Lofting wrong position

Hi guys,

I am trying to extrude a set of surfaces which are produced through a doubly curved surface so I can get this type of results:

The extrusion should not have any bending the components should be straight. 

1)When I subdivide the surface on UV it does not follow the outline of the given surface.

2) And also the extrusion doesn't not follow the surface path.

Any ideas how I can succeed the above result?

Natasa