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Implicitization of Parametric Curves via Lagrange Interpolation

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Abstract

A simple algorithm for finding the implicit equation of a parametric plane curve given by its parametric equations is presented. The algorithm is based on an efficient computation of the Bézout resultant and Lagrange interpolation. One of main features of our approach is the fact that it considerably reduces the problem of computing intermediate expressions.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, School of Sciences, Beijing University of Chemical Technology, Beijing, 100029, P.R. China

    Yongli Sun

  2. Department of Mathematics and Mechanization, School of Applied Sciences, University of Science and Technology Beijing, Beijing, 100083, P.R. China

    Jianping Yu

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  1. Yongli Sun
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  2. Jianping Yu
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Correspondence to Yongli Sun.

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Sun, Y., Yu, J. Implicitization of Parametric Curves via Lagrange Interpolation. Computing 77, 379–386 (2006). https://doi.org/10.1007/s00607-006-0163-5

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  • DOI: https://doi.org/10.1007/s00607-006-0163-5

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