A singly exponential stratification scheme for real semi-algebraic varieties and its applications
Theoretical Computer Science
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Polynomial real root isolation using approximate arithmetic
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Handbook of discrete and computational geometry
Computing the isolated roots by matrix methods
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Dynamic Trees and Dynamic Point Location
SIAM Journal on Computing
Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually!
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Improved construction of vertical decompositions of three-dimensional arrangements
Proceedings of the eighteenth annual symposium on Computational geometry
A Singly-Expenential Stratification Scheme for Real Semi-Algebraic Varieties and Its Applications
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Near-optimal parameterization of the intersection of quadrics
Proceedings of the nineteenth annual symposium on Computational geometry
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
Intersecting quadrics: an efficient and exact implementation
SCG '04 Proceedings of the twentieth 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
Intersecting quadrics: an efficient and exact implementation
Computational Geometry: Theory and Applications
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Near-optimal parameterization of the intersection of quadrics: I. The generic algorithm
Journal of Symbolic Computation
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Topology and arrangement computation of semi-algebraic planar curves
Computer Aided Geometric Design
Using signature sequences to classify intersection curves of two quadrics
Computer Aided Geometric Design
Computing a rational in between
ACM Communications in Computer Algebra
Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere
Computational Geometry: Theory and Applications
Computer Aided Geometric Design
Hi-index | 0.01 |
In this paper, we study a sweeping algorithm for computing the arrangement of a set of quadrics in R3. We define a "trapezoidal" decomposition in the sweeping plane, and we study the evolution of this subdivision during the sweep. A key point of this algorithm is the manipulation of algebraic numbers. In this perspective, we put a large emphasis on the use of algebraic tools, needed to compute the arrangement, including Sturm sequences and Rational Univariate Representation of the roots of a multivariate polynomial system.