Density in a Circle Milestone

http://people.sc.fsu.edu/~jburkardt/classes/urop_2016/density_circle_milestone.html

We need more practice with calculations involving a density! We will start by looking at a circle. Instead of using uniform sampling plus a density function, we can use a nonuniform sampler. In that case, we can go back to the simpler codes that computed centroids rather than centers of mass.

An interesting question then is what kind of options we have for choosing or designing a sampling method, and how does the sampling bias show up in the final CVT point placement.

Topics:

• We can try a weighted CVT in the unit circle. Remember our first guess at a random sampling function for the circle, which turned out to be nonuniform? Let's use that as our sampler, and see what the effect is on our CVT calculation.
• To improve the readability of our plot, we can try to display the boundary circle along with the generator points before and after the CVT iteration.
• We could also try to display the Voronoi diagram of the generator points before and after the CVT iteration.