Verifying the Implicitization Formulae for Degree N Rational Bézier Curves

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.