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I have a square with the length of the sides being 1. This square is transformed by an unknown transformation matrix in the 3D space and then projected back to the plane (the projection is known). I know the coordinates of the 4 angles of the transformed, projected square.

How do I find the unknown transformation matrix?

UPDATE: sorry I forgot to add that the projection is perspective.

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    Just to clarify, you know the original coordinates of the square correct?2012-11-22
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    When you say "projected back to the plane" do you mean the original one in which the square started, or a different plane? I thought the first, but then wondered why you would add "the projection is known" unless it was projection to a different plane.2012-11-22
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    @icurays1: yes, I can even suppose they are let's say (0,0) (0,1) (1,1), (1,0)2012-11-23
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    @Tom Oldfield yes, it's the original plane. And yes, you're right, it's a kind of redundant information. All in all the square is transformed first by the unknown matrix and then by the projection and I would be happy to know either the unknown matrix or the matrix of the concatenated transformations.2012-11-23
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    Do you have access to Hartley and Zisserman? This is explained there.2012-11-26
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    When you say "I know the coordinates of the 4 angles of the transformed, projected square", do you mean you know the coordinates of the four corners after the projective transformation has been applied?2012-11-26

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