用割角多边形产生Bernstein-Bézier曲线的更小包围域

Smaller bounding region of Bernstein-Bézier curve generated by its corner-cutting polygon

基于Bézier曲线的控制多边形，介绍了割角多边形的概念．割角多边形的顶点可以由控制多边形的顶点快速递推得到，其几何意义是对控制多边形进行一系列的中点割角过程．进而提出了利用割角多边形来逼近Bern—stein-Bézier多项式曲线的新方法．当Bernstein-Bézier多项式曲线的次数为4～8时，分别导出了利用割角多边形逼近多项式曲线的精确界，此界值比利用控制多边形和拟控制多边形逼近Bernstein-Bézier多项式曲线所得的界值大为减小，极大地缩小了曲线的包围域，显著提高了逼近精度，节省了计算时间．

A new concept called corner-cutting polygon was introduced based on the control polygon of Bézier curve. The vertices of corner-cutting polygon can be deduced quickly from the vertices of control polygon, and the geometric meaning is that corner-cutting polygon can be produced quickly from control polygon by using central subdivision algorithm. Furthermore, a new method of approximating Bernstein- Bézier polynomial curve using its corner-cutting polygon was proposed. The sharp bounds to approximate Bernstein-Bézier polynomial curves of degree 4- 8 by using the corner-cutting polygons were derived, which were greatly less than the bounds obtained by using the control polygons and the quasi polygons. Thus the bounding regions of the curves were greatly reduced. The method can obviously improve approximating precision and save computing time.