I provided a link to one of Ryan Burch’s sites that shows some of his boards having a reverse curve (hourglass-like) in the outline behind the mid point. The curves are similar to Meyerhoffer/Mackie/Mirandon outlines. I think the basic idea goes back as far as Simmons even - he used parallel or nearly parallel sections in some of his outlines as well as concave bottom contours. Again, not sure if that’s the sort of thing you mean(?)
On shapes I’ve done I tend to follow my instincts and put certain design features in positions that seemingly will work together… I.E. most prominent tail rocker curve approximately where the ‘hips’ in the outline are and place sidebite fins accordingly so the board will have a defined pivot point. On some boards I will add a roll ahead of that area and concave(s) through and behind that area with the intention of providing a ‘squirt’ effect on bottom turns.
To add to the equation, it is interesting to lay a straight edge diagonally through a tail concave and see that with certain designs, a dead flat area will occur where the concave and tail rocker are combined.
I think it is important to differentiate between “area” (X,Y - sq.in. - 2D) vs “volume” (X,Y,Z - cu.in. - 3D) - if the outline is the same, removing foam by introducing concaves is going to reduce volume.
I’m gonna stop there since I’m not sure if I’m even remotely on track.
On most planshapes you couldn’t add enough concave to match the surface width at midpoint. Why would you? I mean, how are you relating that to performance?