Towards the Robust Intersection of Implicit Quadrics

Laurent Dupont 1 Daniel Lazard 2 Sylvain Lazard 1 Sylvain Petitjean 1
1 ISA - Models, algorithms and geometry for computer graphics and vision
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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''.
Mots-clés : robustesse quadrics robustness geometric computations surface intersection calculs geometriques intersection de surface quadriques
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https://hal.inria.fr/inria-00100878
Contributor : Sylvain Lazard <>
Submitted on : Tuesday, December 15, 2009 - 3:10:14 PM
Last modification on : Thursday, January 11, 2018 - 6:20:00 AM
Long-term archiving on : Tuesday, April 6, 2010 - 1:13:45 AM

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Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean. Towards the Robust Intersection of Implicit Quadrics. J. Winkler and M. Niranjan. Uncertainty in Geometric Computations, Kluwer Academic Publishers, pp.59-68, 2002, International Series in Engineering and Computer Science. ⟨inria-00100878⟩

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