We can rotate a point 'circularly' about an arbitrary axis:

the equation is here, but this site doesn't trust me enough yet to post an image.,

But as we walk theta 0 -> 2PI this takes the point around a "unit circle" around the axis you're rotating about

How can we make it so as theta 0 -> 2PI the results are about an **ellipse** of width a, height b?

I do not want to apply transformation matrices to the points after rotating them about the axis - what I'm looking for is an "elliptical" rotation matrix, if anyone knows of such a thing!