
4.2 Geometric State 237
of scales, and T is a translation. Once a world transformation is computed as a
composition of local transformations to obtain M and T, you have to factor M =
LDR using the singular value decomposition—yet another expensive proposition.
Given the discussion of nonuniform scaling and the performance issues arising
from factorization and/or maintaining a consistent representation for transfor ma-
tions, in Wild Magic version 2, I decided to constrain the transformations to use only
uniform scaling. I have relaxed the constraint slightly in Wild Magic version 3. The
Spatial class stores three scale factors, but only the leaf nodes ...