On the computation of an arrangement of quadrics in 3D

doi:10.1016/j.comgeo.2004.05.003

Computational Geometry

Volume 30, Issue 2, February 2005, Pages 145-164

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Abstract

In this paper, we study a sweeping algorithm for computing the arrangement of a set of quadrics in $R^{3}$ . 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.

Keywords

Arrangement

Quadric

Implicit surface

Algebraic number

Rational univariate representation

Certified computation

Cited by (0)

^☆: This work is partially supported by the IST Program of the EU as a Shared-cost RTD (FET Open) Project under Contract No IST-2000-26473 (ECG—Effective Computational Geometry for Curves and Surfaces); http://www-sop.inria.fr/prisme/ECG/.

Computational Geometry

On the computation of an arrangement of quadrics in 3D☆

Abstract

Keywords