Real Time Local Approximation of Deformations using Rotations

Additional realism can be achieved in computer generated images using smooth 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 present several types of applications, such as flowing small objects in a deformation field, animating rigid features connected to some deformed object, or smoothly attached limbs to a deforming body. All the calculations presented here can be applied to any type of deformation, provided that the deformation at each point only depends on the point itself. Even though we can directly compute the result for some analytical deformation fields, we will show 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 rotation that approximates a linear transformation. The proposed method is a superset of the Gram-Schmidt orthonormalization process, and is much easier to compute than global methods based on Taylor series.