Calculating perspective camera size at depth

Questions & Answers
1

I’m working currently on a situation that requires me to know exactly how many units of height the camera is interpreting at a certain depth from itself, and without having to cheat or go around a complex system of cheating my way around it.

So what I’m currently working off of is that field of view on the camera is the vertical angle of the camera. So at 45 degrees I would assume that 1 unit of depth should equate to 1 unit of height, and then for width we simply use the aspect ratio.

So at a depth of 10, with a FOV of 45, and an aspect ratio of 16:9 our viewing area should be:

1 unit of height per depth = 10 height.
10 / 9 = 1.11111111111111

  • 16 = 17.77777777777778

So our viewing area in Unity units should be 17.77777777777778 : 10

However this doesn’t seem to be correct. Can someone explain to me why my calculation is not correct?

2

From drawing out the geometry, I get the following calculation for height:

Height = 2 * Tan(0.5 * field_of_view) * distance;

So for your example, the height should be around 8.28 and the width 14.72.