Anthony Riley emailed me, again claiming:
This is fascinating if it's actually a belief someone has. Assuming he was genuine in his misunderstanding I replied with the following:
Imagine you've got a very long rigid rod, one that can be expanded in length.
Put one end of this rod at your eye (or camera), lower the rod so it just skims the the horizon a few miles away. Extend the rod until it hits the distant mountain. Consider the point where the rod hits the mountain.
Where the rod hits that mountain is where the line of sight from your eye to the horizon hits the mountain. There's a straight line from your eye to the horizon then to the mountain.
Anything above that POINT on the mountain is visible. Anything below that point is hidden.
The calculator calculates the height of that point above the water level. The actual hidden height. The calculator tells you how much of the mountain is hidden.
Applying perspective is calculating what this height would be in an image (like a photo). It's not hard to apply perspective. T
o apply perspective you just multiply actual sizes by f/d where d is the distance to the mountain, and f is the focal length of the camera. That gives you the height on the film or sensor of the camera (or the back of your eye).
In 3D graphics you apply this f/d scale separately to X and Y, with d = Z, but the end result is the same. It's not that complicated. It might look complicated, but it's not.
Look, it's just multiplying by f and then dividing by Z (which is the distance to the object)
The focal length f is really just a scaling factor. If you just want
relative apparent sizes you can given it an arbitrary value, like 1, giving you 1/d
It's really that simple. To get
apply perspective you
divided by the distance.