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Method for determining viewer size
thinnairstudios 2005-Oct-01 19:21:00
A method for determining viewer size in the Quicktime player
This document refers to the following web page for determining
panoramic resolution:
http://www.worldserver.com/turk/quicktimevr/panores.html
Notice that the 12mm perspective format of the calculator always
equals the cube face size. This means that the quicktime viewer uses
a 12mm perspective corrected viewing space.
If this is correct then the following method can be used.
The focal plane of 35mm film is 35mm x 24mm. This is a .686 ratio of
height to width. So I am going to use that ratio for my display size.
According to a table of angles of view for lenses located here:
http://www.acapixus.dk/photography/angle_of_view_15_crop.htm
A 12mm lens in 35mm format has an angle of view of 111 deg horizontal
and 88 deg vertical. If you set the viewer size to the same ratio as
a 35x24mm film format then you will have the same FOV in the viewer
window.
We can set the default field of view in the viewer. The person
looking at the pano can of course zoom in and out and therefore
change the field of view at any time. When this happens the quality
gets worse or better depending on the amount of zooming. But we want
to set the default FOV at the best quality. Keeping the definition of
angular resolution in mind we know that when changing the FOV we also
change the angular resolution. The larger the FOV, the less the
angular resolution and the smaller the FOV the greater the angular
resolution.
What I am getting at is this. The size of the viewing window is
equivalent to 35mm format. So now I ask what is the angular
resolution at a given FOV within the viewer window. Using
the "Resolution of a Perspective Lens" calculator we can find out.
Viewer dimensions are: (823 is .686 of 1200)
1200 wide
823 high
12mm focal length = 111 deg FOV horizontal and 88 deg vertical.
The calculator gives 14.4 angular resolution for an image 1200 wide
with a FOV of 111 deg.
We picked a 13.9 angular resolution to determine our cube faces.
So when viewing the pano in a 1200 x 823 viewer size at 111 deg FOV
we are getting a 14.4 angular resolution. Except that our image does
not have that amount of angular resolution so the image will be
slightly softer than we want. In this case the default FOV angular
resolution should match the pano's angular resolution.
Turns out that 113 deg FOV gives a 13.9 angular resolution. So we set
the default FOV at 113 for this viewer size.
The cube faces are square and the entire image is being mapped to the
inside of the cube. This constitutes our "world". Everything is 1 to
1 in the "world". Now we have to view our world through a viewer,
which is like looking through a lens and panning/rotating the camera.
This is happening on a computer monitor that displays at 72 ?96 dpi.
Method for calculating a viewer size based on our cube face size:
We are starting with an angular resolution of 13.9 and we want to
keep that same resolution in our viewer window at the default FOV we
have set.
First we refer to the "Resolution of a Perspective Lens" calculator.
We input our data as follows:
1594 = this is our cube face size. We use this as the "Dimension of
Image in pixels"
12 = focal length in mm. This is what the viewer is correcting our
perspective to.
24 = We use this number because it represents our viewer heights
ratio to the focal length. Dimension of Objective in millimeters
= 13.9 angular resolution
Notice that 13.9 is the same as the angular resolution we started
with to determine our cube face size. So this confirms our method is
working correctly.
Next we move to the same calculator but calculate angular resolution
based on image size and FOV. Here is where we determine the viewer
size
1200 = width of or viewer window
113 = angle of view we determined earlier
= 13.9 angular resolution.
What this tells me is that I need to set a viewer window size of 1200
x 823 and a default FOV of 113 to achieve a 13.9 angular resolution.
13.9 is what the cube faces are. So when we view the pano the image
will have the same angular resolution that the cube has and therefore
give us the best sharpness possible at this viewer size.
To illustrate further:
Consider a viewer size of 1000 x 686
1000 = window viewer width
111 = angle of view if using a 35mm film format.
= 12.0 angular resolution
12.0 is less than our known cube face angular resolution. We try a
few more numbers to make the size yield a 13.9 angular resolution at
111deg FOV
We find that 1160 wide yields an angular resolution of 13.9 at 111
deg FOV.
Now, realize that you can create a 13.9 angular resolution by
changing the width and FOV.
For example:
670 wide at 80 deg FOV = 13.9 angular resolution.
This means things are on a sliding scale. The larger the viewer
window the greater the FOV can be to keep the same angular
resolution.
In the 670 wide scenario we have to set the FOV at 80 to get 13.9
angular resolution. This creates a zoomed out pano at the start. Now
perform some more calculations but change the FOV only. Notice that
changing the FOV to 111 deg creates an angular resolution of 8.0
This means that to get the FOV to the correct number that represents
the perspective corrected 12mm lens on a 35mm format we have to
increase the size of the viewer window.
In other words a 670 wide window at 80 FOV will have 13.9 angular
resolution but it will look distorted. If you change the FOV to 111
your angular resolution drops to 8.0, therefor making your pano look
like crap. At this size you can have an angular resolution of 13.9
but with a really distorted image. Not good.
Conclusion:
We are striving to create a viewer window with a 111 deg FOV that
will yield an angular resolution equal to our cube face angular
resolution. Further, we are attempting to create a viewer window with
a default FOV that that will match our cube faces angular resolution.
We want the viewer window size and FOV to be perspective corrected to
the focal length the viewer is displaying which is 12mm.
This means if you use a 35 x 24 mm width to height ratio then the
viewer window will have 111 deg FOV horizontally and 88 deg
vertically. If you use another ratio you will have to figure out what
the FOV is for that format size. You could then calculate angular
resolution for your viewer size and FOV. But since the viewer is
using a 12mm perspective corrected format you may have some problems.
Without doing the math I am guessing that it may be possible to use
another ratio and follow the above procedure and end up in the same
place but I am not sure. Beside we are used to looking at a 3 x 5 or
4 x 6 sized photograph. So keeping this same ratio for displaying a
pano makes sense to me.
Troy Ward