Is the example above with the 3D model in different levels of detail essentially just a low pass filter with different cutoff frequencies for geometric data?
@tcl Exactly. The question is: how do you make sense of ideas like “frequency” for data that is a collection of triangles glued together along edges? Standard ideas from classical Fourier analysis don’t work, and you need an alternative definition.
I know that lots of lossy encoding formats (e.g. JPEG, MP3) are based on cosine transforms, but I don't think I've ever seen that applied to 3d model before, probably due to the lack of an obvious way to apply the classical signal processing concepts to 3d geometries (as already mentioned). This makes me wonder if there's potential for signal-decomposition-based lossy encodings to catch on for models as sharing them becomes more and more commonplace (with the benefit of such a format being that one could display a partially-loaded model and iteratively add more and more detail as it loads).
@mdsavage Yes! Here's a fairly early paper that does spectral compression of geometry. A lot of similar techniques have been developed since then; here's a nice overview. Finally, here's a classic paper that does progressive encoding of meshes without spectral techniques; there are lots of variants on this idea such as adaptively adjusting mesh resolution according to the view, a problem which becomes increasingly important for things like VR where you want high resolution only in a small region of interest.