That's a very nice construction, TOK!  :)
It took me a minute look it all over and see what was going on - the diagram and
animation on that page really help.
It's so nice to have many different ways to construct the same shape, but with
different results in the point-by-point details.

I'll need to look at TdG's code, but it seems to be very similar to a way I was
thinking of that would show how the ellipse is the uneven scaling of a circle.

With radius and angle, use transforms to "move" a vector to a place on the
circle, then using scaling transforms, adjust it to be elliptical.
Then an "overall scaling" transform could be applied after that as well.

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