[Sidefx-houdini-list] aperture focal length relations

Jeff Higgins jeffrey.higgins at gmail.com
Fri Jun 22 05:48:28 EDT 2007


cool! lots of useful info i didn't know about!! an asset should really be
put up on the exchange.

my only one very minor comment would be that maybe atan2( l/2, f ) instead
of atan would be preferred to prevent any 180 degree flips!

my 2cents,

jeff


On 6/22/07, Adrian Lee <dryrainstudios at gmail.com> wrote:
>
> All bastards aside...I think an asset would be a very useful thing.
>
> I got this back from the guy who made the aov site. It backs up alot of
> whats said here but I like the txt image. Difference for 35mm film well
> noted -thanks Mario
>
> #####
> That code is not very clean. Anyway the formula is very simple:
>
> --------+---------      image plane
> \      |      /
> \     |     /
>   \    |    /
>    \   |   /
>     \  |  /
>      \ | /
>       \|/
> --------*---------      lens center
>       /|\                         }
>    h / | \                        } f = focal
>     /  |  \                       } length
>    /   |   \                      }
> --------+---------      focal plane
>    |<----->|                      }
>        l
>
> We have above 4 triangles rectangles. So using a bit of trignometry we
> can see the relation between alfa (the angle-of-view), f (focal length),
> l (the dimension in the focal plane) and h (hypotenuse):
>
> (1)     l/2 = h * sin (alfa/2)
> (2)     f = h * cos (alfa/2)
>
> dividing (1) by (2) h disappears:
>
>        (l/2)/f = tan(alfa/2)   <=>
> <=>     alfa/2 = arctan((l/2)/f)
> or      alfa = 2 * arctan((l/2)/f)
>
> In most programming languages arctan gives the result in radians so one
> needs to convert to degrees:
>        alfa = 2 * arctan((l/2)/f) * 180 / PI
>
> #####
>
> Ed
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