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# Towards the Robust Intersection of Implicit Quadrics

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''.
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https://hal.inria.fr/inria-00100878
Contributor : Sylvain Lazard Connect in order to contact the contributor
Submitted on : Tuesday, December 15, 2009 - 3:10:14 PM
Last modification on : Friday, February 4, 2022 - 3:15:23 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 1:13:45 AM

### File

sheffield_09_2001.pdf
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### Identifiers

• HAL Id : inria-00100878, version 1

### Citation

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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