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Journal Articles Computational Geometry Year : 2005

## On the Computation of an Arrangement of Quadrics in 3D

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1
Bernard Mourrain
Jean-Pierre Técourt
• Function : Author
Monique Teillaud

#### 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.

### Dates and versions

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

### Identifiers

• HAL Id : inria-00350858 , version 1
• DOI :

### Cite

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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