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 1meter, 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 tranlate the angle that I get to a size or scale?
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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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