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rigid body combined rotation/translation with Mathematica

Hello all,

I have a problem trying to compare the (2D) results of a coordinate
measuring machine inspection (CMM) of a grid of data points to the actual
design values of the points.  Minute errors in positioning of the workpiece
result in deviations in the datasets.

Has anyone come across a mathematica notebook (or other algorithm) which
would provide the (x,y,theta) values which minimize the positioning errors

Any input would be appreciated

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