A bit out of order, but this post will deal with my work on using quads for area lights. Okay, here's the deal, how do you pick a random point from the interior of a quadrilateral and ensure that the distribution is as uniform as possible? Good question ehh? My math prof thinks so too. We discussed several methods. We are doing this because we need to emit photons from the surface of the light.
The following pictures of distributions are plotted with 2500 points.
Method A: Corners Method
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Its easy to select a point inside the parallelogram defined by a triangle, so divide the quad into four triangles, pick a point inside each corresponding parallelogram and average them together. Nice and simple, but it creates a distribution that is obviously not uniform, it shows a strong bias for the center of the quad. To be fair, this was of my own invention. (The red, green, yellow, and cyan dots are from the four triangles, the blue are the actually points.)
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So far all of our objects are dull and flat, we could easily make this more cool by adding in reflections. The technique is simple, we cast the ray from the eye, hit the object, and then cast another ray reflected off the object. This creates nice reflective objects, the first one only allows things to reflect once.