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
Topology and arrangement computation of semi-algebraic planar curves
Computer Aided Geometric Design
Axial moving planes and singularities of rational space curves
Computer Aided Geometric Design
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
Using Smith normal forms and µ-bases to compute all the singularities of rational planar curves
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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We describe a new algorithm for the visualisation of implicit algebraic curves, which isolates the singular points, compute the topological degree around these points in order to check that the topology of the curve can be deduced from the points on the boundary of these singular regions. The other regions are divided into x or y regular regions, in which the branches of the curve are also determined from information on the boundary. Combined with enveloping techniques of the polynomial represented in the Bernstein basis, it is shown on examples that this algorithm is able to render curves defined by high degree polynomials with large coefficients, to identify regions of interest and to zoom safely on these regions.