Abstract: The technique of free-form deformation for parametric surfaces by extension factor is improved.A new extension factor on convex polygon region is introduced and an operator matrix is constructed.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，CAD/CAM.

Key words: parametric surface, extension factor, free-form deformation, polygon region

摘要： 为了改进参数曲面自由变形方法，构造了凸多边形域上的伸缩因子函数，它具有已往文献所引入的伸缩因子的特性。可使用新的伸缩因子去作用待变形曲面的参数方程，从而使曲面发生形变。可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不规则实体的外型。实验表明，该方法的数学背景简单、易于控制、重复使用可以达到获得丰富变形效果的目的。可用于几何造型、计算机动画以及CAD/CAM等领域。

关键词: 参数曲线, 伸缩因子, 自由变形, 凸多边形域