Question: 'Estimate' intersections between surfaces

I want to solve for the intersecting curve between two surfaces. The figure demonstrates what I mean in a plot, I'm interested in the curve between the red and the blue areas. (The surfaces are seen from above.) 6874_a-d-plot1.jpg Ideally, I would just ask Maple to 'solve(surface1>surface2)', where the surfaces would depend on some parameters. This do, however, not work. (The functions (surfaces) has up to 7 input parameters, and combines heavyside functions and the max function.) I'm sure there is a way, though. Given my ignorance, I'm now pursuing to 'estimate' the curve, by somehow reading off the intersection numerically and using some regression or whatever. Any idea how to do this efficiently? Thanks, Sturla
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