Faster shading by equal angle interpolation of vectors

We show how spherical linear interpolation can be used to produce shading with a quality at least similar to Phong shading at a computational effort in the inner loop that is close to that of the Gouraud method. We show how to use the Chebyshev's recurrence relation in order to compute the shading very efficiently. Furthermore, it can also be used to interpolate vectors in such a way that normalization is not necessary, which will make the interpolation very fast. The somewhat larger setup effort required by this approach can be handled through table look up techniques.