On the computation of an arrangement of quadrics in 3D

DOI10.1016/j.comgeo.2004.05.003zbMath1063.65018OpenAlexW2065117466MaRDI QIDQ705551

Jean-Pierre Técourt, Monique Teillaud, Mourrain, Bernard

Publication date: 31 January 2005

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.comgeo.2004.05.003

zbMATH Keywords

Sturm sequencesAlgebraic numberSubdivisionComputer aided geometric designArrangementCertified computationImplicit surfaceMultivariate polynomial systemQuadricRational univariate representationSweeping algorithm

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Computer-aided design (modeling of curves and surfaces) (65D17) Algorithms with automatic result verification (65G20)

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Uses Software

• ISOLATE

Cites Work

• On the complexity of isolating real roots and computing with certainty the topological degree
• A singly exponential stratification scheme for real semi-algebraic varieties and its applications
• Computing the isolated roots by matrix methods
• Solving zero-dimensional systems through the rational univariate representation
• Efficient isolation of polynomial's real roots.
• Dynamic Trees and Dynamic Point Location
• Improved construction of vertical decompositions of three-dimensional arrangements
• Infimaximal Frames: A Technique for Making Lines Look Like Segments
• Computing a 3-dimensional cell in an arrangement of quadrics
• Near-optimal parameterization of the intersection of quadrics
• Complete, exact, and efficient computations with cubic curves
• Intersecting quadrics
• Algorithms in real algebraic geometry
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