FOV Effect

 

Download scene here: CamRig_DB
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This scene will simulate the effect used many times in films. Where the main object is in the foreground and the whole background moves outward from the camera leaving the main object in the same place.

The relation is trigonometric. Two right triangles formed between your camera and the frame at your object position.

/__FOV
\___ |___ /
_\ __|__ /
__\ _|_ /
___\ | /
__.
cam

and here's the trig triangle

sin(a)
\ ____.____| c
_\ ____.___| o
__\ ___.___| s
__
h \_____ | (a)
__y _\ ____|
__p__ \ .._,,|
______\ __|
_______\a.|
________\ |

a = half the camera angle cos(a) would be your measured distance or "ctr_dist_cam(FOV.)" in expression lingo.

In the sample database, there's an interactive camera rig setup which does exactly what you want.
You can move a rectangle around your scene which controls the camera FOV and image format.