Reconstructing Kite Position and Rotation from a Single Camera Image

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velcrome
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Image a kite (1 m wide, 3 m high, both crossing at a third of the height).
Also imagine a digital camera (800x600 pixel with a horizontal field of view of 45°).

After launching the kite a photo is taken with the camera.

How can I easily calculate the exact position *and* rotation of the kite in a vectorspace defined by the camera at the moment the picture was taken?
I tried with trigonometry but failed. I assume there is an easier way with matrices but i don't know how. I appreciate any help.

*velcrome
 

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there are four corners of the kite with precise pixel values in the picture.

and of course, the dimensions of the kite and the specifications of the camera is known.