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COMPGEOM
2011
ACM

A generic algebraic kernel for non-linear geometric applications

7 years 10 months ago
A generic algebraic kernel for non-linear geometric applications
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...
Eric Berberich, Michael Hemmer, Michael Kerber
Added 25 Aug 2011
Updated 25 Aug 2011
Type Journal
Year 2011
Where COMPGEOM
Authors Eric Berberich, Michael Hemmer, Michael Kerber
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