Talk:Procrustes transformation

This is just Euclidean transformation, no?

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As far as I can tell, these "Procrustean transformations" (never heard the name before) are exactly the similarity transformations of Euclidean geometry. No?

Actually, as far as I know, the "stretch" doesn't need to have the same scale factor in every direction, as long as the scaling factors in each direction "balance" and produce no change in area (eg.   is a valid procrustean stretch). In this sense, I believe a 2-D procrustean transformation is basically an area-preserving affinity, or equiaffinity. Of course, a 3D procrustean transformation should be regarded as a volume-preserving affinity. Wago (talk) 07:34, 17 February 2016 (UTC)Reply