Notes for Wednesday September 23 class -- ray tracing shadows

Implementing Phong reflection for multiple light sources
We implemented multiple light sources in the fragment shader, and added most of the Phong reflection model for multiple light sources.
I only implemented the ambient and diffuse components of Phong reflection. I left instructions in the code to help you implement the specular component, which you will be doing as part of your homework.
In order to do that, you will first need to construct the reflection vector R, which represents the mirror image about surface normal N of the vector from the surface point to the direction LDir_i of light source i. As we showed in class, for any light source direction LDir_i, R is computed by:
R = 2 (N • LDir_i) N - LDir_i

After you have computed R, you then need to take the dot product of R and the direction to the eye E raised to the specular power p, and multiply by the light color LCol_i:
LCol_i max(0, R • E)^p

The direction E to the eye is just the direction tracing back along our ray from V to W, so E is just -W.
The resulting color is added to the total surface color to create a highlight from this light source.
Casting shadows
We also implemented ray traced shadows. This just consists of tracing a ray from the surface point toward each light direction LDir_i to see whether there are any obstacles in the way. If there are, then we don't add the diffuse or specular component for that light source.
Homework
Due next Wednesday before the start of class
Complete the included code in hw3.zip and follow the notes in the fragment shader code to implement the specular component of Phong reflection.
You can also take this opportunity to create a cool new scene with multiple light sources and interesting animations.
A caution: You always need to make sure that the light direction vectors in uLDir are normalized to unit length. I will give extra credit if you manage to animate your light direction vectors and then normalize them to unit length in the Javascript code.
As usual, see if you can create something fun and original. Feel free to add other capabilities if you are feeling ambitious. We definitely give extra credit for work that goes above and beyond. :-)