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To assign opacity, we start with three anisotropy metrics proposed by Carl Westin in 1997. You can think of these as shape measures, since they measure how closely the tensor conforms to the three canonical shapes: c_s for the sphere, c_l for the cigar, and c_p for the pancake. And on the left, you can see the results of these metrics applied throughout one slice of some tensor data. The metrics are formulas involving the three sorted eigenvalues lamba_1, lambda_2, lambda_3. The exact details aren't important, but I should point out two things. First, because of this normalizing factor which divides all the formulas, all the metrics are always between 0 and 1. Second, by their construction, the three metrics will always sum to 1. That means that barycentric coordinates are a natural way to represent them.