Free-Form Deformation Based on Extension Factor for Parametric Curve

A new technique of free-form deformation for parametric curve by the so-called extension factor is presented. First, a special extension factor is introduced and an operator matrix is constructed. Then the original curves are deformed through multiplying by the operator matrix or adding the multiplication of some vector field by the operator matrix. Interactively modifying control parameters, ideal deformation effect can be got. The implementation shows that the method is simple, intuitive and easy to control. It can be used in many fields such as geometric modeling and computer animation.