# QuickTime VR Calculators

## Determining the Field of View from the Lens Focal Length

1. Use table from the QuickTime VR Authoring manual.
2. Compute it with the equation:

`fov = 2 * atan(frameUtilization * filmFrameDim/2 / focalLength)`

3. Use the calculator below:

### Field of View Calculator

Frame Dimension:
units (i.e. mm)
Frame Utilization:
%
Focal Length:
units (i.e. mm)
==>
degrees

The frame size for 35 mm film is 24x36 mm. The utilization is typically 95%.

## Determining the Zoom Ratio Corresponding to 1:1 Pixel Zooming

This is the value you would use for the minimum zoom in order to be at 1:1 magnification. Of course, if you'd like to zoom in closer to see pixels blown up to twice their size, use half this value; to see pixels three times their size, use one third of this value; etc.

1. Compute it with the equation:

`zoomRatio = atan(tan(halfVFOV) * (windowHeight-1) / (cylHeight-1)) / halfVFOV`

where `halfVFOV` is half of the vertical angle subtended by the cylinder, `windowHeight` is the height of the window, in pixels, `cylHeight` is the number of pixels in the axial (not circumferential) direction of the cylinder.

2. Use the calculator below:

### Optimum Zoom Calculator

Window Height:
pixels
Cylinder (axial) Height:
pixels
Cylinder Top Angle:
degrees
Cylinder Bottom Angle:
degrees
==>
degrees
==>
 % for QTVRAS

## Determining Tilt Limits for Asymmetrical Panoramas

Sometimes it is desirable to have a panorama that is not centered on the horizon. This can arise, for example, when there is more interesting stuff above than below. It is difficult to determine the appropriate limits to set on the tilt angle. The calculator below should help. It assumes a square pixel aspect ratio. You need to enter the dimensions of the cylindrical image, as well as a horizon proportion number. This number describes where vertically in the panorama the horizon (tilt = 0) lies, where "0" corresponds to the top, "1" corresponds to the bottom, and "0.5" corresponds to the middle (i.e. 0.5 means the panorama is symmetrical).

1. Compute the limits with the equations:

`top = atan(2 * pi * proportion * (height - 1)) / circumference`

`bottom = atan(2 * pi * (proportion - 1) * (height - 1)) / circumference`

2. Use the calculator:

### Asymmetrical Tilt Angle Limits Calculator

Height
pixels
Circumference
pixels
Horizon Proportion
from top of cylinder
==>
to degrees

Note that the proportion can be less than 0 or greater than 1, though this is rare.

## Determining Panorama Pan and Tilt Ranges

Given a panoramic image size and an idea of the vertical field of view, it is possible to compute the pan range of a partial panorama. By filling in the image dimensions and tilt range into the calculator below, pressing the Pan Range button will compute the symmetric tilt range for an image with a 1:1 pixel aspect ratio. In the following, if the vertical field of view is FOV degrees, then the tilt range is +/- FOV/2 degrees.

Similarly, if you know the pan range but not the tilt range, you can fill in the image dimensions and pan range, then press the Tilt Range button to compute the symmetric tilt range for an image with a 1:1 pixel aspect ratio.

In our Euclidean world, it doesn't make too much sense to have a non-360 degree panorama that wraps, but the calculator will compute a value anyway.

### Pan and Tilt Range Calculator

Panorama Wraps
Cylinder Width (Circumference)
pixels
Cylinder Height (Axial Dimension)
pixels
degrees
+/-
degrees

## Determining the Number of Photographs Necessary to Achieve the Desired Overlap

With a new focal length lens or a new camera, it is desirable to be able to determine the number of photographs necessary to yield the desired overlap. The calculator below can make this easy.

Number of Photographs Calculator
Focal Length
mm
Horizontal Frame Dimension
mm
Minimum Desired Overlap
%
==>

Angular Separation ==>
degrees
Actual Overlap ==>
%

The frame dimension for 35 mm film is 36mm x 24 mm. When capturing photographs in portrait mode, the horizontal frame dimension is 24 mm; in landscape mode, it is 36 mm. However, the entire frame may not be scanned into a PhotoCD, so you might have to make these numbers smaller.

For electronic cameras with a CCD imaging array, use the physical dimensions of the array.

## Vertical Cropping Calculator

Sometimes it is desired to crop a panorama, either in pixels or angle. The calculator below will compute an angle crop from a pixel crop, or a pixel crop from an angle crop.

Vertical Cropping Calculator
pixel row angle (degrees)
top of source
bottom of source
top of crop
bottom of crop

## Determining Tilt Angles to use for Uncorrected Panoramas

### Uncorrected Tilt Angle Limits Calculator

Width (Circumference)
pixels
Height (Axial Dimension)
pixels
Pan Range
degrees
==>
to degrees

## Field of View from EXIF Data

In the images captured by some digital cameras, there is some data that is useful to determine the field of view for stitching panoramas.

Ideally, this would be the focal length in pixels, but unfortunately the focal length is given in millimeters. In order to determine the field of view, it is necessary to know the density of pixels (in pixels per millimeter) on the virtual imaging sensor associated with the image. Again, this pixel density is usually given in pixels/inch, so conversion to pixels/mm is needed as well. The pixel density may be different for the horizontal and vertical directions.

From the focal length in pixels, and the number of pixels in each dimension of the image, it is possible to compute the field of view in each dimension.

To convert from focal length in mm to focal length in pixels, where pixel density is given in pixels/inch, use:

focalPixels = focalMM * pixelDensity / 25.4

To compute the field of view from focal length in pixels, use:

fov = 2 * atan( (H - 1) / (2 * focalPixels) )

where H is either width or height, for the field of view in the respective direction. These equations are encapsulated into the calculator below.

Field of View from EXIF Data Calculator
E
X
I
F

d
a
t
a
FocalLength mm
PixelXDimension pixels
PixelYDimension pixels
FocalPlaneXResolution pixels/unit
FocalPlaneYResolution pixels/unit
FocalPlaneResolutionUnit

c
o
m
p
u
t
e
d
Pixel FocalLength in X pixels
Pixel FocalLength in Y pixels
Field of View in X degrees
Field of View in Y degrees

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