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### 3D coordinates of two points in room and angle between them

I have a room with 4 cameras. Each camera is in an upper corner in this room. (non-parallel stereo!)
I will have different points which can be detected with these cameras. Let's assume there are only two.
Now my question is as follow:
How can I calibrate all 4 cameras so I can determine real world coordinates of each point?
After I will find out where the points are (X1/Y1/Z1) and (X2/Y2/Z2) I will be able to determine the angle between them but this is not the problem part.

My assumtion is this like:

• I thought to calibrate each pair of cams (i.e. 1 <-> 2 <-> 3 <-> 4 <-> 1)
• with stereoCalibrate I would get rvec, tvec and then the fundamental matrix
• I thought to simply use the chessboard which would be seen with every camera at the same time
• after getting rvec, tvec, F I could reproject a 2D Point from every image (cam-1, cam-2 a.s.o.) and I could verify if every single reprojection is the same in 3D

It will be very helpful for me to know if my idea to solve my problem is correct and where are the aspects which can be done more easier and more correct.

P.S.: I have done homography for just 2D and with Z=0 but the problem here is more complex for me.