两类特殊三次空间Bézier曲线的挠率特征分析

Analysis on Torsion Characteristics of Two Kinds of Special Cubic-spatial Bézier Curves

空间Bézier曲线的挠率在几何造型中被广泛应用.文中利用笛卡尔符号法则讨论了两种特殊三次空间Bézier曲线的挠率单调性问题,最后得出当空间三次Bézier曲线的控制边相等且中间控制边和相邻两控制边的夹角相等时,挠率仅有一个极小值;而当两夹角相等但控制边长成等差数列时,文中给出了挠率单调及极值存在的充分条件.

The torsion of the spatial Bézier curve is widely used in geometrical modelling. In this paper, we mainly discuss the torsion monotonicity problem of two special cubic Bézier curves by use of Descartes’ rule of signs. Based on the study, it is concluded that when the control sides are of equal length and the angles between two adjacent control sides are equal, the only minimum of torsion is always available; and in the case that the two angles are equal while the control side lengths are in arithmetic progression, the sufficient conditions can be determined for the torsion monotony and the existence of extremum.