Implicitization and parametrization of nonsingular cubic surfaces

DOI10.1016/S0167-8396(01)00048-6zbMath0983.68221OpenAlexW2106148210MaRDI QIDQ5958639

Thomas G. Berry, Richard R. Patterson

Publication date: 3 March 2002

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-8396(01)00048-6

zbMATH Keywords

parametrizationimplicitizationcubic surfaces

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

Related Items (12)

A survey of the representations of rational ruled surfaces ⋮ Computing \(\mu\)-bases from algebraic ruled surfaces ⋮ Implicitization and parametrization of quadratic and cubic surfaces by \(\mu\)-bases ⋮ Parameterization of rational translational surfaces ⋮ A remark on parameterizing nonsingular cubic surfaces ⋮ Geometric information and rational parametrization of nonsingular cubic blending surfaces ⋮ Numerical stability of surface implicitization ⋮ Local parametrization of cubic surfaces ⋮ Characterization of rational ruled surfaces ⋮ Basic lines, axes and geometric modeling on implicit algebraic surfaces ⋮ Universal parametrization and interpolation on cubic surfaces ⋮ Determination and (re)parametrization of rational developable surfaces

Cites Work

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• Degree, multiplicity, and inversion formulas for rational surfaces using \(u\)-resultants
• Implicit representation of rational parametric surfaces
• The geometry of some special arithmetic quotients
• Implicitization, inversion, and intersection of planar rational cubic curves
• Curve implicitization using moving lines

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