Reflections: So Smooth, Yet So Rough

So far our reflections only work on surfaces made of materials that are perfectly smooth. In the real world not all surfaces are pefectly smooth yet are still reflective. So to simulat this for doing refletions we cast multiple rays out from the reflection point to caclulate the direction they are cast we take the normal of the surface at the hitpoint and purterb it using a random gaussian variable. The roughness/smoothness is the standard deviation of the gaussian distribution used for perturbing the normals. So the larger the standard deviation the rougher the surface appears. So here's an example image.

Now lets enable the adaptive super-sampling with a circular sampling area and take a look at both the render and the frequency map of the rays per pixel. And we will lighten up the image a bit by adding another light.