Sylvester—Habicht sequences and fast Cauchy index computation
Journal of Symbolic Computation
Comparison of interval methods for plotting algebraic curves
Computer Aided Geometric Design
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
Root isolation for bivariate polynomial systems with local generic position method
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Visualizing Arcs of Implicit Algebraic Curves, Exactly and Fast
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
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In this work we propose an algorithm for the exact rasterization of a given real algebraic plane curve, which is the set of real solutions of a bivariate polynomial equation F(x, y) = 0. Our algorithm first divides the image plane into simple rectangles, where the curve has no local extreme values. In these blocks the topology is known and the direction of the curve can easily be determined. Subsequent we efficiently trace the curve from one row of pixels to the next by using either tests for a sign changes of F(x, y) in simple cases or real root counting via Sturm-Habicht sequences in presence of dense curve arcs. In contrast to other approaches, the curve tracing is performed at the given resolution and will never subdivided the image plane below pixel level to obtain a correct result.