Halcon - Generate new pose based on 2 poses

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I have 2 Parallel poses with different origins and different X axis directions (Y is parallel):

  • First pose is my ground plane. X is horizontal, Y is vertical, Z is depth.
  • Second pose, is somewhere above the first pose floating in the room, with the Y Axis parallel to the first pose's Y axis.. X and Z can be rotated along the Y axis...

What I need, is a third pose that is The second pose, but lowered onto the first pose, so that Y0 of the third pose is the same as the Y0 of the first pose.

I am going crazy about this, cant figure out how to do it. any help appreciated...

EDIT: I have updated the question to simplify the problem a little bit.

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