mosaic mode maths - an equation, please!

[kfj]

Hi all!

I'm trying to help in a parallel thread

http://groups.google.com/group/hugin-ptx/browse_thread/thread/873b58166bd2ff33/74891be947b6e4b6#74891be947b6e4b6

There is a guy who needs to know how varying the Z parameter
translates into a scaling factor. I thought this was straightforward,
but found it is not: I thought the Z parameter translates into a
linear distance along the optical axis measured from the center of the
panosphere, since the X and Y parameters translate into linear shifts
parallel to the image plane. This would be easy. But I can set Z
beyond 1.0, even up to 100 and further, and the image 'comes closer'
but I never quite get there. So it must be some asymptotic nonlinear
function, and I can't be bothered poking around in the code to find
the formula. Maybe someone can just tell me what it is or point me to
the appropriate place?

with regards
Kay

[kfj]

Hi all!

Maybe my request was overlooked, so I take the liberty to push it up
to the top of the list again before I try again under a different and
maybe more tempting heading ;-)
I did try to look into the code, and gave up after half an hour - I
just couldn't find where the calculation is done.

with regards
Kay

On 7 Dez., 16:59, kfj <_...@yahoo.com> wrote:
>...

[T. Modes]

No equation, but a description can be found in the wiki:
http://wiki.panotools.org/Stiching_a_photo-mosaic

[kfj]

On 10 Dez., 23:59, "T. Modes" <Thomas.Mo...@gmx.de> wrote:
> No equation, but a description can be found in the wiki:

http://wiki.panotools.org/Stiching_a_photo-mosaic

Thank you very much! I was confused, because I thought the Z axis was
going the other way. Now it all became clear: you can have Z values
down to -1, which is when you actually touch the projection plane.
With Z values <= -1 you can't see anything, since the virtual camera
position is on or behind the plane. With rising Z values you move away
fron the projection plane - if an image with the same hfov is then
projected onto the plane, it becomes ever bigger with rising Z values.
So it's linear after all, just my understanding was nonlinear ;-)

So I suppose the following holds true (with rectilinear projection,
all other parameters at default values):

Let d be the distance of the virtual camera from the image plane: d =
Z + 1 , Z > -1

If an image is projected with different Z values, the output sizes
will differ by a scaling factor proportional to the respective d
values

e.g. if an image is processed once with Z = -0.25 and once with +0.5,
the resulting second projection will be twice as large (in width and
height; surface will be four times as large) as the first, since

d1 = -0.25 + 1 = 0.75
d2 = 0.5 + 1 = 1.5
d2 = 2 * d1

with regards
Kay