Building a buffer over a terrain model

Question

I have a polygon and a terrain model (can be either grid or TIN). I'd like to a build, say, a 1km buffer so that the 1km is measured over the surface of the terrain, i.e. not planimetric. The buffer must always be at least 1km from the polygon and prefer a measure over the flattest part of the terrain.

Anyone know a good way to do this that is robust for all the edge cases you get with real terrain?

An algorithm or solution using FOSS tools is preferred.