P3D Re: RE: What is the "Stereo-Base"?

[abram klooswyk <abram.klooswyk@xxxxxx>]

David B. [B. for Ben-Gurion?] wrote (5 Nov 1998, P3D Digest 3056):
>(...) And some would say: 1/30 from the nearest object. 
>*Rubbish* - Those answers is good for amateurs!  
>(...)I found this formula provided by David Kuntz in the ISU 
>STEREOSCOPY:
[Which nr, year ? Please  don't cut down on reference details]
>   i   *   b  
> ----------     =    n
>       p
>i = focal length, in mm.   b =baseline, in feet. 
>p = parallax (1.2 mm for infinity far point) 
>n = near point, in feet.
>And I have got some q. about this formula (...)
>C. I know the near point, and I want to calculate
>   the "base-line" - How can I do that?

Michael Kersenbrock answered (same day,P3D Digest 3057, excerpt):
>         n * p  
>  b =  ---------
>           i

George Themelis (again 5 Nov 1998, P3D Digest 3057):
>>A. What "parallax" is?
>Another term for it is "on film deviation" or OFD. (...)
>Please direct further mathematical discussion on this to tech-3d.
-------------

I'm sorry to interfere in such a peaceful discussion.  Just a few 
remarks, even if I'm risking a FB Investigation, before going to 
Tech-3d. But we cannot leave subscribers to this list strolling 
around in errors, can we? :-)  

1. The formula as quoted from Kuntz is *not* a stereo base formula. 
If anything, it is a formula for near point distance, it computes
minimal near point distance for a *known* stereo base. 
When you know your stereo base in *advance*, by using a stereo
camera or a fixed coupling of monocamera's, then all you need 
is to compute the near point distance once and for all.

But Michael rearranged the equation to get a stereo base formula, 
answering David's question C.  Indeed, a formula for X should 
read:  X = ....   (I hate *Rubbish* :-)) 

2.But the quoted definition of parallax is incorrect; 
"p = parallax (1.2 mm for infinity far point)" is *not* a good 
definition.
Parallax is *not* the same as on film Deviation. Leaving apart 
a Star Trek Voyager episode, the definition of Parallax should follow
the one in astronomy, so it is a difference of direction, it is an 
angle, measured in degrees, minutes, arcseconds, radians.

Deviation is a distance, measured in millimeter, meter, inches, feet,
miles, light years,...
(I know you said it George to simplify basics. But I believe we must
stick to correct definitions, even if that is a little more
complicated, and even on this list :-). )

Parallax is independent of focal length, deviation not.
[The FBI formula quoted by George (5 Nov 1998, P3D Digest 3057)  
seems to use the same strange definition of parallax. I could 
not find it on Dan Shelley's 3D-CD in the p3d archives.]

3. So the rearranged formula still is confusing.
Replace p (parallax) by d (deviation); and please use f for focal 
length (instead of i) to get:
       n * d  
b =  ---------
         f
Rearranging this a little again at last (:-)) gives a meaningful
stereo base equation:

      d  
b =  --- * n        
      f
 
It is meaningful because f is what you got in buying a lens, d is 
what you need for your stereo mounting and viewing system, so 
you *know* both in advance when you set out to take pictures, 
so you can compute d / f in advance too (working focal length
ignored). 
When you can vary base length, then n is what you choose on the 
spot where you take a picture, and finally you can compute b.

Now the quotient d / f  *is* the parallax (the parallactic angle in
radians).  If  d = 1.2 mm (the standard for 5P mounts) and f = 35 mm
(as it is in 5P camera's, the Realist family) then we get:
b= 1/30 n
Indeed! Base is 1/30 from the distance of nearest object.
This works for *any* format, when using a focal length which is 
'normal' for that format, and when viewing is 'normal' too.

When sitting in the 'orthostereo seat', viewing projection of a standard
5P slide, the change in eye convergence, from looking at the stereo
window
to looking at 'infinity', is about 2 degrees or 1/30 radian. 
>From there come the parallax and deviation constraints in the 5P system, 
it starts with viewing. 
Indeed, all stereo base computation or estimation should be based on 
the mounting and viewing system that will be used.

I don't say anyone should use 1/30, or any formula for anything ever.
I  dismiss any warranty. :-) We're all amateurs of something. 
Further discussion on Tech-3d. 

Abram Klooswyk


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