Can I "impress" one object's shape upon another object? I have a landscape, but it turns out it is rotated by approximately 15°. Yet, I like the shape of it.




I would very much like to transfer the shape (the height of the various points on this plane) onto another plane, that has its grid aligned with the world grid:



So, my question is
Is there a method to do this? If so, how?

Note:
Yes, I'm aware that some information would be lost, both on the non-overlapping edges and because the two grids don't exactly match up. Both this loss of information would still be much better than trying to recreate the height information by hand.

Note 2:
I have a feeling this should be possible with scripting, and I would be willing to try and program one, but for now, I would prefer some non-custom script solution :-)
Create your final grid mesh and place it above the original one. Add a ShrinkWrap modifier to added plane, pick the original mesh as target. Set the  Mode to Project and Direction to both negative and positive.
Make sure to add enough subdivisions for newly created plane to make it catch as many details  from the original one as possible.