Approximated Phong Shading by using the Euler Method

Abstract

After almost three decades and several improvements, Gouraud shading is still more often used for interactive computer graphics than Phong shading. One of the main reasons for this is of course that Phong shading is computationally more expensive. Quadratic polynomial approximation techniques like Bishop’s method could reduce the amount of computation in the inner loop to just the double of what is done in Gouraud shading. By using Euler’s method we get another quadratic polynomial approximation technique which is just as fast in the inner loop, but it will also give correct intensities on the edges, which we will not get with Bishop’s method. By computing the maximum difference over a scan line between Gouraud shading and the proposed method, we could decide if Gouraud will suffice. It is also shown that linearly interpolated normals are normalized by a symmetric function. This means that we could reduce the amount of square roots by the half in Phong shading.