A survey of the representations of rational ruled surfaces

DOI10.1007/s11424-020-0018-8zbMath1483.14106OpenAlexW3120388821MaRDI QIDQ2121177

Sonia Pérez-Díaz, Li-Yong Shen, Chun-Ming Yuan

Publication date: 1 April 2022

Published in: Journal of Systems Science and Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11424-020-0018-8

zbMATH Keywords

parametrizationcharacterizationimplicitizationbirational transformationreparametrizationrational ruled surface

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Computational aspects of algebraic surfaces (14Q10) Geometric aspects of numerical algebraic geometry (14Q65) Numerical algebraic geometry (65H14)

Uses Software

• CASA

Cites Work

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• Determination and (re)parametrization of rational developable surfaces
• Computing self-intersection curves of rational ruled surfaces
• Implicitization using univariate resultants
• Proper real reparametrization of rational ruled surfaces
• Collision and intersection detection of two ruled surfaces using bracket method
• Homeomorphic approximation of the intersection curve of two rational surfaces
• A computational study of ruled surfaces
• Implicitization of rational ruled surfaces with \(\mu \)-bases
• On a projection theorem of quasi-varieties in elimination theory
• Degree, multiplicity, and inversion formulas for rational surfaces using \(u\)-resultants
• On the parameterization of algebraic curves
• Implicitization of rational parametric equations
• Rational parametrizations of algebraic curves using a canonical divisor
• On the computational geometry of ruled surfaces.
• Revisiting the \(\mu\)-basis of a rational ruled surface.
• Computing \(\mu\)-bases from algebraic ruled surfaces
• Implicitizing ruled translational surfaces
• Special curves and ruled surfaces
• Ruled invariants and associated ruled surfaces of a space curve
• A symbolic-numeric approach for parametrizing ruled surfaces
• Characterization of rational ruled surfaces
• Affine equivalences, isometries and symmetries of ruled rational surfaces
• On the computation of singularities of parametrized ruled surfaces
• Reparametrization of a rational ruled surface using the \(\mu\)-basis
• The \(\mu \)-basis and implicitization of a rational parametric surface
• A univariate resultant-based implicitization algorithm for surfaces
• On the problem of proper reparametrization for rational curves and surfaces
• Computing μ-bases of rational curves and surfaces using polynomial matrix factorization
• Covering rational ruled surfaces
• Computational line geometry
• Implicitization and parametrization of nonsingular cubic surfaces

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