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Register two point clouds with different proportions, clik ''align ( point pairs picking )'', then select several point pairs and select "adjust scale" , two point clouds are registered. What is the principle or algorithm behind this ？How does it calculate the affine matrix？

It's the classical 'Horn' point set registration process ('Closed-form solution of absolute orientation using unit quaternions', B.K.P. Horn, 1987), with a small refinement for scaling.

See https://github.com/CloudCompare/CCCoreL ... s.cpp#L945