Using polynomial interpolation for implicitizing algebraic curves

Authors:
A. Marco;J. J. Martnez
Affiliations:
Departamento de Matemáticas, Universidad de Alcalá, Campus Universitario, 28871-Alcalá de Henares, Madrid, Spain;Departamento de Matemáticas, Universidad de Alcalá, Campus Universitario, 28871-Alcalá de Henares, Madrid, Spain
Venue:
Computer Aided Geometric Design
Year:
2001

Citing 4
Cited 8

Improperly parametrized rational curves

Computer Aided Geometric Design
Symbolic parametrization of curves

Journal of Symbolic Computation
Implicitizing rational curves by the method of moving algebraic curves

Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves

Computer Aided Geometric Design

Implicitization of rational surfaces by means of polynomial interpolation

Computer Aided Geometric Design
Partial degree formulae for rational algebraic surfaces

Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Implicitization of Parametric Curves via Lagrange Interpolation

Computing
Structured matrices in the application of bivariate interpolation to curve implicitization

Mathematics and Computers in Simulation
Bernstein-Bezoutian matrices and curve implicitization

Theoretical Computer Science
Real implicitization of curves and geometric extraneous components

Proceedings of the 2007 international workshop on Symbolic-numeric computation
Computation of the singularities of parametric plane curves

Journal of Symbolic Computation
Implicitization of rational curves

AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

A simple algorithm for finding the implicit equation of a rational plane algebraic curve given by its parametric equations is presented. The algorithm is based on an efficient computation of the resultant by means of classical bivariate polynomial interpolation. One of the main features of the used approach is the fact that it considerably reduces the problem of intermediate expression swell, which is usually present in many computer algebra algorithms.