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On the Computation of an Arrangement of Quadrics in 3D

Bernard Mourrain 1 Jean-Pierre Técourt 1 Monique Teillaud 1
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (... - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : In this paper, we study a sweeping algorithm for computing the arrangement of a set of quadrics in $\RR^{3}$. We define a ``trapezoidal'' decomposition in the sweeping plane, and we study the evolution of this subdivision during the sweep. A key point of this algorithm is the manipulation of algebraic numbers. In this perspective, we put a large emphasis on the use of algebraic tools, needed to compute the arrangement, including Sturm sequences and Rational Univariate Representation of the roots of a multivariate polynomial system.
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Submitted on : Wednesday, January 7, 2009 - 4:46:05 PM
Last modification on : Monday, October 12, 2020 - 10:27:38 AM
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Bernard Mourrain, Jean-Pierre Técourt, Monique Teillaud. On the Computation of an Arrangement of Quadrics in 3D. Computational Geometry, Elsevier, 2005, 30 (2), pp.145-164. ⟨10.1016/j.comgeo.2004.05.003⟩. ⟨inria-00350858⟩



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