一类有理交错样条曲线的逼近性及形状修改

APPROXIMATION AND MODIFYING SHAPE OF A CLASS OF RATIONAL ALTERNATE SPLINE CURVES

本文提出一类Ｃ２连续的四阶有理交错样条曲线，它能整体或局部逼近于控制多边形．

In CAGD, free-form curves and surfaces are main object of study, their shapes frequently need to be modified. A class of 4-order rational alternate spline curves with a parameter ε and weights {ω_i} is presented in this paper. They have continuous second derivatives vectors. By varying the parameter ε or weights {ω_i}, the curves can entirely or locally approximate their control polygon. Therefore, they provide a convenient and flexibly way for modifying shape,