Does anyone know a good algorithm for finding the intersection(s) between 2 arcs (2D, not 3D)?

What kind of arcs are these? Can they be described as partial arcs of circles or elipses? If so, then there are specials equations that exist for rotated elipses that you can probably use. But because they aren''t straight lines, it''s a bit more involved to get an exact intersection.

Hopefully someone can fill in the details, I''m in a small rush

suppose your two arcs are both quadratic functions
y = A1*x*x + B1*x + C1
y = A2*x*x + B2*x + C2

(A1-A2)*x*x + (B1-B2)*x + C1-C2 = 0

solve normally and plug the solution for x into either function for y