NDLI: A generic algebraic kernel for non-linear geometric applications

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A generic algebraic kernel for non-linear geometric applications

Content Provider	ACM Digital Library
Author	Kerber, Michael Berberich, Eric Hemmer, Michael
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.
Starting Page	179
Ending Page	186
Page Count	8
File Format	PDF
ISBN	9781450306829
DOI	10.1145/1998196.1998224
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-06-13
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Robust computation Algebraic kernel Algebraic curve Generic programming Cgal
Content Type	Text
Resource Type	Article

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