PanoTools:
RE: Are Nomad Nodal Points really Circles of Confusion?
Erik Krause 2006-Mar-05 16:06:59
On Sunday, March 05, 2006 at 13:44, Serge Maandag wrote:
> Michel Thoby measured the NPP for various angles some time ago. That
> inspired me to do some thinking about the subject and I summarized it
> on this page: http://pano.maandag.com/index.php?id=57
>
> Later I came up with this idea:
> http://permalink.gmane.org/gmane.comp.graphics.panotools/38677
http://article.gmane.org/gmane.comp.graphics.panotools/38677 works
better.
...but it is probably not worth bothering with the different
locations of the NPP: From your diagram I see that the seam location
varies between 60° (around) and 90° (zenith). From Michel's diagram
<http://michel.thoby.free.fr/Blur_Panorama/Nikkor10-
5mm_or_Sigma8mm/Sigma_or_Nikkor/Graph_No-Parallax10-5.jpg> I see that
for the Nikkor 10.5 the NPP varies between 16.3mm and 14mm for this
angles.
Even if you place the NPP in the extremes parallax will be low for
standard shooting situations. Given the nearest point in an overlap
is 1 meter away and the farthest is at infinity. Maximum displacement
of the NPP will be 2.3mm. For 6 shots around (each 60° apart) the
parallax for the 1m away point will be 0.13° which in a 6000x3000
pixels equirect will be an error of 2.2 pixels. For the Zenith the
seam is at 90° which gives 0.18° (3 pixels) parallax for the 1m
situation.
If you place the NPP in between the extremes the maximum displacement
will be 1.15mm, the parallax for the 1m situation will be 0.07° (1.2
pixels) around and 0.09° (1.5 pixels) for zenith.
I suspect that stitching errors are higher in most cases - especially
if the lens correction parameters are not calibrated well.
The formula to calculate the above:
Alpha - half the rotation angle of the camera.
Beta - half the parallax angle for a point in a given distance.
d - distance of that point from the rotation axis.
r - displacement of the NPP from the rotation axis.
There are two exact formulas (I hope I got them right ;-) for a
displacement in front and rear of the NPP:
Beta=arctan((r*sin(Alpha))/(d-r*cos(Alpha)))
Beta=arctan((r*sin(Alpha))/(d+r*cos(Alpha)))
They give almost same results for practical values of r and d,
because d normally is far larger than r. Hence they can be
approximated by:
Beta=arctan((r*sin(Alpha))/d)
best regards
--
Erik Krause
Resources, not only for panorama creation:
http://www.erik-krause.de/
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