T3D Distortion

[john bercovitz <bercov@xxxxxxxxxxx>]

A friend asked me off-list about measuring distortion using a 
square as the target.  I did a little figuring and the result is 
so simple as to be interesting.  Therefore, I thought it might be 
nice to share the conclusions here.

Distortion is the displacement of an image point from its correct 
position and it goes with the cube of the correct distance from 
the center of the image.  Percent distortion is the displacement 
divided by the correct distance from center so it goes with the 
square of the correct distance (a cubic function divided by its 
own input is a square function).  

If we measure from the center of a square to its side and then 
from the center to a corner, we find the distance to the corner is 
the square root of two times the distance to the side.  If percent 
distortion goes with the square of the image height, then the 
distortion in the corner must be the square root of two squared or 
twice the distortion in the middle of a side.

To apply this info, if we find that the distance to the corner is 
10% longer than it should be compared to the distance to the side, 
then we know the distortion in the corner is 20% and the 
distortion at the side is 10% because 20% - 10% = 10%, the value 
we found when we measured

So distortion in the corner is twice whatever we measure when we 
compare distance to the corner to distance to the side.

John B


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End of TECH-3D Digest 398
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