[photo-3d] 3d equations- New Scientist

["bart kelsey" <attraxe@xxxxxxxxxxx>]

G’day

I have a couple of queries regarding formulae for stereoscopic calculations 
which were published in New Scientist 26 April 1984. I thought it reasonable 
to assume that some of you would be using these equations and may be able to 
clarify some details for me. I have scanned an excerpt from the journal and 
provided it as a .pdf file 1.7MB which can be downloaded from the following 
address:

ftp://photo.med.monash.edu.au/alfred/Pick_Up/3d_equations.pdf


In the following example, to illustrate my confusion, I compared the 
equations when using no axial offset and axial offset of the lenses. You 
will see that the solutions agree when axial offset is employed, but not so 
when h = 0, ie. no offset.

No axial offset of lenses				Axial offset of lenses

M=30								M=30
s = 63 mm							s = 63 mm
e = 63 mm							e = 63 mm
f = 50 mm							f = 50 mm
p = 2000 mm						p = 2000 mm
V = 2200 mm						V = 2200 mm
h = 0 mm							h = 0.6 mm

z = sf/p = 1.575 mm					z = 2h-(sf/p) = -0.375 mm

Z = Mz = 47.25 mm					Z = Mz = -11.25 mm

P = (Ve)/(e-Z) = 8800 mm				P = (Ve)/(e-Z) = 1867 mm

P = (Vep)/(Mfs-[p(2Mh-e)])	equation I		P = (Vep)/(Mfs-[p(2Mh-e)])
when h = 0 						    = 1867 mm
P = (Vep)/(Mfs+ep) = 1257 mm

Notice the two different values for P
However, when I substitute
Z = Msf/p into P = (Ve)/(e-Z)
P = (Vep)/(ep-[Mfs]) = 8800

Why doesn’t equation I work when h = 0 ?
If P = (Vep)/(ep-[Mfs]) has to be used instead of equation I when h = 0, 
then do I have to do new derivations for equations II to IV?

Equation IV reduces to V = Mf when 2Mh-e = 0. In this case the shape ratio 
is uniform throughout the scene. When h = 0,  is it correct to assume that a 
shape ratio of unity can still be achieved?

Finally, in regards to an example relating to figure 7,  it is mentioned 
that the parallax limitation is given by 1/30 times the screen width. Is 
this the accepted way of determining the parallax limitation in front of and 
behind any screen?

If you can help with any of these questions, I would appreciate it.

Thanks

Bart

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