Abstract: The technique of free-form deformation for parametric surfaces by so called extension factor is improved.Firstly，a new extension factor is introduced and an operator matrix is constructed.The new extension factor not only has the excellence of the existed extension factors，but also can achieve its maximum in the region.So it can improve the imperfections of the existed extension factors which achieve the maximum in one point.Then the original surface is deformed through multiplying by the operator matrix or adding the multiplication of some vector field by the operator matrix.Interactively modifying control parameters，the outside of object can be described well.The implementation shows that the method is simple，intuitive and easy to control.It can be used in many fields such as geometric modeling，computer animation and CAD/CAM.

Key words: parametric curve, free-form deformation, extension factor

摘要： 为了改进参数曲面自由变形方法，构造了一种新的伸缩因子函数，它不仅具有以往文献所引入的伸缩因子的特性，还可以在区域上达到峰值，从而克服现有的伸缩因子仅在一点达到峰值的不足。使用新的伸缩因子去作用待变形的曲面方程，从而使曲面发生形变，通过交互改变控制参数来控制曲面的形状，使其能够更好地表示一些实体的外型。实验表明，该方法数学背景简单，易于控制，重复使用可获得丰富的变形效果。适用于几何造型、计算机动画、CAD/CAM等领域。

关键词: 参数曲线, 伸缩因子, 自由变形