Interpretation of 403 Bounded biharmonic weights

It says the TiT_i is a 4 ×\times 3 matrix, then xix_i should be expressed as a row vector. Therefore, the formulation should be like this:
x′=∑i=1mωi(x)(xi1)Tix'=\displaystyle\sum_{i=1}^{m}\omega_i(x)(x_i\enspace1) T_i
the fourth row of matrix TiT_i is in charge of the translation part.

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Interpretation of 403 Bounded biharmonic weights

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