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That explanation of the physics can help us understand deflection as a function of anisotropy. The more anisotropic the tensor is, the more deflection there can be. This diagram (top) shows the deflection for a sequence of orientations of two different ellipsoids. You can see that when they have the same orientation (vertical pairs) the more anisotropic of the two ellipsoids always deflects the tensor more. But at the same time, the amount of deflection also depends on the orientation of the ellipsoid. This informs how we should set up our spherical colormap. (going back one slide) There is gray at the top and bottom poles, and around the equator there are saturated colors. Also, we set up our input vector to point at one of the gray poles. That way, if there was no deflection, then the output vector also points at a gray pole, and we don't assign a noticable color. Only the the regions that do cause deflection, because of anistropy, get any saturated colors. And this (lower right) is what one slice of some measured data looks like, when mapped through the hue-ball. Here's the corpus collosum, which is colored red, and you can see that all the gray matter around the outside is basically gray.

So we've assigned color. Now for opacity.