How can I transform a coordinate system into the origin coordinate system

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I have two cameras, camera 1 which is also the origin coordinate system and camera 2. I also have a rigid Object which contains 88 points that the camera 1 detected.

I now have another coordinate system, let's call it coordinate system X which is somewhere located at the vector T. The vector T is the baseline which connects the optical center of camera 1 and camera 2, a.k.a the Translation of camera 2 relative to camera 1. The vector T and also the rotation of camera 2 relative to the origin coordinate system is given

The location of coordinate system is unknown. I also have the same object displayed in coordinate system x.

I now want to align the coordinate system X into the origin coordinate system such that the orientation of the object is displayed in both coordinate systems the same way. That means I want to determine the transformation matrix which consists of the rotation and translation align coordinate system x into origin coordinate system

How do I approach this task ?

In the following are a sketch of the camera orientation and the object displayed in the origin coordinate system and the coordinate system x.

camera orientation

object displayed in origin coordinate system

object displayed in coordinate system x