1. If we want to render a typically-sized room with textures at centimeter-square resolution, approximately how many particles should we send to get an average of about 1000 hits per texel?
2. Develop a method to take random samples with uniform density from a disk
3. Develop a method to take random samples with uniform density from a triangle
4. Develop a method to take uniform random samples on a "sky dome" (the inside of a hemisphere).