In generating an elevation profile, samples from the underlying raster must be taken. If the objective is to create a profile of maximum quality, how should the locations of sample points be determined? What approach should be taken to interpolating those sample points?
Answer
If you want create a profile of maximum quality, then your algorithm has to basically include every single cell that is intersected by your query path and then it becomes a simple 2D curve fitting problem. However, if you want to just sample a subset of those points and create a profile that is more visually pleasing, you may that find that this paper from geocomputation has a lot of different interpolation technique for sampling elevation as well as the math behind it.
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