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, 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.
Document type :
Journal articles
Liste complète des métadonnées

https://hal.inria.fr/inria-00350858
Contributor : Monique Teillaud <>
Submitted on : Wednesday, January 7, 2009 - 4:46:05 PM
Last modification on : Thursday, January 11, 2018 - 4:57:39 PM
Document(s) archivé(s) le : Tuesday, June 8, 2010 - 6:58:41 PM

Files

CGTA-final.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

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⟩

Share

Metrics

Record views

294

Files downloads

235