Volume 17, Issue 1
Verifying the Implicitization Formulae for Degree N Rational Bézier Curves

Guo-Jin Wang & T. W. Sederberg

J. Comp. Math., 17 (1999), pp. 33-40.

Published online: 1999-02

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  • Abstract

This is a continuation of short communication$^{[1]}$. In [1] a verification of the implicitization equation for degree two rational Bézier curves is presented which does not require the use of resultants. This paper presents these verifications in the general cases, i.e., for degree $n$ rational Bézier curves. Thus some interesting interplay between the structure of the $n × n$ implicitization matrix and the de Casteljau algorithm is revealed.

  • Keywords

Rational Bézier curve, Implicitization, Resultant, de Casteljau algorithm.

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COPYRIGHT: © Global Science Press

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@Article{JCM-17-33, author = {Wang , Guo-Jin and Sederberg , T. W.}, title = {Verifying the Implicitization Formulae for Degree N Rational Bézier Curves}, journal = {Journal of Computational Mathematics}, year = {1999}, volume = {17}, number = {1}, pages = {33--40}, abstract = {

This is a continuation of short communication$^{[1]}$. In [1] a verification of the implicitization equation for degree two rational Bézier curves is presented which does not require the use of resultants. This paper presents these verifications in the general cases, i.e., for degree $n$ rational Bézier curves. Thus some interesting interplay between the structure of the $n × n$ implicitization matrix and the de Casteljau algorithm is revealed.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9080.html} }
TY - JOUR T1 - Verifying the Implicitization Formulae for Degree N Rational Bézier Curves AU - Wang , Guo-Jin AU - Sederberg , T. W. JO - Journal of Computational Mathematics VL - 1 SP - 33 EP - 40 PY - 1999 DA - 1999/02 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9080.html KW - Rational Bézier curve, Implicitization, Resultant, de Casteljau algorithm. AB -

This is a continuation of short communication$^{[1]}$. In [1] a verification of the implicitization equation for degree two rational Bézier curves is presented which does not require the use of resultants. This paper presents these verifications in the general cases, i.e., for degree $n$ rational Bézier curves. Thus some interesting interplay between the structure of the $n × n$ implicitization matrix and the de Casteljau algorithm is revealed.

Guo-Jin Wang & T.W. Sederberg. (1970). Verifying the Implicitization Formulae for Degree N Rational Bézier Curves. Journal of Computational Mathematics. 17 (1). 33-40. doi:
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