Said-Bézier曲线的等距曲线的有理逼近

Rational Approximation of the Offset Curves of Said-Bézier Curves

等距曲线逼近的关键在于对其参数速度的逼近,给出了Said-Bézier曲线参数速度的Tchebyshev逼近和Tchebyshev-Padé逼近,在此基础上得到了Said-Bézier曲线的等距曲线的2种有理逼近函数.因为n次Said-Bézier曲线在参数K =[n/2]时,即为n次Bézier曲线,所以文中方法同样适用于Bézier曲线的等距曲线逼近.最后通过2个实例验证了这2种逼近方法,并与Legendre逼近方法进行了比较.

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