Continuously building parabolas from 3 points

Hy guys ,

Another problem I have is I can't find a way to build parabola arches for 3 defined points.

I think it is easier to see from attached images what I want to get.

- I have 2 points projected to curve and one point moved down which should form a base for future parabolic arc. These arches should continuously go across the base curve on which points where projected.

How to:

1. Spread points to give a gap between arches

2. Create parabolic arc

3. Make it continuous , so it repeats and follows the curve

Thank you!