T3D Re: MAOFD in words and pictures

[abram klooswyk <abram.klooswyk@xxxxxx>]

Dear John,

I have read the draft. I am planning a text on the history of stereobase
calculations. Then I will also discuss some of the issues of your draft. 
Preparations will take some time.

For now only a small detail which probably is hair splitting (or
mosquito 
sifting, as said in Dutch). But as you seem to plan a FAQ, details
should
also matter.

Parallax is a notion which originally comes from astronomy. Koo Ferwerda
studied astronomy and mathematics, he wrote a thesis on an astronomy
subject.
As I have quoted in TECH-3D Digest 379, 07 Oct 1998, he has said of
parallax:
[In accordance with the] definition of parallax given in astronomy,
[the]
parallax of a point of the subject is the angle between the lines
connecting
the subject point with two different viewing points (...) for instance
two 
eyes ...[or] two lenses (...). 
[from The Third Dimension, No 69, spring 1976, pages 24-38]

A similar description is in Ferwerda's book "The world of 3-D" 
(3-D Book Productions 1987,  http://www.stereoscopy.com/3d-books),
in chapter 24.1, pages 233-234.

The Penguin Dictionary of Science (quoted from the fourth edition) says:
Parallax. 1. The difference in direction, or shift in apparent position,
of a body due to the change in position of the observer. 
2. [follows a similar definition with an astronomy example].

These definitions are consistent with the notion of viewfinder parallax,
well known in (mono)photography.

So the angles rp and lp of your draft are *not* parallax angles, and I
think we should *not* re-define parallax to mean what you wrote.
In your "real life example" both angles subtented at object a and at
object b are parallax angles, lets call them angle A and B.

The difference between A and B is the *parallax difference* which
matters in stereo viewing, and therefore in stereo picture taking.
In more loose discussions the "parallax difference" often is called
"parallax" for short, I have done this too, but in a FAQ this should
not be done in my opinion. 
Parallax difference is also an angle of course, and it is easy to show
 that the difference between A and B is the same as the difference 
between rp and lp. 
That however is no justification for changing the definitions.

In your drawing "projected stereo example" it would be clearer (in my
opinion) if the viewing lines were continued as dotted lines behind 
the screen.

A similar issue (not adressed in detail in your text) is the definition
of "deviation".
Ferwerda uses the term deviation for the difference of the on-slide
separation of the homologues of a certain point with the separation of
infinity homologues. 
On an uncut filmstrip only infinity homologues have the same separation
as the optical axes of the lenses of the stereocamera (toe-in excluded).
So only infinity homologues have a zero deviation.

This strict definition means that a far point, closer than infinity
has a small deviation, and that near points have a larger deviation.
Again the *difference* in deviation plays a role in stereo viewing
(which also depends on other viewer or projection parameters).

Here too "deviation" often is used for "difference of deviation".
There is no harm in using the shorter forms as long as the concepts
are clear. But in a text *on the concepts* strict formulations are
required in my opinion.

It is easy to show that, in using a stereocamera, the parallax 
difference, expressed in radian, is equal to deviation difference 
divided by the (working) camera focal length.

Abram Klooswyk


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