Some experiments using clustering on meshes to create semi-regular planar tilings of surfaces. I use a variant of a technique called Variational Shape Approximation (VSA), from one of the most cited papers published by the Caltech Applied Geometry group. The algorithm is simple, and moreover has the nice property that it's easy to retrofit with new error functions. The so-called L2,1 metric that they use in the paper, which is based on similarity of normals, resulted in too many long, skinny regions, and gave tilings which differed considerably from the clusters. After a bit of experimentation I came up with a cost function which favours compact regions, along with similarity in normals, and it works really well, resulting in planar regions which are very close indeed to the clusters.
It works well on a big range in numbers of clusters. The above example uses 300; this one uses 50 (the first frame is mostly blank due to an ffmpeg glitch):