I think I saw some of these spatial deformations you mention in 3DS Max, under "space warp" (iirc). Not sure if it was for animation or not, but basically it warped space inside a given volume according to some displacement function. Well, actually, it just warped the vertices and objects within - the space itself remained Euclidean.
I'm not sure how applicable this is as a general-purpose solution, though. Generally, the more information you want to encode in your animation spatial transformation, the more complex the transformation will be (information theory) so unless you have really simple or self-similar animations (like fractals) I'm afraid the spatial transformation would end up being approximately as complex to evaluate as just displacing every vertex the traditional way (if that makes any sense). But it could have its uses, you mention organic animation, that could be an approach worth pursuing.
Edited by Bacterius, 08 January 2013 - 11:11 PM.
The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.
- Pessimal Algorithms and Simplexity Analysis