A direct approach to computing the \(\mu\)-basis of planar rational curves

DOI10.1006/jsco.2001.0437zbMath0978.65008OpenAlexW2055431849MaRDI QIDQ5938549

Thomas W. Sederberg, Jianmin Zheng

Publication date: 22 July 2001

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/4b8cb90d8d66c661071a28a7ff132a71333f4e6f

zbMATH Keywords

algorithmcomputational complexitynumerical exampleparametrizationGröbner basesimplicitization\(\mu\)-basisconic sectionplanar rational curves

Mathematics Subject Classification ID

Rational points (14G05) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Complexity and performance of numerical algorithms (65Y20)

Related Items (17)

Implicitizing rational surfaces using moving quadrics constructed from moving planes ⋮ An improved algorithm for constructing moving quadrics from moving planes ⋮ A new algorithm for designing developable Bézier surfaces ⋮ Algebraic distance estimations for enriched isogeometric analysis ⋮ Computing \(\mu\)-bases of univariate polynomial matrices using polynomial matrix factorization ⋮ Survey on the theory and applications of \(\mu\)-bases for rational curves and surfaces ⋮ Approximate GCD of several univariate polynomials with small degree perturbations ⋮ Matrix-based implicit representations of rational algebraic curves and applications ⋮ Algorithm for computing \(\mu\)-bases of univariate polynomials ⋮ The \(\mu \)-basis and implicitization of a rational parametric surface ⋮ The moving curve ideal and the Rees algebra ⋮ The \(\mu\)-basis of a rational ruled surface ⋮ Inversion, degree, reparametrization and implicitization of improperly parametrized planar curves using \(\mu \)-basis ⋮ Division algorithms for Bernstein polynomials ⋮ A computational study of ruled surfaces ⋮ On the Structure of μ-Classes ⋮ A new implicit representation of a planar rational curve with high order singularity

Cites Work

• An implicitization algorithm with fewer variables
• The Cayley method in computer aided geometric design
• Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves
• Automatic parameterization of rational curves and surfaces. III: Algebraic plane curves
• Symbolic parametrization of curves
• Implicitization of rational parametric equations
• The moving line ideal basis of planar rational curves
• Implicitization of parametric curves and surfaces by using multidimensional Newton formulae
• Implicitizing rational curves by the method of moving algebraic curves
• Curve implicitization using moving lines
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