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Coordinate transformation

Hi,

I am trying to figure out how to compute the transformation of a coordinate system (O_2) from a reference coordinate system (O_0).

The information I have are as follows:

- Transformation of one coordinate system (O_1) from the reference (O_0), i.e. R_1 and t_1.

- Transformation from O_1 to O_2, i.e. R_12 and t_12 - note that R_12 and t_12 are with respective to O_0, the reference coordinate system.

What I want to find is R_2 and t_2, the transformation of O_2 from O_0. I know for a transformation you use the homogeneous transformation matrix:

But am stuck as to how this is applied in this situation...

Please refer to the diagram below if the description is too confusing :)

Many thanks in advance!