How far can you see something?

I know it seems like a silly question, but...

i find myself asking this question often, especially when thinking about distance scales to use in a new title. so whether its a person, a building, an airship, or a planet, how far can you see something?

it seems to me that there should be some pretty straightforward formula or rule of thumb approximation for:

given an object [sphere] of radius R, how far away must it be before it should no longer be drawn?

keep it generic, in d3d units.

so if my sphere is at: range = 1, it appears to be almost 2R wide. at some distance: range = D, it appears to be about 2R/D wide. correct?

so when D gets big enough that 2R/D is so small its not worth it (given screen rez etc), you should no longer draw it, correct?

and you could plug in your horizontal and vertical resolutions and solve for 2R/D=1 pixel (or < 1 pixel), correct?

does this make sense?

how do YOU figure out what is big enough / close enough to be drawn?

Tom KQT makes some good points - regarding air clarity, etc. If the OP is asking about the human eye, there is more than just resolution involved. In a war plane simulation (as Tom mentioned), an observer may not notice a pixel that's only slightly different in hue than the sky, but may notice movement across the screen of such a pixel.

how about:

if D > RH/W, don't draw.

where:

D is the distance from the object to the camera

R is the radius (half the width/height) of the object

H is the horizontal resolution of the screen in pixels (just considered the horizontal case so far)

W is the width of the screen.

all must be in the same units of measure.

using a scale of 1 meter = 1 d3d unit,

given an object of radius 1 meter, a screen width of 0.5 meters (being generous), and a horizontal resolution of 1600 pixels, the object would appear to be 1 pixel wide at a distance of 3200 meters.

which coincidentally is the horizontal resolution times the object width. this is only because the 0.5 screen width and width=2*radius cancel each other out.

so for a screen width of 0.5 meters, it simplfies to:

if D > 2RH dont draw

if course, odds of running 1600 on a 0.5 meter wide screen are slim.

so "if D > RH/W, don't draw" should usually be used.

but then you have to go around measuring the user's monitor to get W! <g>

you could use a default "standard" value.... "the average monitor is X meters wide"

or make it a menu pick, with a default value (0.4 meters?). much more better - as capn jack would say.

On a perfectly flat plane, you can see about 12 miles.

dues to atmospherics? limitations of the human eye? both?

i'm talking about theoretical pinhole camera graphics pipeline stuff.

Curvature of the earth.

i thought it was something like 6 feet in 5 miles.

It's great when you are at sea and get a really clear day. You can actually see a ship on the horizon slip below it.

been there, like to be there again! : )

Of course most of the time all you can see is the next wave about to break over your head or the smog drifting out to sea from an oil refinery....

need a bigger boat! and clearer waters! might i recommend the Florida Keys or Chesapeake bay? well, the Bay is only ok... but yeah, Florida Keys, green water, white sand, can't bet it with a stick! Probably even nicer than the waters around Hawaii - except from a surfing point of view, of course. Something over 30 feet (10 meters), sail or powr, your choice. probably get away with 20' (7 meters) in a power boat without getting too wet. but nothing beats the thrill of wind power on a hard keel over run with a strong wind. trust me, i know, i drive a 700 horsepower chevelle street machine.