一种新的自由变形方法及其建模研究

自由变形技术（ Ｆ Ｆ Ｄ）正在发展为 Ｃ Ａ Ｄ系统中一种新的几何造型方法。本文提出基于 Ｂ样条的自由变形方法，该方法具有变形函数的连续阶可调，变形网格疏密程度可调，变形速度快，既可全局变形又可局部变形的优点。并提出基于 Ｂ样条的自由变形方法的一种新的建模思想，该技术可以模拟现实中物体因某一外因所产生的变形，在雕塑曲面变形及对物体进行受力分析等方面的初步应用考核中，证明了该方法的优越性。

A New FFD(Free Form Deformation) Method for CAGD

Existing FFD methods have tried to solve problems encountered in CAGD without achieving much success because, in our opinion, their thinking is limited to computer science. We propose a new method that draws on the concept of continuity in theory of elasticity and allows the designer to do geometric modeling intuitively and more easily. The concept of continuity is embodied in the basic function H which first appears in section 1.3. We take B spline as the basic function H because: (1) it is potentially C 2 continuous, (2) its deformation speed is high, (3) it is capable of local or global deformation. We discuss B spline FFD in detail in section 1.4. The application of our new FFD method to sculpture surface modeling demonstrates preliminarily that our method is promising.