Re: The Gordonian knot

[T3D john bercovitz <bercov@xxxxxxxxxxx>]

I had a period of time of enforced inactivity last night so I 
thought some more about the problem I delineated in T3D digest #4.  
Turns out the problem was only in my own mind, as I suspected.  
8-)  Let me review the problem:

If you take a picture of a flag pole at night against a background 
of stars, and the stereo camera's back lies in a plane which is 
parallel to the pole, then the two images of the pole are parallel 
to each other and also have a constant parallax relationship with 
the stars behind them.  So how do we establish the distance of the 
different sections of the pole and how do we properly determine 
its distance relationship with the stars? 

The solution is to think of the pole as being against a unique 
background of stars; these stars form a line which is parallel to 
the pole but located at infinity.

As you look at the two images of the pole on the projection screen 
(with no polarizing glasses on), you see that the pole images are 
the same distance apart all the way up and down the screen.  When 
they are at the top of the screen they are farther away from you 
so that that constant separation translates into a smaller 
parallax which makes the upper end of the pole appear farther 
away.  I got that far in my previous post.

Now look at the relationship of the pole to the line of stars 
behind and parallel to it.  Again the separation on screen is 
constant but as you look up to the top of the pole, that 
separation between the pole and the line of stars is farther away 
from you and therefore subtends a smaller angle at your eyes 
indicating that the upper end of the pole is closer to the stars 
than the the lower end which is of course closer to you.

In conclusion, there is no inconsistency in spite of the fact that 
all of these various images are parallel to each other and lie at 
a constant separation on the screen.

John


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End of TECH3D Digest 24
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