Surface trim

Hi, 

Ideally I would have liked to triangulate the surface achieved from the irregular boundary line. I can't work out how to do that so I'm trying to apply an orthogonal grid to this surface.

I'm a little stuck. When I try to do this I get a grid which actually stretches out to the extents of the xy of the boundary. This is what I expected, but how do I trim away all of the curves outside of the boundary.

What I eventually want to do is then subtract some of these squares away. I know how to do all of this if I have a regular square or rectangle as my surface, but I can't work out how to do it for this surface. 

Thanks,