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I want to render a simple scene to png image 800x600 size. png image has 2d (u,v) pixel based coordinate system such that top left corner is (0,0) and moving right u increases and moving down v increases so that u and v is always 0 or positive integer. I want to write a script that would generate 3d mapping table that looks like:

(0,0) -> (-11.23, 20.34, 5.24)
(0,1) -> (-11.13, 18.20, 5.11)
......
(799,599) ->  (2.24, 4.56, -3.56)

Basically what I want is to find the point in 3d space in the scene that maps to the 2d pixel coordinate given above in the image that was rendered matching to the same scene.

I would prefer a solution using python or java and open source rendering libs and modeling tools.