The use of a homology error that is isotropic, the residual between the configurations as a measure of registration error and totally randomized point distributions are some of the weaknesses of past studies with point simulations. Validation procedures must account for these these faults so that what is actually being validated reflects clinically realistic distributions. The use of the difference between transformations and point configurations which better reflect real bounded configurations are implemented in the point simulations studies presented in this chapter. Since the distribution or configuration of chosen homologous points are in general disperse within a sphere, or spherically symmetric, because of the shape of the brain, the rotational errors may be expected to depend on the radius of homologous point pairs from the configuration's centroid. This is because the second step in the Procrustes algorithm is a rotation about the centroid at the origin. From simple geometrical considerations, if the distance between a homologous point pair reflects the magnitude of the homology error, then the angle between the two points at the configuration's centroid is smaller the farther the two points are from the configuration's centroid. The dependence of rotational error on the radius of the homologous points from the configuration's centroid is investigated by randomly generating points within two spherically symmetric objects of different radii - spheres and shells. It is expected that the delineation of the radial dependence of the rotational error will be smoother for more radially symmetric objects. Since radial symmetry is not fully conserved in the random point generation, shells are used in addition to the spheres to help obtain a smoother radial dependence.