Converging fields of view

[P3D Neil Harrington <nharrington@xxxxxxxxxxxxx>]

John Roberts writes:

>>If you define the "field of view" as the pyramid within which points will be
>>imaged on the film, then you may think of these pyramids as converging.  This
>>contains little information about the geometry of the cameras and is why we
>>avoid the use of the term.
>
>I think that's a good point. In principle one could have a 2-lens camera
>the axes of which *diverge* by 30 degrees, but if they have a wide field
>of view and all but the (more or less) overlapping parts of the field of view
>are masked off, we could say that the camera has "converging fields of view",
>but that would leave out some important parts of the geometric description. :-)

Well, 30 degrees of divergence seems a little extreme, but you could indeed
say that the camera had converging fields of view as long as there was
enough overlap and the appropriate parts were masked off.  Obviously it is
pretty hard to imagine why anyone would want to build a camera that way,
other than to prove this particular point.

As John Bercovitz has pointed out, the lens axes are parallel in order to
keep the planes of best focus coincident with the parallel film planes, and
the film planes are parallel in order to avoid keystoning.  So _those_ are
the "important parts of the geometric description" when one is considering
those particular characteristics, while convergence of the fields of view is
the important part of the description when considering window distance.

>The word "convergence" has many definitions and interpretations - by the
>broadest definitions, any 2-camera system where the two views are not
>*totally* different would have convergence - the term doesn't really mean
>anything significant. 

In previous messages here, convergence of fields of view has been defined as
convergence of the lines passing from the centers of the frames through the
centers of the lenses.  That seems descriptive enough and "significant"
enough to me.

>A narrower definition which has sometimes been used
>in the field of 3D implies a toe-in of the lenses (the axes of the two lenses
>intersect at some finite distance). 

It's been explained a number of times here that converging fields of view
neither means nor implies converging lens axes.  That's another issue entirely. 

>In this sense, saying that "the two
>fields of view converge", while technically true by the broader definition,
>can be misleading to people who work in 3D, because they see the word
>"convergence" and jump to the narrower interpretation of toed-in lenses.

The remedy, then, is simply not to jump to that different interpretation.

>It certainly misled *me* - I own a Toshiba 3D camcorder, and when I read
>about how to adjust the "convergence", I automatically assumed that it meant
>toe-in of the lenses - it never occurred to me that it might refer to a
>lateral adjustment of the sensor. 

Same remedy.

>The (main) purpose of language is to convey information as clearly as
>possible. There are usually several different ways to express a given
>concept. If one of these ways confuses people and causes them to get the
>wrong idea, then it's time to decide whether to use an alternate expression
>or to launch an educational campaign to convince people to accept the "true
>interpretation" of the expression. If the expression in question is really
>pretty vague and doesn't convey much information, and alternative expressions
>are much more precise and already widely accepted, then it will probably be
>more useful to go to an alternate expression.

Some concepts may be a bit more complex than they seem at first glance, and
it is probably unavoidable in such cases that at least some people will "get
the wrong idea" at first.  If the complaint about converging fields of view
is that that expression "is pretty vague and doesn't convey much
information," it certainly is no improvement to use any "alternate
expression" which _ignores_ the fact of converging fields of view, since
without that grasping that fact one cannot really understand the concept of
window distance.


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