Talk:Procrustes transformation

This is just Euclidean transformation, no?

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. $y'=a\cdot y;x'={\frac {x}{a}}$ 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)