Angle of view formula

[Guest GeneticAlgo]

To calculate the angle of view in a pinhole camera the formula:

 

[MATH]\theta = 2 tan^{-1}\frac{h}{2d}[/MATH]

 

where:

 

theta is the angle of view

h is the height of the camera

d is the depth of the camera

 

To help visualize this, I will try some ASCII art showing the camera...

                y axis
  ______________
 |             |
h |             |
 |-------------|------------ z axis
 |             |
 |_____________|
         d

If you draw a line from the top left of the camera through the intersection of y and z and draw a line from the bottom left of the camera through the intersection of y and z the angle between these two lines (on the +z side) is the angle of view (or theta).

 

 

My problem is I am reading the formula to say 2 times tan power negative 1 which doesn't seems to be valid. How exactly do I read this formula?

 

Then, lets say I know theta (the angle of view) and h (the height of the camera), I should be able to work out d (the depth) by solving the equation right? I'm not sure exactly how to do this, it could be because I don't know how to interpret 2 tan ^ -1 but can anyone help?

[The Rebel]

It means inverse tan. Another way of writing it would be

 

theta = 2 * arctan(h/2d)

 

also

 

d = h / {2 * tan(theta/2)}

[Guest GeneticAlgo]

Thanks Rebel, solved it now.