This assignment builds on the previous one. If yours worked, I strongly recommend using your own code as a starting point for this assignment. If you were not able to get the first part of your ray tracer working, I will provide access to sample code in `~olano/public/trace` (after the late submission deadline for assignment 1). You could either use this code to figure out what was wrong with your assignment, or use it as a base for this one.

## The Assignment

For this assignment, you will add mirror reflection and diffuse and Blinn-Phong specular lighting with shadows to your ray tracer. I have provided an edited `teapot.nff` that you can use for testing (In addition to the other spd models).

You will need to use additional parameters from the '`f`' lines in the nff file. The full set of '`f`' parameters is

f `r g b Kd Ks e Kt ir`

Where `r,g,b` is the base surface color, `Kd` is a coefficient to scale the overall diffuse contribution, `Ks` is the coefficient for both reflection rays and a Blinn-Phong glossy specular component with exponent `e`, `Kt` is the coefficient for refracted rays, and `ir` is the index of refraction.

In assignment 1, you needed to track the color at the closest intersection. For this assignment, you will also need to track the surface normal, intersection location, and additional surface parameters. Once you find that intersection, you will need to compute the surface shading. Given unit normal, `N`; unit vector from the surface intersection point toward the light, `L`; unit vector halfway between the light and ray, `H`; and light intensity of `1/sqrt(numLights)`, sum the contribution from each light. For each light, cast a shadow ray from the surface to the light. If that light is not shadowed, the diffuse and specular contribution from that one light would be computed as:

diffuse = max(0, dot(N,L))
specular = pow(max(0, dot(N,H)), e)
localColor.r += (Kd*r + Ks*specular) * diffuse * lightIntensity
localColor.g += (Kd*g + Ks*specular) * diffuse * lightIntensity
localColor.b += (Kd*b + Ks*specular) * diffuse * lightIntensity

Since the color of each reflection ray is the total color of whatever it hits, including its own diffuse, specular and reflection, compute the color in a recursive process:

Color trace(ray) {
...
totalColor = localColor;
if (Ks > 0 && !recursionLimit)
totalColor += Ks*trace(reflectionRay)
return totalColor
}

Stop the recursion if the total contribution to the final color would be less than 1/255 (one bit in the final color) or if the number of bounces would be greater than 5. The easiest way to do this is to add data to each ray to track the number of bounces left and the total contribution so far. For example, a ray that is the result of one reflection with coefficient `Ks`_{1}, then one with coefficient `Ks`_{2} would have three bounces left and a maximum possible contribution of `Ks`_{1}*Ks_{2}