中文摘要：

为得到理想的参数曲面造型效果,构造了一种新的基于多项式的伸缩因子,它不仅具有已有伸缩因子的特性,还具有区域峰值性;同时,扩展了参数曲面自由变形方法,将变形区域由圆域推广至四边域。在将伸缩因子作用于待变形曲面方程时,通过交互改变控制参数来控制曲面的形状,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、CAD/CAM等领域。

英文摘要：

In order to obtain ideal modeling effectiveness of parametric surfaces,a new polynomial extension factor was constructed.The new extension factor had the excellence of the existing extension factors,and can achieve its maximum in the region.In the extended technique for free-form deformation of parametric surfaces,the original surface can be deformed at four-sided region.The deformation of a surface was achieved through multiplying the equation of the surface by the extension factor.And 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.It can be used in many fields such as geometric modeling,computer animation and CAD/CAM.