Rational Approximation of the Offset Curves of Said-Bézier Curves

Parametric speed approximation is crucial to the approximation of offset curves.Both the Tchebyshev approximation and the Tchebyshev-Padéapproximation of parametric speed of Said-Bézier curves are presented and two rational approximation functions of the offset curves of Said-Bézier curves are also obtained.Since Said-Bézier curve of degree n reduces to Bézier curve of degree n in the case of K=n/2,the proposed methods are also applicable to Bézier curves.Two examples are given to show the effectiveness of these two methods,and the results are compared with Legendre approximation.