometric analysis of real algebraic plane curves
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Visualisation of Implicit Algebraic Curves
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
ACM Transactions on Graphics (TOG)
Visualizing Arcs of Implicit Algebraic Curves, Exactly and Fast
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
New bounds for the Descartes method
Journal of Symbolic Computation
Regularity criteria for the topology of algebraic curves and surfaces
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Approximating Implicit Curves on Triangulations with Affine Arithmetic
SIBGRAPI '12 Proceedings of the 2012 25th SIBGRAPI Conference on Graphics, Patterns and Images
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Continuation algorithms usually behave badly near to critical points of implicitly defined curves in R^2, i.e., points at which at least one of the partial derivatives vanishes. Critical points include turning points, self-intersections, and isolated points. Another problem with this family of algorithms is their inability to render curves with multiple components because that requires finding first a seed point on each of them. This paper details an algorithm that resolves these two major problems in an elegant manner. In fact, it allows us not only to march along a curve even in the presence of critical points, but also to detect and render curves with multiple components using the theory of critical points.