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Fundamentals for Coping
To get accurate solves when a nonzero anamorphic distance is present, we need to take it into account, with a simple modification to the basic perspective transform. Simplifying that a bit, the normal perspective transform is like this:
U = (k / s) X / Z and V = k Y / Z
where (X, Y, Z) are the 3-D coordinates of some point in the camera’s local coordinate system, and (U, V) are the points 2-D coordinates in the image plane, and s is the anamorphic squeeze.
With an anamorphic distance ad, those equations are simply these:
U = (k / s) X / Z and V = k Y / (Z + ad)
Notice that ad appears only in the V (vertical) coordinate.
From these equations, you can see that if Z , the distance to the object, is much larger than anamorphic distance ad, then U and V are very similar to their original values; the anamorphic distance only affects closer objects.
It’s mathematically impossible to replicate this modified perspective transform with a 2-D lens distortion; a lens distortion is the wrong tool for the job.
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