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

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.

Domaines: Géométrie algorithmique [cs.CG]

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⟩