In a first step I would actually be okay if the terrain was infinite and flat.

It can be extended to do heightfield raycasting later. I have plenty
of papers about this topic (e.g. cone step mapping and more advanced
methods).

The main difficulty for me is how to cast rays from the screen aligned
quad into the scene, i.e. finding the right matrices and
transformations to do this in the vertex and pixel shaders. Once I
have a ray vector per pixel, intersection with a ground plane should
be trivial.

Christian.
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