6533b7d8fe1ef96bd12699a9
RESEARCH PRODUCT
A Complete, Exact and Efficient Implementation for Computing the Edge-Adjacency Graph of an Arrangement of Quadrics
Michael HemmerLaurent DupontElmar SchömerSylvain Petitjeansubject
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_DISCRETEMATHEMATICSdescription
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 computes the mathematically correct result. It is efficient measured in running times, i.e. it compares favorably to the only previous implementation.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-04-01 |