"Point coordinate transformation" and "coordinate system (pose) transformation" in three-dimensional space

1. Points represent transformations in different coordinate systems
   

2. Transformation between different coordinate systems (poses)
   

3. Key
   Point coordinate transformation, 左乘
   transformation between coordinate systems, 右乘
   points use one subscript
   and poses use two subscripts to indicate the transformation from where to where, such as Tw1 means the transformation from w to 1, that is, 1 pose.
   The R21, t21 of the transformation of the coordinates under 1 to the coordinates of 2 is the same as the transformation R21, t21 of the coordinate system 2 to the coordinate system 1, and the order of the two is just opposite, so pay more attention.