Visualisation of implicit algebraic curves

Lionel Alberti 1, 2 Bernard Mourrain 1
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : 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.
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Conference papers
Marc, Alexa and Steven, Gortler and Tao, Ju. Pacific Conference on Computer Graphics and Applications 2007, Oct 2007, Lahaina, Maui, Hawaii, United States. IEEE Computer Society, pp.303-312, 2007, Pacific Conference on Computer Graphics and Applications
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https://hal.inria.fr/inria-00175062
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Submitted on : Wednesday, September 26, 2007 - 2:19:00 PM
Last modification on : Monday, February 7, 2011 - 11:07:20 AM
Document(s) archivé(s) le : Friday, April 9, 2010 - 2:55:57 AM

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Lionel Alberti, Bernard Mourrain. Visualisation of implicit algebraic curves. Marc, Alexa and Steven, Gortler and Tao, Ju. Pacific Conference on Computer Graphics and Applications 2007, Oct 2007, Lahaina, Maui, Hawaii, United States. IEEE Computer Society, pp.303-312, 2007, Pacific Conference on Computer Graphics and Applications. <inria-00175062>

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