Next up- soft shadows (raytraced shadows, in Maya terms).
First, however I will make it just as if it was a grid of shadow casting lights on the area light, and then I will make my program a Monte Carlo tracer! Yay!

Monte Carlo is simply a method that goes like this:

Enough random samples and their average will become the correct answer.

So then I will randomly jitter the position of the samples for the area light, and that will replace the banding that will occur with noise. Then I will increase the samples until- voila, a perfect soft shadow.