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

[chrisp@xxxxxxxxxxxxxxxxxxxxxxxx]

Hello Bart

I now understand where your problem lies, and I now see that I had 
not spotted the problem in the article. I had just accepted that z = 
2h-(sf/p).

I think you are correct that z = 2h-(sf/p) is not the case.

In your calculations for z, Z and P when h>0, a negative value of 
parallax would mean that you would have to cross eyes to see the 
image - clearly not the intention of the author of the article. And 
the object in the image (P) has now shot from 6.6 metres behind the 
screen to 31cm infront, just by decreasing the inter-lens separation 
from 63 mm to 61.8 mm. Anybody experienced in stereo imaging will 
tell you this does not ring true.

Thinking logically, if h is the movement of each lens inwards, then 
parallax (which begins at z = sf/p) would decrease by 2h.

So surely z = (sf/p)-2h.

You are correct that equation I does not work, because it is based 
upon false equations for z and Z. The correct equations are, if I am 
correct:-

z = (sf/p) - 2h

Z = M(sf/p - 2h)

     Ve          Vep
P = ----- = -------------       equation I
     e-Z     ep-Msf+2hMp

And likewise equations II, III, and IV  DO have to corrected, as you 
originally wrote. However, I think it would be easier to forget the 
special case of h=0 and create equations that include h and would 
work whatever the value of h.

It is possible that this problem in the article has been noticed 
before. Was an errata note published in a later issue ?

Do you agree with my result for equation I ? When h=0 is substituted 
into this, P=Vep/(ep-Msf) which you believe gave the correct answer.


Chris






--- In photo-3d@xxxx, "bart kelsey" <attraxe@xxxx> wrote:
> Dear Chris
> 
> Thankyou for taking the time to respond to my questions regarding 
3d 
> equations.
> 
> You clarified the second and third questions I posed however, I am 
still a 
> bit unsure when applying equation 1. May I trouble you one last 
time to end 
> my frustration?
> 
> I can see from the geometry where z= sf/p comes from, but not z = 
2h - 
> (sf/p).
> I have it in my head that the total parallax should be z = 2h + 
(sf/p).
> Could you straighten me out on this one please.
> 
> I understand that the value of P will change depending on the value 
of h. 
> This wasn't the point of confusion. In the example of no axial 
offset I 
> substituted Mfs/p for Z in the equation P = (Ve)/(e-Z). The 
equation reduced 
> to P = (Vep)/ (ep – Mfs) which gave the correct answer.
> However, substituting  h = 0 into equation 1 did not reduce it to P 
= (Vep)/ 
> (ep – Mfs), but to P = (Vep)/ (ep + Mfs), thus giving the incorrect 
answer. 
> This is why I asked, why doesn't equation 1 work when h = 0? I'm 
still 
> unsure of this one.
> 
> Thanks for pointing out my error in the case of axial offset.
> 
> I look forward to a response at your convenience.
> 
> Thanks
> 
> Bart