Intro

In this assignment you will implement the Ward Anisotropic BRDF$.$

The Ward model uses a $2$D Gaussian function to map the angle H makes with the surface directions u and v$,$ to the fraction of light reflected from the surface$$for a given viewing and lighting angle to the surface normal N$.$

The Ward BRDF computes the following using the unit$-$length N$,$ L$,$ V$,$ H$,$ u$,$ and v vectors:

cos $\backslash$theta i $-$ cosine of the angle between N and L$.$

cos $\backslash$theta r $-$ cosine of the angle between N and V$.$

cos $\backslash$theta n $-$ cosine of the angle between N and H$.$

cos $\backslash$theta u $-$ cosine of the angle between H and u$.$

cos $\backslash$theta v $-$ cosine of the angle between H and v$.$

And uses the following parameters:

u$\_$roughness $-$ roughness in the u surface direction.

v$\_$roughness $-$ roughness in the v surface direction.

The Ward BRDF looks like the following two renders. The left rendering has u$\_$roughness $=0\mathrm{.}25$ and v$\_$roughness $=1\mathrm{.}0.$ The rendering on the right has u$\_$roughness $=1\mathrm{.}0$ and v$\_$roughness $=0\mathrm{.}25.$ The specular color was set to $[011].$