A Generic Algebraic Kernel for Non-linear Geometric Applications - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2010

A Generic Algebraic Kernel for Non-linear Geometric Applications

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.
Fichier principal
Vignette du fichier
RR-7274.pdf (439.09 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

inria-00480031 , version 1 (03-05-2010)

Identifiers

  • HAL Id : inria-00480031 , version 1

Cite

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⟩
373 View
323 Download

Share

Gmail Mastodon Facebook X LinkedIn More