A comment on the math: the article portrays it as quite verbose to say the least, which I think might indicate to some that it is "scary" or really complicated.

A comment on the math: the article portrays it as quite verbose to say the least, which I think might indicate to some that it is "scary" or really complicated. I get the hunch that it need not be that way, if approached differently. Affine transformations, conceptually, are quite elegant: https://en.wikipedia.org/wiki/Affine_transformation https://en.wikipedia.org/wiki/Affine_transformation. Figuring out the values to use for a particular transformation is the key here. This is where the blog post gets really verbose in the math. The complexity of the solution, as written, seems much higher than the inherent complexity of the problem. So my intuition suggests the mechanics of the solution (e.g. the amount of notation required, at least, if not the amount of computation) can be dramatically simplified if done a different way. I'd think that playing around with polar coordinates and various frames of reference would help find an elegant calculation.