A generic algebraic kernel for non linear geometric applications Conference Paper

Author(s): Berberich, Eric; Hemmer, Michael; Kerber, Michael
Title: A generic algebraic kernel for non linear geometric applications
Affiliation IST Austria
Abstract: We report on a generic uni- and bivariate algebraic kernel that is publicly available 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 design is generic, that is, various number types and substeps can be exchanged. It 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 experiments showing that our general implementation is competitive and even often clearly outperforms existing implementations that are explicitly tailored for specific types of non-linear curves that are available in CGAL.
Conference Title: SCG: Symposium on Computational Geometry
Publisher: ACM  
Date Published: 2011-06-13
Start Page: 179
End Page: 186
DOI: 10.1145/1998196.1998224
Notes: We thank Monique Teillaud and editorial board of Cgal for comments concerning the design of the package and all Cgal developers who contributed supporting packages and code. Figures 1, 3, 4, and 5 have been created using a rendering software for algebraic segments written by Pavel Emeliyanenko.
Open access: yes (repository)
IST Austria Authors
  1. Michael Kerber
    21 Kerber
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