A Generic Algebraic Kernel for Non-linear Geometric Applications

Eric Berberich 1 Michael Hemmer 2, * Michael Kerber 3
* Corresponding author
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We report on a generic (uni- and bivariate) algebraic kernel that becomes available to the public with CGAL~3.7. It comprises complete, correct, though efficient state-of-the-art implementations on polynomials, roots of polynomial systems, and the support to analyze algebraic curves defined by bivariate polynomials. The kernel is accompanied with a ready-to-use interface to enable arrangements induced by algebraic curves, that have already been used as basis for various geometric applications, as arrangements on Dupin cyclides or the triangulation of algebraic surfaces. We present two novel applications: arrangements of rotated algebraic curves and Boolean set operations on polygons bounded by segments of algebraic curves. We also provide exhaustive experiments showing that our implementation is competitive and often outperforms existing implementation on non-linear curves available in CGAL, which demonstrates the general usefulness of the presented software.
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Eric Berberich, Michael Hemmer, Michael Kerber. A Generic Algebraic Kernel for Non-linear Geometric Applications. [Research Report] RR-7274, INRIA. 2010, pp.20. ⟨inria-00480031⟩

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