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Journal Articles Computational Geometry Year : 2005

On the Computation of an Arrangement of Quadrics in 3D

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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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Dates and versions

inria-00350858 , version 1 (07-01-2009)

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Bernard Mourrain, Jean-Pierre Técourt, Monique Teillaud. On the Computation of an Arrangement of Quadrics in 3D. Computational Geometry, 2005, 30 (2), pp.145-164. ⟨10.1016/j.comgeo.2004.05.003⟩. ⟨inria-00350858⟩
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