How should I measure distance on a curved surface? (NEW more accurate question)

How should I measure distance on a curved surface? (NEW more accurate question)

Hi, 

I need to measure the distance from A to B, in a surface that seems to be parabolic-ish and,  honestly, I am stuck as I don't know exactly how should I approach to this situation...I don't even know how should I properly align the part.  

My points are located ON THE EDGES (the arrows on A nd B try to show the approximate approach vectors) and the distance should be not a straight line, from A to B,  but a curved one, following the red dots path.  Unfortunately I don't have a CAD file nor any other information other than the nominal for the distance A-B that I'm trying to measure.

How would you measure something like this? Any suggestions?

All ideas will be absolutely welcomed!

Thanks in advance for taking the time to help me.