One post tagged with "geometry"

In this article, I will derive these famous Specular and Diffuse BRDFs from scratch.

$\boxed{\text{BRDF}_{\text{spec}} = \frac{F(\omega_i, \omega_h)\, G_1(\omega_i, \omega_o, \omega_h)\, D(\omega_h)}{4\,|\omega_g \cdot \omega_i|\,|\omega_g \cdot \omega_o|}}$

$\text{BRDF}_{\text{diff}} = \frac{1}{|\omega_g \cdot \omega_i|\,|\omega_g \cdot \omega_o|} \int_\Omega \frac{1}{\pi}\, \langle \omega_i \cdot \omega_m \rangle\, G_1(\omega_i, \omega_o, \omega_m)\, D(\omega_m)\, \langle \omega_o \cdot \omega_m \rangle\, d\omega_m$

I will try to make the derivations as intuitive as possible with figures and explanations. The interactive HTML sections have been written by AI (The free version of Claude) as I don't know how to do frontend HTML programming. The other figures were made by me using inkscape.

This derivation is not novel, I read through 5 very important papers shuffling all of them at once, and I got the idea while going through them, to create a straight-forward article for someone like me, who is interested in mathematics and derivations of equations, but for whom, certain jumps in derivations don't come so naturally.