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The fifth iteration must generate a proper two-dimensional image through a three-dimensional camera. This model must allow for the light to enter the camera at any angle and offset. To simplify this, the two-dimensional model is used for each axis. The user will input an entry angle in both the X and Y directions, and he will input an entry offset in the same fashion.  
 
The fifth iteration must generate a proper two-dimensional image through a three-dimensional camera. This model must allow for the light to enter the camera at any angle and offset. To simplify this, the two-dimensional model is used for each axis. The user will input an entry angle in both the X and Y directions, and he will input an entry offset in the same fashion.  
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We know logically that the image will not be compressed or stretched by passing through the lenses, as this cannot be seen in photography. First, therefore, we will track the center of the image as it passes through the lenses. This is done using the equation
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We know logically that the image will not be compressed or stretched by passing through the lenses, as this cannot be seen in photography. First, therefore, we will track the center of the image as it passes through the lenses. This is done by calculating the offsets using the equation
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<math> \arctan{\tan{\theta_p}-\frac{X_p}{F}}</math>
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<math>O = F_p * \tan{(\theta_p)}+{(S_p-F_p)}*\tan{(\theta)}</math>
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where the entry angle is defined by
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<math> \theta = \arctan{(\tan({\theta_p})-\frac{O_p}{F}})</math>
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where <math>\theta</math> is the entry angle at a given lens, <math>\theta_p</math> is the entry angle at the previous lens, <math>O_p</math> is the directional offset at the previous lens, and F is the focal length of the given lens.
    
== Aperture ==
 
== Aperture ==
135

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