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I was a bit disappointed that a library was used to solve the system of equations instead of going one step further using Cramer's Rule.

Otherwise, this was a fun read!

Since no aliasing is applied (at least on Firefox), these transforms endup looking terrible and illegible.
A simple workaround is to render at double the size and then scale down in the same transform. Makes it edible in most non-ridiculous transforms.
Looks wonderful on Safari on my retina iPad mini :)