This is an absolutely fantastic piece of code. 5* well deserved. Thank you!
That said I really regret writing this but...
To me the returned values for I and J feel awkward. Because X0 and Y0 return the intersection points in terms of the original space in which the curves lie (X,Y), I would expect the second set of returned values to give coordinates in terms of the curves themselves. So if a curve has (Euclidean) length 4.8, then I would expect 2.4 to be halfway the curve, not at 4 tenth of the second line segment.
This way we could also compute derivatives and integrals along a curve and interpolate these values simply by looking op the value at I (or J for that matter). Furthermore, the distance along the curve is a nice linear function, whereas the currently returned values for I and J are piecewise linear and non-differentiable it the points.
I understand that such a change of I and J would not be backwards compatible, and also it might be slightly (but hardly) more involved to compute, so I see the big arguments against. Nevertheless, I would be very happy if you would at least give it a thought :-)