HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation

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.
Complete list of metadata

Cited literature [29 references]  Display  Hide  Download

Contributor : Michael Hemmer Connect in order to contact the contributor
Submitted on : Monday, May 3, 2010 - 1:41:46 PM
Last modification on : Thursday, January 20, 2022 - 5:29:07 PM
Long-term archiving on: : Friday, October 19, 2012 - 2:17:16 PM


Files produced by the author(s)


  • HAL Id : inria-00480031, version 1



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⟩



Record views


Files downloads