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Math Help - Coordinate transformation

  1. #1
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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:

    <br />
H = \left[ \begin{array}{cc} R & t \\ 0 & 1 \\ \end{array} \right]<br />

    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!
    Attached Thumbnails Attached Thumbnails Coordinate transformation-coordinate_transformation.png  
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