Hi ticbol!

I need a solution METHOD to apply on many pairs of ellipses. And the solution needs to be done algorithmically without human interference (and with some computational efficiency).

The form you suggest looks like the formula for an untilted elipse, i.e. an ellipse whose axes are parallell to the axes of the coordinate system. I don't know how tilted ellipses could be expressed in that form.

But maybe since tilt can be assumed to be the same for both ellipses, there is a way to "turn" the coordinate system by that angle and then proceed in this form with only four degrees of freedom?

Please see

Ellipse - Wikipedia, the free encyclopedia to see what I mean with "parametric form". Except for the tilt, all other four variables in the parametric form correspond directly to the variables in the form you suggest.