Near-Optimal Parameterization of the Intersection of Quadrics

Laurent Dupont (1) , Daniel Lazard (2, 3) , Sylvain Lazard (1) , Sylvain Petitjean (1)

1 ISA - Models, algorithms and geometry for computer graphics and vision
2 CALFOR - Calcul formel
3 SPACES - Solving problems through algebraic computation and efficient software

In this paper, we present the first exact, robust and practical method for computing an explicit representation of the intersection of two arbitrary quadrics with rational coefficients. Combining results from the theory of quadratic forms, linear algebra and number theory, we show how to obtain parametric intersection curves that are near-optimal in the number and depth of radicals involved.

Mots clés: intersection de quadriques; intersection of quadrics

Domaines: Autre [cs.OH]

Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean. Near-Optimal Parameterization of the Intersection of Quadrics. 19th Symposium on Computational Geometry - SoCG 2003, Jun 2003, San Diego, United States. pp.246-255, ⟨10.1145/777792.777830⟩. ⟨inria-00099789⟩