用五次Pythagorean-Hodograph样条曲线构造三次B样条曲线等距线

Constructing offset to cubic B-spline curve by quintic Pythagorean-Hodograph spline curve

提出了一种三次B样条曲线等距线生成的算法.研究用C1连续的五次Pythagorean-Hodograph样条曲线逼近一给定的三次Bézier曲线,证明了这种逼近算法在常用误差测度下的收敛性.然后,生成该PH样条曲线的精确有理形式的等距线,该等距线可作为原Bézier曲线的逼近等距线.估计了PH样条曲线与Bézier曲线的逼近误差以及对应等距线误差.用Boehm定理把B样条曲线转化为多段Bézier曲线,从而得到其等距线.

A new algorithm for offset to cubic B-spline curve is proposed. Firstly, a quintic PH-spline curve is used to approximate a cubic Bézier curve within a bound. The convergence for the approximation is proved. Then, render the offset to the PH-spline curve which can be regarded as the offset to Bézier curve. The errors between the PH-spline and the cubic Bézier curve,the offset to PH-spline and the offset to cubic Bézier curve are also estimated. Thus offset to a cubic B-spline can be constructed.