The Mathematics of Field of View and Vanishing Points

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In order to understand the vanishing point in Plane-Maker, we first have to look at field of view and the process by which X-Plane simulates a 3-d world on a 2-d monitor.

 

Field of View

 

Field of View is the angle that you get if you go from the left edge of your vision to your eye, then back up the right edge. In the case of a monitor, we can calculate this (depending on how far back I am sitting). For example, my 19" LCD is 14.8 inches across the top; to have a 45 degree FOV I need to sit about 17.8 inches away from the monitor.

 

X-Plane lets you set the field of view. Imagine that you were sitting in front of a window on an airplane. As you put your face closer to the window, you can see more of the world outside. Effectively you are increasing your field of view. X-Plane works the same way - turning up the field of view parameter will increase the amount of "stuff" you can see.

 

Where Is The Horizon?

 

So where is the horizon? The answer is: it depends. Assuming you are looking straight forward, the most logical place to put the horizon is exactly half-way up the monitor. And this is what X-Plane does in any external view.

 

As you rotate your head up and down, the center of your vision changes relative to the horizon. But if you simply move your head up and down, the horizon doesn't move. This is due to parallax. The closer an object is, the more it moves as you move your head. This is what lets me look "over" the dashboard of the car by sitting on a phone book: as my head goes higher, the dash board (close) appears a lot lower but the road (far) appears only a little bit lower. The horizon (very, very far away) doesn't move at all.

 

This effect works in X-Plane. Try moving the view point up and down in a plane with a full 3-d cockpit, like the Cessna 172. As you move your head up and down, your ability to see the runway out the window will change.

 

2-D Panels

 

Things get weirder when we have a 2-d panel. A 2-d panel is sort of a flat image of what a 3-d cockpit might look like. We need some kind of correlation between the 2-d world and 3-d world...that is, where does the horizon appear through this 2-d panel. That location is the "vanishing point" in Plane-Maker.

 

Here's where things get strange: what do we do when we scroll the panel? Do we move our head or tilt our head? The answer is: neither. Scrolling the 2-d panel simply scrolls the "window" within the 3-d world that we look through. This has the effect of moving the horizon (by the exact number of pixels the panel scrolled) without rotating your view point.

 

This isn't necessarily the best way to scroll the panel, but it looks pretty good, and anything we do with 2-d panels is going to be an approximation.

 

And Now The Bug

 

Of course, there must be a bug in here somewhere...these blog posts are usually the result of an investigation into an edge-case in the sim. In X-Plane 930b6, we pick a vanishing point based on the 2-d panel when we are in 3-d cockpit mode.

 

Why would we do such a silly thing? Originally it was to keep the horizon from jumping when there is no 3-d cockpit object. This behavior is okay in that case, but here's how we get burned: if the 2-d cockpit has to scroll, the vanishing point might be off the top of the screen. Authors who have made very large 2-d panels and separate 3-d cockpits see this as the 3-d viewpoint being stuck straight down. What's happening is the vanishing point (and thus the center for the mouse) are off the top of the screen.

 

For beta 7 I am fixing this:

 

• If there is a 3-d cockpit object, the vanishing point will be the center of the screen, which is almost certainly the right thing to do for a real fully 3-d view.
   
   
  
• If there is no 3-d cockpit object (but instead X-Plane's default of the 2-d panel floating in space) the vanishing point will match the 2-d view, but taking the default scroll position into account. This should keep the horizon at a reasonably sane point.
   
   
  

 

 

As a final note, it is possible to specify a 3-d panel without a 3-d cockpit object in X-Plane. Don't make a plane like this. It's a silly thing to do!