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We can organize all the different forms of diffusion ellipses into a barycentric coordinate space, like this. In case you aren't familiar with them, the idea of barycentric coordinates is that for each point in this triangle, the barycentric coordinates are the masses that would have to be placed at the vertices in order for this point to be the center of gravity.

At the vertices, one of the measures is 1, and along the opposite edge, that same measure is 0. Because this is a nice compact space that represents all the different possible kinds of ellipsoid shapes, we use this space as the domain of our opacity function. For each tensor, we calculate its barycentric coordinates, and then find the opacity from the function or lookup table defined on this domain. Let's look at what kinds of structure we can see in the volume using this approach.