I want to find the coordinates where two ellipses meet. They each have five degrees of freedom (axes lengths, center coordinates and tilt angle) although we could assume that both have the same tilt angle.
I suppose that no managable algebraic solution exists.
How should I proceed in order to solve it numerically, for example with the secant method?
For each point I pick on one ellipse, I need to numerically search for the point on the other ellipse which is closest to it. But I want the solution algorithm to be computationally fairly efficient. Is there no smarter way?