中文摘要：

为了改进参数曲线自由变形方法,构造了一种新的基于乘幂函数的伸缩因子,它不仅具有已有伸缩因子的特性,还具有区域峰值性,并且变形操作对Bézier曲线和NURBS曲线具有封闭性。在将伸缩因子作用于待变形曲线方程时,通过交互改变控制参数来控制曲线的形状,从而得到变形效果。实验结果表明,该方法计算简单、易于控制,可以得到丰富的变形效果,适用于几何造型、计算机动画等领域。

英文摘要：

A new power extension factor is constructed for improving free-form deformation of parametric curves.The new extension factor has the excellence of existed extension factors and can achieve its maximum in the region.The closure property can be kept in the deformations of Bézier and NURBS curves.The deformation of a curve is achieved through multiplying the equation of the curve by the extension factor.And by interactively modifying control parameters,the outside of object can be described well.Experiments show that the method is simple,intuitive and easy to control,and desired deformations can be easily achieved.The method can be used in many fields such as geometric modeling and computer animation.