0000000000311466

AUTHOR

Sylvain Petitjean

showing 2 related works from this author

A Complete, Exact and Efficient Implementation for Computing the Edge-Adjacency Graph of an Arrangement of Quadrics

2011

International audience; 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 comp…

pencils of quadricsIntersection curveComputation010103 numerical & computational mathematics02 engineering and technology[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]01 natural sciencesInterval arithmeticCombinatorics0202 electrical engineering electronic engineering information engineering0101 mathematicsAlgebraic numberMathematicsDiscrete mathematics[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC]Algebra and Number TheoryImplicit functionDegenerate energy levels020207 software engineeringComputational Mathematicsintersection of surfacesAdjacency listcurve parameterizationGravitational singularityArrangementquadricsMathematicsofComputing_DISCRETEMATHEMATICS
researchProduct

Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangement of Quadrics

2007

The original publication is available at www.springerlink.com ; ISBN 978-3-540-75519-7 ; ISSN 0302-9743 (Print) 1611-3349 (Online); International audience; We present a complete, exact and efficient implementation to compute the adjacency graph of an arrangement of quadrics, \ie 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 adjacency graph of the arrangement. Our implementation is {\em complete} in the sense that it can handle all kinds of…

Discrete mathematicsDegree (graph theory)ComputationDegenerate energy levelsACM: I.: Computing Methodologies/I.1: SYMBOLIC AND ALGEBRAIC MANIPULATION/I.1.2: Algorithms/I.1.2.0: Algebraic algorithms020207 software engineering010103 numerical & computational mathematics02 engineering and technology[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]01 natural sciencesACM: G.: Mathematics of Computing/G.4: MATHEMATICAL SOFTWARE/G.4.3: EfficiencyCombinatoricsIntersection0202 electrical engineering electronic engineering information engineeringGraph (abstract data type)Adjacency listGravitational singularity0101 mathematicsAlgebraic numberACM: G.: Mathematics of Computing/G.4: MATHEMATICAL SOFTWARE/G.4.0: Algorithm design and analysisMathematics
researchProduct