Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
Computational geometry: an introduction
Computational geometry: an introduction
There is no “Uspensky's method.”
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
The complexity of robot motion planning
The complexity of robot motion planning
Elements of computer algebra with applications
Elements of computer algebra with applications
Singular points of algebraic curves
Journal of Symbolic Computation
Mathematics for computer algebra
Mathematics for computer algebra
Algorithms for computer algebra
Algorithms for computer algebra
Algorithm-oriented generic libraries
Software—Practice & Experience
A course in computational algebraic number theory
A course in computational algebraic number theory
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
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Handbook of discrete and computational geometry
Computational geometry software
Handbook of discrete and computational geometry
Generic programming and the STL: using and extending the C++ Standard Template Library
Generic programming and the STL: using and extending the C++ Standard Template Library
Sign determination in residue number systems
Theoretical Computer Science - Special issue on real numbers and computers
Elementary geometry of algebraic curves: an undergraduate introduction
Elementary geometry of algebraic curves: an undergraduate introduction
Modern computer algebra
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
MAPC: a library for efficient and exact manipulation of algebraic points and curves
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
On the Bézout construction of the resultant
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
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
New structure theorem for subresultants
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
The Subresultant PRS Algorithm
ACM Transactions on Mathematical Software (TOMS)
On the design of CGAL a computational geometry algorithms library
Software—Practice & Experience - Special issue on discrete algorithm engineering
A new constructive root bound for algebraic expressions
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Sylvester—Habicht sequences and fast Cauchy index computation
Journal of Symbolic Computation
The design and implementation of panar maps in CGAL
Journal of Experimental Algorithmics (JEA)
Computational Discrete Mathematics
Rasterizing Algebraic Curves and Surfaces
IEEE Computer Graphics and Applications
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
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
Comparison of interval methods for plotting algebraic curves
Computer Aided Geometric Design
Theoretical Computer Science - Latin American theoretical informatics
An elementary approach to subresultants theory
Journal of Symbolic Computation
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third 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
Complete, exact, and efficient computations with cubic curves
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
Various New Expressions for Subresultants and Their Applications
Applicable Algebra in Engineering, Communication and Computing
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
EXACUS: efficient and exact algorithms for curves and surfaces
ESA'05 Proceedings of the 13th annual European conference on Algorithms
The diamond operator: implementation of exact real algebraic numbers
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Precise vector textures for real-time 3D rendering
Proceedings of the 2008 symposium on Interactive 3D graphics and games
Exact and efficient 2D-arrangements of arbitrary algebraic curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Topology of real algebraic space curves
Journal of Symbolic Computation
Improving the topology computation of an arrangement of cubics
Computational Geometry: Theory and Applications
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The Bentley-Ottmann sweep-line method can compute the arrangement of planar curves, provided a number of geometric primitives operating on the curves are available. We discuss the reduction of the primitives to the analysis of curves and curve pairs, and describe efficient realizations of these analyses for planar algebraic curves of degree three or less. We obtain a complete, exact, and efficient algorithm for computing arrangements of cubic curves. Special cases of cubic curves are conics as well as implicitized cubic splines and Bézier curves.The algorithm is complete in that it handles all possible degeneracies such as tangential intersections and singularities. It is exact in that it provides the mathematically correct result. It is efficient in that it can handle hundreds of curves with a quarter million of segments in the final arrangement. The algorithm has been implemented in C++ as an EXACUS library called CUBIX.