摘要
Bézier曲线的正则性,完全由它的控制顶点决定.理想的情况是由Bézier曲线的控制顶点的几何关系,就可以判断它的正则性.本文由Bézier曲线的导矢曲线在[0,1]不等于零这些代数条件,推导出了与之等价的Bézier曲线的控制顶点之间的几何关系,即只需知道顶点之间的相对位置或计算相邻线段的斜率就可快速判断Bézier曲线的正则性.最后给出了数值例子.
The regularity of Bézier curve is determined by its control points. Perfect situation is that we can determine the regularity of Bézier curve according to the geometry relation of control points. In this paper, we get geometry relation between the points of Bézier curves by its derivative curves which is not equal to zero during the interval 0 and 1, we only need to know the opposite location of control points or compute the slopes of bordered lines, then we can determine the regularity of Bézier curve quickly. There is no need to determine whether the origin is on the derivative curve. Some numerical examples are given.
出处
《大学数学》
北大核心
2007年第5期79-83,共5页
College Mathematics
