Project multiple arc/ curve on a surface

I have polysurface on rhino that I want to project onto a arc that I drew. I want the arc to project multiple times through the surface - until the surface is covered with the arc.
attaching an images: you can see the polysurface and the arc (on the right). I drew blue line of what im trying to get. I knowhow to divide the surface and get points on it but it have no idea how should I select 2 points at time and draw a arc between them…