Intersecting quadrics: an efficient and exact implementation

DOI10.1016/j.comgeo.2005.10.004zbMath1103.65021OpenAlexW2210410641MaRDI QIDQ2507161

Luis Mariano Peñaranda, Sylvain Petitjean, Sylvain Lazard

Publication date: 10 October 2006

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

Full work available at URL: https://hal.inria.fr/inria-00104003/file/SoCG_final.pdf

zbMATH Keywords

quadricsimplementationgraphical examplesintersection of surfacescurve parameterizationpencils

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items (9)

Computing the Voronoi cells of planes, spheres and cylinders in \(\mathbb{R}^3\) ⋮ Topological classification of the intersection curves of two quadrics using a set of discriminants ⋮ Computing the intersections of three conics according to their Jacobian curve ⋮ Near-optimal parameterization of the intersection of quadrics. I. The generic algorithm ⋮ Near-optimal parameterization of the intersection of quadrics. II. A classification of pencils ⋮ Near-optimal parameterization of the intersection of quadrics. III. Parameterizing singular intersections ⋮ Enumerating the morphologies of non-degenerate Darboux cyclides ⋮ Tools for analyzing the intersection curve between two quadrics through projection and lifting ⋮ New properties about the intersection of rotational quadratic surfaces and their applications in architecture

Uses Software

• Surf
• ISOLATE
• ESOLID

Cites Work

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• On the computation of an arrangement of quadrics in 3D
• Simultaneous block diagonalization of two real symmetric matrices
• Quadric-surface intersection curves: Shape and structure
• Efficient isolation of polynomial's real roots.
• Enhancing Levin's method for computing quadric-surface intersections
• Automatic parsing of degenerate quadric-surface intersections
• A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
• Computing quadric surface intersections based on an analysis of plane cubic curves
• ON THE DISTANCE BETWEEN ROOTS OF INTEGER POLYNOMIALS
• The computational geometry algorithms library CGAL
• Computing a 3-dimensional cell in an arrangement of quadrics
• Near-optimal parameterization of the intersection of quadrics
• An exact, complete and efficient implementation for computing planar maps of quadric intersection curves

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