Yes, that’s probably the simplest approach. I designed the following algorithm which seems to provide with a ConvexCurve. Someone smarter than me can probably simplify the algorithm (Edit: What puzzles me is why I couldn’t make the for-loop clean up all the “inward” points in its first round):
ConvexCurve_Forum_00.gh (18.7 KB)
I haven’t tried it on extreme curvatures but it seems to work for this case. Edit: Illustration of the strategy in the algorithm which is to remove Point(B - mid) if the VectorAngle(a) is less than the VectorAngle(b) compared to the Vector(Centroid):
From this I can now pick the two deepest “inward dents” based on longest distance (deepest “dent”) from the ConvexCurve.
Thanks for help and inspiration, this is fun! 
// Rolf