# BRDF Comparison

December 9, 2013 - 10:33 am by Joss Whittle C/C++ Graphics PhD UniversityI thought I’d make some high quality comparison shots of some of the shaders I’ve been working on. Above you can see a side by side comparison of a perfect mirror BRDF and a Phong *based* BRDF with exponents of one million and ten for the centre and right images respectively.

While the Phong-like BRDF does give nice glossy reflections at a relatively small cost it does not model a physically accurate shader. I’m currently looking into implementing a Cook–Torrance model shader which while being more time consuming to compute gives nice results which are based off of physical phenomena. The Cook–Torrance shader also has the inherent ability to model microfacets within the surface of objects which is a big plus.

Because the Phong BRDF is not physically accurate I needed to find a PDF that would look correct in the renderings. The Mirror BRDF for instance has a `PDF = 1`

and the Diffuse BRDF has a `PDF = 2 * (normal . newDirection)`

. After some experimenting from reading a paper that claimed the Phong marginal pdf was `cos(theta)^e`

which I understood *(possibly incorrectly as it did not work)* to mean `PDF = (normal . newDirection)^e`

I found *(gave up)* that the Diffuse BRDF in fact worked reasonably well for the Phong model.

**Edit** I have found a better paper with what looks like a good Phong model. They even give a run down of using their model in a Monte Carlo style simulation with a marginal PDF. I might try implementing this before I move onto Cook-Torrance.