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yahastu

tricky transformation relationship [solved]

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Start with a set of coplanar points in 3 dimensions. Now given an arbitrary camera point, project those coplanar points onto the cameras image plane and then throw away the Z component. Do the same thing for another camera point. Now, how can the transformation between these two sets of 2D points be described? If the first camera point was looking normal to the plane, such that all of the Z components were constant, then the final transformation could be represented by a 3D rotation and translation matrix followed by a perspective projection...but I'm not sure if this still holds if neither of camera points were looking normal to the plane. [Edited by - yahastu on December 2, 2008 12:18:45 AM]

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The transformation between those two sets of 2D points is a morphism of projective spaces (sometimes called a "projectivity"). This basically means that if you express the 2D points using homogeneous coordinates (so 3 coordinates per point, not all zero and where two triples represent the same point if they are proportional), the transformation can be described as multiplying by a 3x3 matrix.

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