If I understand the Geometry module's umeyama function correctly, it takes source points X and destination points Y and returns a transformation T corresponding to

Y_approx = T * X = scale * X + t_scaled
t_scaled = mean(Y) - scale* R *mean(X)

when called with scaling. When called without scaling, it returns

Y_approx = R* X + t_scaled

that is, it removes the scale factor from the linear part but computes the translation in the same way. I would expect it to return
Y = R* X + t
t = mean(Y) - R *mean(X)

when called without scaling. Put differently, I would expect

Y_approx = scale*R*[X-mean(X)] + mean(Y) (with scaling)
Y_approx = R*[X-mean(X)] + mean(Y) (without scaling)

I realize that I may be misreading the code, but if not, is the present version the intended one?

Hi Dandelin,

Thanks for the report. I think this is fixed in the devel branch. Which version are you using?

Regards,
Hauke

I'm using version 3.1. Indeed, it looks fixed in the development branch, great! I should have looked there first.