[tech-3d] Re: Different F.L.s

["Michael K. Davis" <zilch0@xxxxxxxxxxxx>]

Hi David!

>Date: Sun, 04 Feb 2001 03:48:13 -0000
>From: siggyblue@xxxxxxxxx
>Subject: Re: Different F.L.s
>
>Thanks Mike, 
>this answers my question.  I'll give it a try.  Just out of curiousity 
>why do you use your formula over the other two you referenced in 
>your letter?
>Thanks again,
>David

I consider "my" formula to be identical to the one Bercovitz uses with the
only enhancement being to accomodate the fact that my camera lens FL's
don't match the 78mm viewer FL I use.  I'm fairly certain, without having
to ask, that folks like Bercovitz, Spicer, Deering and others who use the
so-called "Bercovitz" formula (a.k.a. The General Solution), understand
that this formula assumes camera FL is equal to viewer FL and thus, would
also adjust the calculated stereo base proportionate to any mismatch in
FL's, just like I do.  

That said, your question above is reduced to: "Why do you prefer your
formula over David Lee's formula."  First, I'm not as quick as I used to be
and my geometry and math skills aren't what they were twenty yearts ago,
but with considerable brain strain, I one day managed to correlate the
formula Bercovitz uses to the geometry illustrated at the top of this page:

   http://home.mira.net/~kiewavly/bases.html

In short, I use the formula because it matches the geometry perfectly.  The
math is correct.  That's all there is to it.  Any other formula is just an
approximation of the truth, which isn't necessarily a bad thing at all, if
you want to take a short cut that delivers enough accuracy to satisfy your
personal requirements.  

For example, David Lee's formula is actually very clever.  I think he
home-brewed it from his raw understanding of how to adjust the base to
deliver a consistent look of depth, or "stereo bite", as some people call
it.  I have a spreadsheet that accepts all the variables for calculating
base using both formulas.  Having run many scenarios through both formulas
I can tell you that David Lee's formula delivers results that are nearly
always very close (+/- 5% or less) to the results I get using the formula
Bercovitz uses.  Let me qualify that by saying this is true ONLY when one
specifies a deviation value in the Bercovitz formula EQUAL to MAOFD.  So, I
can say that David Lee's formula nearly always comes close to calculating
the same stereo base that will deliver Maximum Acceptable On-Film
Deviation.   

Where Bercovitz's documentation on the subject specifically encourages
users of the General Solution to specify a DESIRED value for the deviation
variable (i.e. something other than 100% of MAOFD, where MAOFD equals
Camera FL/30) David Lee's formula has a hard-coded deviation of FL/30,
which is expressed as the constant 1/30 in his formula shown here:

http://home.mira.net/~kiewavly/bases.html

So, where those who understand the Bercovitz formula treat the deviation
variable as A VARIABLE, David Lee's formula is FIXED to calculate only the
maximum base an audience would find acceptable.  Before anyone thinks I'm
beating him up for being rigid about this, let me intercept that by saying
it's my observation, from his writings, that David Lee is not at all bound
to his calculator nor the formula shown at that link.  In fact, he
encourages us to use his formula without a calculator, if possible, since
the math is far simpler than that of the General Solution.  AND:  He
doesn't lock himself to the figure his formula generates.  Again, from his
writings, I think I'm correct in saying that he relies on his experience to
decrease or even increase the base calculated by his formula as he sees fit.  

I on the other hand, have not yet invested the time he obviously has in
shooting stereo, so I am unwilling to depart from the geometry - I'm forced
to stick close to the math.  I've done my homework and to date, my
stereography has empirically proven that the General Solution can be
trusted to deliver consistent results.  Many people who have tried it
failed to employ the deviation as a variable and thus calculated only base
separations that delivered 100% of the Maximum Acceptable On-Film Deviation
- a deviation that is right on the cusp of what the average person
considers to be comfortable to look at - never mind the undesirable
aesthetics of having so much "bite" in every image.   

The "right" way to employ the General Solution is to treat deviation as a
variable, not as a constant fixed equal to FL/30.  That's why the acronym
MAOFD begins with the words "Maximum Accetable".

Try shooting several scenes, where you make test exposures for each scene
at 100% of MAOFD, 90%, 80%, 70% and 60% of MAOFD.  (If using a two-camera
setup, make sure to select subjects where the Near Point is far enough away
that a calculated base for 60% MAOFD can still be achieved before your
cameras run into each other on the slide bar.)  I suspect you will find
that you don't want to shoot at 100% of MAOFD all the time.  As I stated in
my earlier post, I have settled on calculating a base that will deliver 70%
of MAOFD.  

I'm currently using this deviation (0.70 * FL/30) for every situtation
except when the Far:Near ratio drops below 2:1 - where I use an adaptation
of the 1/15th rule (Near/15) because at these ratios, when the subject
itself becomes quite shallow from Near to Far, if I stuck with the General
Solution, I would want to use increasingly smaller values for the deviation
variable as the Far:Near ratio approaches 1:1 - and frankly, that's too
much work.  So instead, I rely on the linear nature of Near/15 to
"automatically" reduce my on-film deviation appropriately.  In short - I
like the results this gives.  This choice I've made does not at all
diminish the accuracy or validity of the General Solution.  Remember, the
General Solution allows you to specify ANY value you want in the deviation
variable.  Sticking with 70% of MAOFD just doesn't appeal to me when the
Near:Far ratios drop below 2:1, and again, tapering it for various sub-2:1
ratios is just inconvient compared to shifting to a linear solution.

Above, I said I use an adaptation of the 1/15th rule - I don't actually use
Near/15.  I use this formula at Far:Near ratios less than 2:1

	Base = (Viewer FL / Camera FL) * 0.70 * Near/15

The linear equation (i.e. this plots as a straight line):

	Base = Near/15

just happens to intercept the 100% MAOFD General Solution curve (i.e. not a
straight line), when the Far:Near ratio equals 2:1.

Since I don't shoot at 100% MAOFD deviation when calculating the General
Solution, I synchronize my use of the linear Near/15 rule to my use of the
General Solution, by applying the same modifiers (for 70% MAOFD and
accomodating FL mismatch.)

Here are the actual formulas I use in the field (with an HP48G+ calculator):

Base=(FL/30*(VFL/FL)*(%MAOFD/100)*(304.8*Near*Far/(Far-Near))*
                  (1/FL-1/(2*(304.8*Near*Far/(Near+Far))))

Base21=(VFL/FL)*%MAOFD*Near/15


Base:	Stereo Base Separation (mm) for use when the Far:Near ratio is
greater than or equal to 2:1

Base21: Stereo Base Separation (mm) for use when the Far:Near ratio is less
than 2:1

Variables:  
FL:		Camera Lens Focal Length (mm)
VFL:		Viewer Lens Focal Length (mm)
%MAOFD:	Percentage of MAOFD desired (expressed as 70 for 70%, for example)
Near:		The distance to the Near subject (feet)
Far:		The distance to the Far subject (feet)

Mike Davis


------------------------ Yahoo! Groups Sponsor ---------------------~-~>
eGroups is now Yahoo! Groups
Click here for more details
http://click.egroups.com/1/11231/1/_/520353/_/981315448/
---------------------------------------------------------------------_->