带形状参数的C~2连续类三次三角样条曲线

传统的三次均匀B样条曲线在给定控制顶点时其形状不能调整,以及不能精确表示圆锥曲线。针对三次均匀B样条曲线的不足,提出了一种带形状参数的C2连续的类三次三角样条曲线。该曲线不仅与三次均匀B样条曲线具有相似的性质,而且在控制顶点保持不变时其形状可通过形状参数的取值进行调整。在适当条件下,类三次三角样条曲线比三次均匀B样条曲线更能逼近于控制多边形,且能精确表示圆、椭圆、抛物线等圆锥曲线。

C~2 continuous quasi-cubic trigonometric spline curve with shape parameter

The shape of the normal cubic uniform B-spline is fixed when the control points are given. And the cubic uniform B-spline can not describe the quadratic curves accurately. For these reasons, a kind of C2 continuous quasi-cubic trigonometric spline curve is presented. The curve inherits the major advantages of the cubic uniform B-spline curve, and the shape can be adjusted by using the shape parameter when the control points are fixed. Furthermore, in proper conditions, the curve approximates to the control polygon closer than cubic uniform B-spline, and the curves can also be used to precisely represent quadratic curves, such as circular, ellipse, parabola arcs.