一类C^3-连续的B-型样条曲线及其插值与逼近性

A CLASS OF C3-CONTINUOUS B-TYPE SPLINE CURVE AND ITS INTERPOLATION AND APPROXIMATION

本文提出一类Ｃ３－连续的带有因子的Ｂ－型参数样条曲线，它的每一段只要四个 控制点就能生成，可用它直接插值或逼近于任意控制点或对控制边多边形作局部或整体逼 近。利用因子间的某些关系可将其次数降到最低．与普通的四次Ｂ－样条曲线相比，这类 曲线更加方便灵活。

This paper presents a class of C3-continuous B-type parametric spline curves with factors. Each segment of the curve is only generated by four consecutive control points. It can directly interpolate or approximate to any control points and locally or globally approximate the control polygon. By using some relations among the factors, the segment's degree can be decreased to the lowest. Our curve is more convenient and fiexible than common quartic B-spline curve.