Detecting real singularities of a space curve from a real rational parametrization

DOI10.1016/j.jsc.2007.09.002zbMath1159.14036OpenAlexW2032353567MaRDI QIDQ1012138

J. Martínez

Publication date: 14 April 2009

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2007.09.002

zbMATH Keywords

singular pointsalgebraic curvesrational parametrizationsgeneralized resultants

Mathematics Subject Classification ID

Polynomials over commutative rings (13B25) Computational aspects of algebraic curves (14Q05) Singularities of curves, local rings (14H20) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (12)

The T-function of a parametric curve ⋮ \texttt{PTOPO}: computing the geometry and the topology of parametric curves ⋮ Projective and affine symmetries and equivalences of rational curves in arbitrary dimension ⋮ The limit point and the T-function ⋮ Factorization of complex analytic functions algebraically dependent on space curves and applications to compatible functional and differential equations ⋮ Topology of 2D and 3D rational curves ⋮ Computing the shapes arising in a family of space rational curves depending on one parameter ⋮ A new method to compute the singularities of offsets to rational plane curves ⋮ Analysis and construction of rational curve parametrizations with non-ordinary singularities ⋮ An in depth analysis, via resultants, of the singularities of a parametric curve ⋮ Certified approximation of parametric space curves with cubic \(B\)-spline curves ⋮ Computing the singularities of rational surfaces

Cites Work

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• On multivariate rational function decomposition
• Singular points of algebraic curves
• Plotting missing points and branches of real parametric curves
• Improperly parametrized rational curves
• Detecting cusps and inflection points in curves
• Identification of inflection points and cusps on rational curves
• Effective computation of singularities of parametric affine curves
• Polynomial algorithms in computer algebra
• Computation of the singularities of parametric plane curves
• The 𝐷-resultant, singularities and the degree of unfaithfulness
• $D$-resultant for rational functions

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