A resultant approach to detect intersecting curves in the projective space

Laurent Busé 1 André Galligo 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 : Given two curves in the projective space, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the inputs which vanishes if and only if the two curves intersect. This could be useful in Computer Aided Design, for computing the intersection of algebraic surfaces.
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Laurent Busé, André Galligo. A resultant approach to detect intersecting curves in the projective space. MEGA 2003, Jun 2003, Kaiserslautern, Germany. ⟨inria-00100315⟩

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