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

[chrisp@xxxxxxxxxxxxxxxxxxxxxxxx]

--- In photo-3d@xxxx, "bart kelsey" <attraxe@xxxx> wrote:

"I have a couple of queries regarding formulae for stereoscopic 
calculations 
which were published in New Scientist 26 April 1984. ... 
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 


Hello Bart

I dont want to put myself forwards as an expert, but I eventually 
managed to download your pdf and get my head around the mathematics. 

"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 dont know if you realise, but the calculations in the New Scientist 
article were created specifically for moving pictures. Stereo stills 
photographers,who predominate on this list, tend to use other 
mathematics or, more often, just their own judgement.

"In the following example ... No axial offset of lenses  s = 63 mm 
Axial offset of lenses  s = 63 mm"

Surely if there is axial offset then s, the distance between lenses, 
changes. The article defines offset as the movement of each lens 
inwards, towards each other. Therefore when h>0, s=63-2h. Your 
calculations for the case of axial offset are surely therefore 
incorrect.

"Notice the two different values for P"

Are you saying this is where your confusion lies ?  P  DOES vary 
depending upon the value of h chosen. You can control the appearance 
of the third dimension in the final image in this way

"However, when I substitute
Z = Msf/p into P = (Ve)/(e-Z)
P = (Vep)/(ep-[Mfs]) = 8800"

Again I am not certain where your lack of understanding lies. This is 
the correct value for P when h=0, as your calculation showed.

"Why doesn't equation I work when h = 0 ?"

Again I am not certain. How does it not work ?

"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?"

You can if you wish, or just put h=0 into the equations. Whatever you 
feel comfortable with. I gather it is common to use tables drawn up 
from these equations when "in the field". Experienced camera 
operators should already have a good idea of what adjustments to 
make. You dont even need to be mathematically exact. Indeed, artistic 
license can be used to expand or contract the depth - eg elongating 
someones nose when filming a face.

"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?"

Equation IV only reduces to V=Mf when 2Mh-e=0  AND  shape ratio =  1.
When h=0 I think you have to assume that no human eye separation (e) 
can make 2Mh-e=0. So NO, when h=0 there will never be a unity of 
shape ratio.

"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?"

Parallax limit of 1/30 of the image width is a generally accepted but 
not strictly exact measurement. It is determined by the ability of 
eyes and brain to fuse the two images, which varies widely in humans. 
1/30 can be comfortably fused yet still provides a fair amount of 
depth effect.

Whether the effect is in front of or behind the screen depends upon 
where the object (as measured by P) is in relation to the "stereo 
window", which is a whole new set of calculations.

Chris Pickering