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So let's look at some previous work on the specific problem of diffusion tensor visualization. There has been a lot of work in the medical community in how to look at SLICES of tensor data. And one popular way of doing that is to simplify the whole tensor down to a single vector, specifically, by looking only at the tensor's principal eigenvector. You use that direction as a lookup into some spherical colormap which is fixed relative to the coordinate frame, such as this one. This assigns a color to the tensor. There's a second step, which is to darken or desaturate the color where the anisotropy is low. You can pretty clearly see the various structures inside the white matter.