The computation of polynomial greatest common divisors over an algebraic number field
Journal of Symbolic Computation
Oriented projective geometry
Computing GCDs of polynomials over algebraic number fields
Journal of Symbolic Computation
The Subresultant PRS Algorithm
ACM Transactions on Mathematical Software (TOMS)
The design and implementation of panar maps in CGAL
Journal of Experimental Algorithmics (JEA)
Local box adjacency algorithms for cylindrical algebraic decompositions
Journal of Symbolic Computation
Efficient Collision Detection for Curved Solid Objects
Proceedings of the seventh ACM symposium on Solid modeling and applications
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Applications of the Generic Programming Paradigm in the Design of CGAL
Selected Papers from the International Seminar on Generic Programming
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
On square-free decomposition algorithms
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Exact computation of the medial axis of a polyhedron
Computer Aided Geometric Design
Intersecting quadrics: an efficient and exact implementation
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Fast and exact geometric analysis of real algebraic plane curves
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Near-optimal parameterization of the intersection of quadrics: I. The generic algorithm
Journal of Symbolic Computation
Exact and efficient 2D-arrangements of arbitrary algebraic curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Exact geometric-topological analysis of algebraic surfaces
Proceedings of the twenty-fourth 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
A descartes algorithm for polynomials with bit-stream coefficients
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
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We present a complete, exact and efficient implementation to compute the edge-adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the edge-adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always computes the mathematically correct result. It is efficient measured in running times, i.e. it compares favorably to the only previous implementation.