This is an interesting problem but you actually have two questions, it seems to me.
1. how to determine if the high point between two point is smooth or sharp(?) Which really depends on how you distinguish either in terms of your wave diffraction equation. Seems like a directional slope change problem, 2nd polynomial or running slope tool twice.
2. how to do this in ArcObjects. You really can't tackle this until you'v answered question 1.