How to create an interactive 3D axis

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I have this vision in my mind that I would hope it could be possible.
So consider the following image which I let MATLAB read
I want to know if there's a code where a user has to define a 3D axis by identifying 4 points on the figure like this :
After the user plots these points, MATLAB should create a 3D axis that connects these points as follow :
Once this is accomplished MATLAB should take this axis reference into account if a user wishes to identify points on this image where MATLAB should calculate (x,y,z) coordinates with respect to the origin that the user had identified earlier.
I would be really grateful if such algorithm is possible to make and I would be happy for any suggestions

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