Rigid transformation and similarity transformation in MLS

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I am reading the paper Image Deformation Using Moving Least Squares of Schaefer. I attach the link below: https://people.engr.tamu.edu/schaefer/research/mls.pdf

In Section 2.3 Rigid Deformations, I am stuck at the calculation of the constant $\mu_r$ in $M$. Anyone knows how to use the Theorem 2.1 to get $M$ and $\mu_r$?

Thank you!