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- W2158299375 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" @default.
- W2158299375 created "2016-06-24" @default.
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- W2158299375 date "2011-06-13" @default.
- W2158299375 modified "2023-09-27" @default.
- W2158299375 title "A generic algebraic kernel for non-linear geometric applications" @default.
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- W2158299375 doi "https://doi.org/10.1145/1998196.1998224" @default.
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