Phong Shading Reformulation for Hardware Renderer Simplification

The specularity calculation of the Phong shading method is reformulated to use the squared length of a difference vector in place of a dot product to characterize the closeness of the viewpoint to the specularity. The new formulation is easier to compute, using only a modest numbers of multiplications and additions, and is much better behaved numerically. Due to the better numerical properties, the new method also allows much simpler approximations to vector normalization. The reformulation does not reproduce the standard cos n Phong specularity shape exactly, but allows a range of options in approximating that shape. This new method is especially well suited for fixed-point hardware implementation.