This is something I've been wondering for a long time. Is there a law that states when something is x meters away, it's apparent size is modified by a factor y?
I'm asking out of pure curiousity. So far I haven't been able to find anything.
Is there a law of perspective?
Moderators: gmalivuk, Moderators General, Prelates
 danpilon54
 Posts: 322
 Joined: Fri Jul 20, 2007 12:10 am UTC
Re: Is there a law of perspective?
Yes. Read about solid angle
http://en.wikipedia.org/wiki/Solid_angle
It is not exactly what you mean by a measure in meters how big it looks, because then you'd have to define what a meter looks like (how far away do you stand from the meter before you look at it?). Instead you can define a perspective dependent size of an object by how much solid angle it subtends.
http://en.wikipedia.org/wiki/Solid_angle
It is not exactly what you mean by a measure in meters how big it looks, because then you'd have to define what a meter looks like (how far away do you stand from the meter before you look at it?). Instead you can define a perspective dependent size of an object by how much solid angle it subtends.
Mighty Jalapeno wrote:Well, I killed a homeless man. We can't all be good people.
 You, sir, name?
 Posts: 6983
 Joined: Sun Apr 22, 2007 10:07 am UTC
 Location: Chako Paul City
 Contact:
Re: Is there a law of perspective?
It is pretty simple if you figure out what you need to calculate. Imagine you are looking at the object through a window a distance R' away (this is your reference plane, an object in this plane will appear to be it's exact height), and the object is a distance R from the screen and has an actual height of h. Calculating where the line from our reference point (eye, camera, or whatever) to the top of the object intersects the window yields the apparent height of the object.
See attached diagram.
Dusting off and clearing out the cobwebs from the concept of similar triangles from back in geometry, you find that
[math]\frac{R'}{d}=\frac{R'+R}{h} \rightarrow d=h\frac{R'}{R'+R}[/math]
For R >> R'[math]d\simeq h\frac{R'}{R}\propto\frac{1}{R}[/math]
Did some rough calculations with the formula to see I didn't make a mistake, and it predicts that the moon's apparent size compared to an object one meter away is one centimeter. Doesn't seem horribly wrong.
It also seems to work with R' < 0 (corresponding to a tiny object close to the camera appearing larger than large objects far away)
See attached diagram.
Dusting off and clearing out the cobwebs from the concept of similar triangles from back in geometry, you find that
[math]\frac{R'}{d}=\frac{R'+R}{h} \rightarrow d=h\frac{R'}{R'+R}[/math]
For R >> R'[math]d\simeq h\frac{R'}{R}\propto\frac{1}{R}[/math]
Did some rough calculations with the formula to see I didn't make a mistake, and it predicts that the moon's apparent size compared to an object one meter away is one centimeter. Doesn't seem horribly wrong.
It also seems to work with R' < 0 (corresponding to a tiny object close to the camera appearing larger than large objects far away)
 Attachments

 appheight.png (5.16 KiB) Viewed 2662 times
Last edited by You, sir, name? on Tue Mar 17, 2009 2:54 pm UTC, edited 1 time in total.
I edit my posts a lot and sometimes the words wrong order words appear in sentences get messed up.
 quartrmster007
 Posts: 111
 Joined: Thu Apr 24, 2008 2:58 am UTC
 Location: Atlanta, Georgia...but if "home is where the heart is", London. <3
Re: Is there a law of perspective?
ArgonV, you beat me to it. I've been wondering about this as well. Nice to know that there is a "law of perspective".
SlightlyEvil wrote:
Heh, you just missed the forest and hit the tree headon.
 gmalivuk
 GNU Terry Pratchett
 Posts: 26726
 Joined: Wed Feb 28, 2007 6:02 pm UTC
 Location: Here and There
 Contact:
Re: Is there a law of perspective?
Yeah, for artistic approximations, you're just projecting onto a plane and using similar triangles to figure out how big something looks. (When talking about actual sight, though, it's perhaps more accurate to project onto a sphere and talk about solid angles.)
Re: Is there a law of perspective?
All right, I got it. Thank you guys!
Who is online
Users browsing this forum: No registered users and 11 guests