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What we did was to introduce an anisotropy type measure c_theta, which varies between 0 in the linear anisotropy case, and pi/2 in the planar anisotropy case. Then, this (at bottom) is the formula for lit-tensors, which is basically just an expression to use in place of doing dot products with N. Here's why its useful. In the linear case, c_theta is zero, and the formula reduces to the formula for lit lines, if you consider the tangent direction to be along the principal eigenvector. In the planar case, when c_theta is pi/2, the contribution of the two eigenvectors is equal. Which means that by Pythagorus's theorem, this actually evaluates to U.N, where N is the normal to the plane spanned by e_1 and e_2. Actually, its the absolute value of the dot product, so in the planar case, we're stuck with two sided lighting. Let's see how this works to illuminate different kinds of tensor volumes.