Posted: March 18th, 2022
Prove the Orthocenter Theorem by geometric arguments: Let T be the triangle on the image plane defined by the three vanishing points of three mutually orthogonal sets of parallel lines in space. Then the image center is the orthocenter of the triangle T (i.e., the common intersection of the three altitudes. Note that you are asked to prove the Orthocenter Theorem rather than that the orthocenter itself as the common interaction of the three altitudes, which you can use as a fact.
(1) Basic proof: use the result of Question 1, assuming the aspect ratio of the camera is 1. (20 points)
(2) If you do not know the focal length of the camera, can you still find the image center using the Orthocenter Theorem? Can you further estimate the focal length? For both questions, please show why (and then how) or why not.
(3) If you do not know the aspect ratio of the camera, can you still find the image center using the Orthocenter Theorem? Show why or why not.
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