一类控制多边形及其三次Bézier曲线之间的关系
On the Relationship of Shapes between a Class of Control Polygons and Their Cubic Bézier Curves
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摘要: 文章对一类控制多边形及其三次Bézier曲线形状之间的关系进行研究,根据控制多边形的边长情况分别给出其对应的三次Bézier曲线含有尖点、重点以及两个拐点的充分必要条件,并举例说明构造含有奇异点(拐点,尖点和重点)的三次Bézier曲线的方法.Abstract: In this paper,the relationship of shapes between a class of control polygons and their cubic Bézier curves are studied.The necessary and sufficient conditions for cups,loops and inflection points of the cubic Bézier curves are given according to the side length of the control polygons respectively.The method of building Bézier curves with singularities(inflection point,cusp and loop) is illustrated via an example.
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