关键词: 参数曲线, 伸缩因子, 自由变形

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