A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
On the design of CGAL a computational geometry algorithms library
Software—Practice & Experience - Special issue on discrete algorithm engineering
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Some inequalities about univariate polynomials
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Efficient isolation of polynomial's real roots
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Towards and open curved kernel
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
An exact, complete and efficient computation of arrangements of Bézier curves
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Fast and exact geometric analysis of real algebraic plane curves
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Classroom examples of robustness problems in geometric computations
Computational Geometry: Theory and Applications
Exact and efficient 2D-arrangements of arbitrary algebraic curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Exact arrangements on tori and Dupin cyclides
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Univariate Algebraic Kernel and Application to Arrangements
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
Experimental evaluation and cross-benchmarking of univariate real solvers
Proceedings of the 2009 conference on Symbolic numeric computation
An efficient algorithm for the stratification and triangulation of an algebraic surface
Computational Geometry: Theory and Applications
Visualizing Arcs of Implicit Algebraic Curves, Exactly and Fast
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Sweeping and maintaining two-dimensional arrangements on surfaces: a first step
ESA'07 Proceedings of the 15th annual European conference on Algorithms
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
EXACUS: efficient and exact algorithms for curves and surfaces
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Motion planning via manifold samples
ESA'11 Proceedings of the 19th European conference on Algorithms
A worst-case bound for topology computation of algebraic curves
Journal of Symbolic Computation
Arrangement computation for planar algebraic curves
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Lines through segments in 3d space
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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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