Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
A Tracking Algorithm for Implicitly Defined Curves
IEEE Computer Graphics and Applications
Comparison of interval methods for plotting algebraic curves
Computer Aided Geometric Design
Isotopic approximation of implicit curves and surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry 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
Exact arrangements on tori and Dupin cyclides
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Visualizing and exploring planar algebraic arrangements: a web application
Proceedings of the twenty-fourth annual symposium on Computational geometry
Complete subdivision algorithms, II: isotopic meshing of singular algebraic curves
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
On the topology of planar algebraic curves
Proceedings of the twenty-fifth annual symposium on Computational geometry
Isolating real roots of real polynomials
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Reliable and efficient geometric computing
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
A generic algebraic kernel for non-linear geometric applications
Proceedings of the twenty-seventh annual symposium on Computational geometry
On the shape of curves that are rational in polar coordinates
Computer Aided Geometric Design
On exact rasterization of real algebraic plane curves
Proceedings of the 27th Spring Conference on Computer Graphics
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Given a Cylindrical Algebraic Decomposition [2] of an implicitly defined algebraic curve, visualizing distinct curve arcs is not as easy as it stands because, despite the absence of singularities in the interior, the arcs can pass arbitrary close to each other. We present an algorithm to visualize distinct arcs of algebraic curves efficiently and precise (at a given resolution), irrespective of how close to each other they actually pass. Our hybrid method inherits the ideas of subdivision and curve-tracking methods. With an adaptive mixed-precision model we can render the majority of curves using machine arithmetic without sacrificing the exactness of the final result. The correctness and applicability of our algorithm is borne out by the success of our web-demo presented in [11].