基于广义元球的一般约束变形

General Constrained Deformations Based on Generalized Metaballs

在计算机动画和形状设计中，变形是一个非常重要的工具．基于广义元球所具有的特殊势函数分布，提出了一个新的包含点、线、面和体约束的一般变形模型．用户定义一系列约束、每个约束的影响半径和偏移量，变形模型根据每个约束和其影响半径产生该约束的广义元球．广义元球确定了一个以约束点集为中心的势函数，该势函数在约束点集处为１，在影响半径处渐变为０．模型直接对整个空间进行变形，而与物体的表示无关，并且变形可由偏移量和广义元球的参数来细微调整．实验表明，该一般约束变形模型不仅有效，而且使传统方法难以做到的线、面、体约束变形成为可能．

Space deformation is a very important tool in computer animation and shape design. In this paper, the authors propose a new general deformation model containing point, line, surface and volume constraints based on the special distribution of the potential function of a generalized metaball. The user specifies a series of constraints, the effective radius and displacement of each constraint, then the deformation model creates a generalized metaball for each constraint according to each specified constraint and its effective radius. The generalized metaball produces a potential function centered on the constraint, it drops from 1 on the constraint to 0 on the effective radius. This deformation model operates on the whole space and is independent of the underlining representation of the object to be deformed. The deformation can be finely controlled by adjusting the parameters of the generalized metaballs. Experiments show this general deformation model is efficient and can deal with line, surface and volume constrains which are difficult for the traditional deformation models.