Assignment 4: Monte Carlo

Due: March 24

For the following problems, please show all your work.

1. Derive an algorithm for uniformly sampling points on the surface of a cylinder with height h.
2. Derive an algorithm for uniformly sampling points on the surface of a cone with height h and base radius r.
3. Derive an algorithm for uniformly sampling points on the surface of a sphere with radius r.
4. Suppose you are rendering a scene of a glossy plane lit by an area light source. When reflecting rays off the plane, you are faced with the choice of either importance sampling the glossy reflection (distributing rays carefully around the mirror direction), or importance sampling the light source (sending rays to points chosen on the light). Describe properties of the scene (e.g., the glossiness of the plane and the size of the light source) that would make one technique preferable over the other.

Submission

Write your answers to the questions above as a web page.  Then, just mail the URL to the TA.  If you are severely technologically challenged, you can write your solutions by hand on paper and turn it in to Nolan.

When submitting assignments, NEVER mail the TA anything other than a URL.