Texture projection, compute UV coordinates

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Hi everybody, I’m trying to project an image to the plane. I was using this approach from opencv and also read this post. The question is how do I get a UV coordinates for the image.

Here is my scenario: plane 16x12 ( blue) and image with the translation at 0,4,0 (red cross) and the rotation matrix ( 100 010 001 )

I was using this, but I get really wrong UV coordinates i was using this formulas from opencv article:

Result for example for the point ( -8, 0 , -6 ) -> (1.33, -0.66) and i expect it to be -> (0,0)

Do you have any ideas, what I do wrong and how it should be done?

Thanks!