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I'm not sure it works with only one point. Costum Calibration patterns are however possible with openCV. https://www.youtube.com/watch?v=Cm4YbwL43Ww does something similar.
I think the only way to find out is to try it. Where I see a problem arise is the following scenario: You provide only one point in each imagePoint and objectPoint array. This seems pointless to me, you cannot calculate rodriguez rotations on a point, as a point is 0-dimensional.
Or you collect e.g. 10 image points and put them into one array as if they were taken from one image. You can imagine it as holding an arbitrary 3d calibration pattern (like the 2nd one from here with a custom pattern https://www.signkwik.com/security-camera-calibration.html) in the camera using 10 markers from it. Now you have to provide the object Points. The objectPoints Array would include the real-world x-y-z coordinates. I'm not entirely sure this works, but It could work.
