Increase Composition Performance

[jzwar]

This is already a TODO in Compose

In the multi-dimensional case the composition is performed by multiplying the precomputed Basis functions to the control points T of thee deformation function C = T_{ijk...} Bi Bj Bk ....
Currently this is done by looping over all i j k ... which is very inefficient, as many splines Products are computed multiple times. If the product can be organized as follows, the computational cost can significantly be reduced.

for i:
    for j:
        Bij = Bi * Bj
        for k:
            Bijk = Bij * Bk
            for l:
              [...]

In this example for every k -- (k-1) fewer spline products are computed as Bij can be reused for every iteration of k. This effect becomes more important for parametric dimensions of the deformation function.