Space-time and higher dimensional modeling for animation

There are limitations to the current BRep based “model then animate” paradigm when animating time-dependent (dynamic) objects. This paper describes an approach to modeling dynamic objects directly in space-time or even higher dimensional space. The use of the function representation (FRep) is proposed due to the ease with which it handles higher dimensions. After creating a multidimensional FRep object, it then needs to be mapped to “multimedia” space. In the case of animation this means at least one geometric coordinate must be mapped to a dynamic coordinate (time). A case study is presented to explain the technique and demonstrate its use in the animated metamorphosis between several shapes of differing topology