Using polynomial interpolation for implicitizing algebraic curves

DOI10.1016/S0167-8396(01)00033-4zbMath0971.68178MaRDI QIDQ5941146

Ana Marco, José-Javier Martıńez

Publication date: 20 August 2001

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

zbMATH Keywords

interpolationcurveimplicitizationresultant

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

Related Items (11)

Implicitization of parametric curves via Lagrange interpolation ⋮ Parallel computation of determinants of matrices with polynomial entries ⋮ A simple method for implicitizing rational curves and surfaces ⋮ Computing curve intersection by means of simultaneous iterations ⋮ Structured matrices in the application of bivariate interpolation to curve implicitization ⋮ Bernstein-Bezoutian matrices and curve implicitization ⋮ Computation of the singularities of parametric plane curves ⋮ Fast computation of determinants of Bézout matrices and application to curve implicitization ⋮ A hybrid method for computing the intersection and tangency points of plane curves ⋮ An effective algorithm of computing symbolic determinants with multivariate polynomial entries ⋮ Implicitization of rational surfaces by means of polynomial interpolation

Cites Work

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• Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves
• Improperly parametrized rational curves
• Symbolic parametrization of curves
• Implicitizing rational curves by the method of moving algebraic curves
• Polynomial algorithms in computer algebra
• A generalized Kronecker product and linear systems
• Solution of Vandermonde systems of equations

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