why transBt = transBegin.inverse() * transEnd;?

[llxClover]

   Eigen::Affine3f transBt = transBegin.inverse() * transEnd; in imageProjection.cpp line 568

why not trans_e_s = transEnd * transBegin.inverse() , It make me very confused！

[PurplePegasuss]

Because we want to find the delta transformation (increment between final and initial):

We know that: transFinal = transBegin *transBt

The order is exactly like that because that is how coordinate frame change work. First element for matrix product is initial position, and second element is an increment.

Thus we can finds transBt from here:

transBt = transBegin.inverse() * transEnd