基于NURBS权因子调整的FFD直接操作

FFD（Free-Form Deformation）是计算机动画和变形中最重要的方法之一。FFD的直接操作为变形提供了更直观更方便的控制手段。该文用约束优化方法，通过调整张量积网格控制点对应的权因子，解决基于NURBS的FFD直接操作问题，给出了变形物体在单点约束下FFD直接操作的解，使变形后的物体通过给定的目标点。该方法计算简便，易于实现。文中给出的变形实例也表明，变形结果比较自然。

Weight-Based Direct Manipulation of FFD

Free Form Deformation (FFD) is one of the most important methods in computer animation and deformation. Direct manipulation of FFD improves controllability and efficiency of the deformation. This paper presents a new algorithm of direct manipulation of NURBS based FFD via changing weights of lattice using constrained optimization method. With this algorithm, the solution of constraints with single and multiple target points can be obtained, and the deformed shape passes through these given target points naturally. This method involves only simple calculations and is easy to implement. The examples given in the paper also indicate that the deformation is natural.