Towards the Robust Intersection of Implicit Quadrics

Laurent Dupont Daniel Lazard 1 Sylvain Lazard Sylvain Petitjean
1 CALFOR - Calcul formel
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We are interested in efficiently and robustly computing a parametric form of the intersection of two implicit quadrics with rational coefficients. Our method is similar in spirit to the general method introduced by J. Levin for computing an explicit representation of the intersection of two quadrics, but extends it in several directions. Combining results from the theory of quadratic forms, a projective formalism and new theorems characterizing the intersection of two quadratic surfaces, we show how to obtain parametric representations that are both “simple” (the size of the coefficients is small) and “as rational as possible”.
Type de document :
Communication dans un congrès
Workshop on Uncertainty in Geometric Computations, Jul 2001, Sheffield, United Kingdom. Springer, Workshop on Uncertainty in Geometric Computations, 704, pp.59-68, The Springer International Series in Engineering and Computer Science. 〈10.1007/978-1-4615-0813-7_5〉
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Soumis le : lundi 31 juillet 2017 - 16:53:57
Dernière modification le : jeudi 21 mars 2019 - 13:12:48

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Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean. Towards the Robust Intersection of Implicit Quadrics. Workshop on Uncertainty in Geometric Computations, Jul 2001, Sheffield, United Kingdom. Springer, Workshop on Uncertainty in Geometric Computations, 704, pp.59-68, The Springer International Series in Engineering and Computer Science. 〈10.1007/978-1-4615-0813-7_5〉. 〈hal-01570813〉

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