Converging fields of view

[P3D Neil Harrington <nharrington@xxxxxxxxxxxxx>]

John Bercovitz writes:

>>> This relates to the reality of looking through a real window.  Stand 
>>> in front of one in your home.  Close one eye and look.  Then close the 
>>> other eye and look.  The right eye saw more of the left side of what 
>>> was out the window and visa versa for the left eye.
>
>> Right.  Keep in mind, though, that the angles of view of your two eyes must
>> converge and cross _at_ the window in order for the effect you describe to
>> occur.  This is true regardless of whether your eyes themselves are
>> converged on the window or not. 
>
>I'm confused by this.  It seems like at first we're saying that you have 
>to cross your eyes when you look out a window in order to see more of the 
>right side of a scene with the left eye than with the right eye.  That 
>wouldn't be true because if you looked at an object at infinity, you'd 
>see more of the right side of the scene with the left eye.  The next 
>sentence seems to reverse the prior statement.  Anyone care to help me on 
>this?

I probably wasn't as clear as I could have been.  By "the angles of view of
your two eyes" I meant the different, total fields of view _available_ to
both eyes.  Looking at an object at infinity the axes of your eyes are, of
course, parallel.  But there is still more "view" on the right side, looking
through that window, available to your left eye, and vice versa.  If you
watch some object at infinity moving from left to right across your overall
field of view, at some point it will disappear (behind the window frame) to
your right eye, but will still be visible to your left.  The field of view
available to your left eye is not the same as that available to your right.

Now imagine your left eye's field of view, through that window, as a kind of
horizontal pyramid, the apex of the pyramid at the pupil of your eye and the
edges consisting of straight lines from pupil to window corners.  The
pyramid of course extends through the window and to infinity.  (Okay?  I
realize this is one of those things easy to diagram but somewhat clumsy to
describe in words.)  Now imagine the same sort of pyramid for your right
eye.  The two imaginary pyramids _converge_, crossing over as they pass
through the physical window.  On the near side of the window, the right-eye
pyramid is always at least partially to the right of the left-eye pyramid.
On the far side of the window, it's the other way around, which is why the
left eye sees more of the right side of the subject beyond the window and
vice versa.  _At_ the window, the sections of both pyramids are exactly
coincident.

>I think "toed-in" is definitely confusing, but to the cognoscente rather 
>than to the neophyte.  The cognoscente has read "The World of 3D" and 
>similar books which use "toed-in" and "convergence error" to mean taking a 
>pair of cameras and making their axes cross at the window distance or doing 
>the same thing by taking one shot and then moving the camera and taking 
>another shot such that effectively you've done the same thing.  Or by using 
>a rotating or rocker table to get the two views.  I think "converging angles 
>of view" would be in the grey area because it could easily mean "toed-in" 
>although that's certainly not what was meant in this case. 

I'm beginning to think "toed-in" carries some dark or sinister meaning for
others here that it doesn't for me.   :-)   I simply used it in the sense of
"converging at some distance in front of the camera," more or less similar
to the idea of a car's front wheels being toed-in.  I have always tried to
be careful to make it clear I was speaking of convergence of the fields of
view, not the lens axes.



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