---
_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'
...