Additional realism can be achieved in computer generated images using smoot
h and increasingly complex deformations. Though significant effort has been
spent on improving these deformations, no general method has been proposed
yet to deal with rigid pieces connected to soft objects.
This paper proposes a general framework to solve this problem. We will pres
ent several types of applications, such as flowing small objects in a defor
mation field, animating rigid features connected to some deformed object, o
r smoothly attached limbs to a deforming body.
All the calculations presented here can be applied to any type of deformati
on, provided that the deformation at each point only depends on the point i
tself. Even though We can directly compute the result for some analytical d
eformation fields, we will skew that a good sampling of the deformation in
the area, of interest is generally enough.
One intermediate result consists of a practical method to find the best rot
ation that approximates a linear transformation. The proposed method is a s
uperset of the Gram-Schmidt orthonormalization process, and is much easier
to compute than global methods based on Taylor series(26).