Computer algebra: symbolic and algebraic computation (2nd ed.)
Computational geometry: an introduction
Computational geometry: an introduction
The complexity of robot motion planning
The complexity of robot motion planning
Algorithms for computer algebra
Algorithms for computer algebra
An efficient method for analyzing the topology of plane real algebraic curves
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Elementary geometry of algebraic curves: an undergraduate introduction
Elementary geometry of algebraic curves: an undergraduate introduction
Modern computer algebra
MAPC: a library for efficient and exact manipulation of algebraic points and curves
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Algebraic methods and arithmetic filtering for exact predicates on circle arcs
Proceedings of the sixteenth annual symposium on Computational geometry
Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually!
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
The design and implementation of panar maps in CGAL
Journal of Experimental Algorithmics (JEA)
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
High-Level Filtering for Arrangements of Conic Arcs
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Computations with Algebraic Curves
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Towards and open curved kernel
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Towards and open curved kernel
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On the computation of an arrangement of quadrics in 3D
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
An exact and efficient approach for computing a cell in an arrangement of quadrics
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
An approximate arrangement algorithm for semi-algebraic curves
Proceedings of the twenty-second annual symposium on Computational geometry
Exact, efficient, and complete arrangement computation for cubic curves
Computational Geometry: Theory and Applications
An exact, complete and efficient computation of arrangements of Bézier curves
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Advanced programming techniques applied to Cgal's arrangement package
Computational Geometry: Theory and Applications
Real algebraic numbers and polynomial systems of small degree
Theoretical Computer Science
Proceedings of the twenty-fifth annual symposium on Computational geometry
On the computation of an arrangement of quadrics in 3D
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
An exact and efficient approach for computing a cell in an arrangement of quadrics
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
Exact, efficient, and complete arrangement computation for cubic curves
Computational Geometry: Theory and Applications
EXACUS: efficient and exact algorithms for curves and surfaces
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Non-local isotopic approximation of nonsingular surfaces
Computer-Aided Design
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The Bentley-Ottmann sweep-line method can be used to compute thearrangement of planar curves provided a number of geometricprimitives operating on the curves are available. We discuss themathematics of the primitives for planar algebraic curves of degreethree or less and derive efficient realizations. As a result, weobtain a complete, exact, and efficient algorithm for computingarrangements of cubic curves. Conics and cubic splines are specialcases of cubic curves. The algorithm is complete in that it handles all possibledegeneracies including singularities. It is exact in that itprovides the mathematically correct result. It is efficient in thatit can handle hundreds of curves with a quarter million of segmentsin the final arrangement.