四次有理Bézier曲线的形状调整

给出了一种基于权因子调整的四次Bézier 曲线形状控制的有效方法。推导出了曲线肩点的两种新的表达式。这两个表达式对曲线权因子的意义进行了较好的解释,很好地反应出权因子变化对曲线肩点位置的影响。基于这两个表达式,推导出了曲线肩点插值某固定点时各权因子的具体取值公式。最后,实例表明此方法能给曲线形状调整带来实用性指导。

The Shape Modification of Rational Quartic Bézier Curves

In this paper, a effective method of the shape control of rational quartic Bezier curves based on the weights modification was presented. The two kinds of new expression of the shoulder point of the curves was presented. It well explain the meaning of weights of rational quartic Bezier curves, and well respone the infection of the position of the houlder point of the curves while the weights change. Based on the two expression, the formations of computing weights are presented while the shoulder point of the curve interpolates a given point. At last an instance is provided which shows that the direction of shape modification of curves.