I just walked the dogs. What a lovely way to clear the mind of trivia and solve a puzzle.
(Just checking that I can place images where I want them in a post.
Depending upon the nature of the rounds, you can indeed generate a line that will give you a smooth 'mitre' between the pieces. This line will most likely be a curve though, and if you are very unlucky might be a different curve under the work pieces than on top. The line can be deduced geometrically using pencil and paper.
I, personally, would balk at the accuracy required in the cutting of the curve(s) into the workpieces, but if you are not worried about messing up the material and fancy a challenge then I am more than willing to expound my theory (and it is just that) on how to define the curve. I could see it being a fun challenge, especially if saving lots of money.
First we would need to know more about the shape of rounds. Are they 'simple' or 'complex'? These are the terms that I think in - I am not sure what the correct terms are.
Simple: there is no vertical tangent to the curve, or there is only one vertical tangent to the curve that intersects the curve at the bottom of the worktop. Another way of putting it: the curve does not go under the front of the work surface.
Complex: anything else.
If both profiles are simple curves, then there is one line, cut vertically through the worktop, that will solve the problem.
If one profile is simple and the other complex then there will be two curves, one for the underside and one for the top. I would think of the worktop as two pieces laminated together and cut the top curve to one depth and the bottom curve to the remaining depth which would make all mating surfaces vertical or horizontal.
If both profiles are complex then the solution is as the previous if and only if height of the very front edge (the tangent point) above the base is the same for each profile. Otherwise I cannot get my mind round it.
