一类含任意参量的B样条型三次参数曲线

构造了一类含四个参量的B样条型三次参数曲线,它以三次Hermite曲线、Ball曲线、Bezier曲线、Timmer曲线和B样条曲线为其特例。本文还给出了曲线与其特征多边形各边相切的条件。通过调整曲线的四个参量便可改变曲线的形状(包括端点位置、凸向及弯曲程度等)以满足实际需要。

A CLASS OF CUBIC PARAMETER CURVES OF B-SPLINE TYPE WITH ARBITRARY PARAMETER

A class of cubic parameter curve of B-spline type is constructed in this paper with four arbitrary parameters, the cubic Hermite curve, Ball curve, Bezier curve, Timmer curve and B-spline curve as its special cases. The condition in which the curves contact with each edge of characteristic polygon is also given. In order to satisfy the actual riquirements,the shape(i. e. location of end point,direction of convixity and flexion,etc. )of curves can be modified by adjusting the four parameters.