DEFORMATION OF N-DIMENSIONAL OBJECTS

This paper presents a new technique for computing space deformations that interpolate a set of user-defined constraints, Constraints are specified by indicating the images of selected points. The deformation is formulated as the product of a polynomial function f of R-n into a higher-dimensional space, R-m, with a linear projection from R-m back to R-n. The projection matrix is computed using a pseudo-inverse technique. For sufficient m, the degrees of freedom may be used to optimize potential functions controlled by attracting and repulsing points. A prototype implementation is presented, which demonstrates the application of this technique to the interactive design of free-form shapes (when n = 3) and of deformation processes in space-time domain (when n = 4).