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I'm currently in the process of writing a 2.5D application that should display the perceived size of an object. For example, When I have a ball that has a diameter of 1 meter, how big would it appear if the ball would be 5 meters away from me? I know that there is angular diameter, but how can I translate the angle that I get to a size or scale?

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closed as off-topic by dmckee Jul 5 '13 at 0:38

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You have the object's distance and real size and you already know how to calculate the angular diameter. You want to translate this angle to something more intuitive, for readability? –  Diego Oct 22 '11 at 14:43
Our FAQ disavows computational questions and programming questions are clearly off topic here. This sounds like it belongs on either gamedev.stackexchange.com or perhaps ux.stackexchange.com as there isn't a lot of physics in it. There are very standard ways of defining and managing the "camera" and "viewport" to get the projection of objects into the raster frame: you don't need to re-invent this stuff. –  dmckee Jul 5 '13 at 0:37
This question appears to be off-topic because it is about graphics programming techniques. –  dmckee Jul 5 '13 at 0:38
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1 Answer 1

It is not entirely clear from you question which scale you want to translate it to.

An angular diameter corresponds to different spatial distances depending on the distance to the object or surface of projection, so you have to make a choice regarding this before you can get any further.

Once you have done this, if your "ball" is small compared to the distance to it, you can use the small-angle approximation:

$$ \theta_{arcsec} = 206,265 \times\frac{d}{D}, $$

with $d$ and $D$ being the size of and distance to the object, respectively.

How to achieve this in practice depends entirely on the details of your project.

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