General constrained deformations based on generalized metaballs

Space deformation is an important tool in computer animation and shape design. We propose a new local deformation model based on generalized metaballs. The user specifies a series of constraints, which can be made up of points, lines, surfaces and volumes, their effective radii and maximum displacements; the deformation model creates a generalized metaball for each constraint. Each generalized metaball is associated with a potential function centered on the constraint, the potential function drops from 1 on the constraint to 0 on the effective radius. This deformation model operates on the local 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. We also present some extensions and the extended deformation model to include scale and rotation constraints. Experiments show that this deformation model is efficient and intuitive. It can deal with various constraints, which is difficult for traditional deformation model.