--- _id: '3328' abstract: - lang: eng text: '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.' article_processing_charge: No author: - first_name: Eric full_name: Berberich, Eric last_name: Berberich - first_name: Michael full_name: Hemmer, Michael last_name: Hemmer - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: 'Berberich E, Hemmer M, Kerber M. A generic algebraic kernel for non linear geometric applications. In: ACM; 2011:179-186. doi:10.1145/1998196.1998224' apa: 'Berberich, E., Hemmer, M., & Kerber, M. (2011). A generic algebraic kernel for non linear geometric applications (pp. 179–186). Presented at the SCG: Symposium on Computational Geometry, Paris, France: ACM. https://doi.org/10.1145/1998196.1998224' chicago: Berberich, Eric, Michael Hemmer, and Michael Kerber. “A Generic Algebraic Kernel for Non Linear Geometric Applications,” 179–86. ACM, 2011. https://doi.org/10.1145/1998196.1998224. ieee: 'E. Berberich, M. Hemmer, and M. Kerber, “A generic algebraic kernel for non linear geometric applications,” presented at the SCG: Symposium on Computational Geometry, Paris, France, 2011, pp. 179–186.' ista: 'Berberich E, Hemmer M, Kerber M. 2011. A generic algebraic kernel for non linear geometric applications. SCG: Symposium on Computational Geometry, 179–186.' mla: Berberich, Eric, et al. A Generic Algebraic Kernel for Non Linear Geometric Applications. ACM, 2011, pp. 179–86, doi:10.1145/1998196.1998224. short: E. Berberich, M. Hemmer, M. Kerber, in:, ACM, 2011, pp. 179–186. conference: end_date: 2011-06-15 location: Paris, France name: 'SCG: Symposium on Computational Geometry' start_date: 2011-06-13 date_created: 2018-12-11T12:02:42Z date_published: 2011-06-13T00:00:00Z date_updated: 2021-01-12T07:42:41Z day: '13' department: - _id: HeEd doi: 10.1145/1998196.1998224 language: - iso: eng main_file_link: - open_access: '1' url: https://hal.inria.fr/inria-00480031/file/RR-7274.pdf month: '06' oa: 1 oa_version: Published Version page: 179 - 186 publication_status: published publisher: ACM publist_id: '3307' quality_controlled: '1' scopus_import: 1 status: public title: A generic algebraic kernel for non linear geometric applications type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2011' ...