To gain ideal geometric deformation results, the expansion factor and the toric degeneration are applied to the toric-Bézier curve, realizing the free-form deformation of the curve. Firstly, the with parameter t weight factor was constructed by the given lifting function, thereby obtaining the with parameter t toric-Bézier curve. Secondly, according to the selected center of deformation, region of deformation, smoothness of deformation region boundary, and select rule of the control function f (t), the appropriate control function was selected, and the extension factor was determined, thus constructing the deformation matrix. Then, the deformation matrix acted on the with parameter t toric-Bézier curve. At last, when t tended to reach infinity, the target curve was obtained, and the free-form deformation of the toric-Bézier curve could be achieved. By changing the control parameters interactively, the expected deformation result could be attained, and the deformation animation demo of the toric-Bézier curve could be yielded. The experiments showed that the technique was simple and easy to control. The curve could be deformed freely both globally and locally, and the technique was of adjustability and foreseeability. Such a technique could be in repeated use, thereby generating the rich deformation animation results, which could be applicable to many fields, such as geometric modeling and computer animation. 

">  , geometric modeling, toric-Bézier curve, lifting function, extension factor, free-form deformation ,