DEFORMATION OF N-DIMENSIONAL OBJECTS
- 1 December 1991
- journal article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Computational Geometry & Applications
- Vol. 1 (4) , 427-453
- https://doi.org/10.1142/s0218195991000281
Abstract
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 ℝn into a higher-dimensional space, ℝm, with a linear projection from ℝm back to ℝn. 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).Keywords
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