T3D center of perspective

[john bercovitz <bercov@xxxxxxxxxxx>]

I can't do as good a job in half a page as Kingslake does in a 
couple of pages with illustrations, but I'll try to do a no-math 
something for those who can't afford to buy a book.  

Best is to start with a pinhole camera.  If you put yourself at 
the pinhole, and you look out at the world, you might see a couple 
of objects out there.  If you draw lines from each of the objects 
to the pinhole, you will have an angle between the two lines where 
they meet at the pinhole.  Now if you draw lines from the pinhole 
to the images on the film of those two objects, you'll find these 
lines have the same angle between them as the lines from the 
pinhole to the objects did.  I guess this isn't too amazing but 
it's important.

The center of perspective for the scene is that pinhole.  It's 
where the eye of the camera is located in three-space.  To view 
the image properly, you have to place your eye where the pinhole 
was.  That's pretty close so we generally use a magnifier to get 
that close or we enlarge the image ten times so we can put our eye 
ten times as far away and thereby still conserve the center of 
perspective.  As you can imagine, if your image is ten times as 
big and your eye is ten times as far away, the sight lines to the 
image points still have the correct angles between them.

So what happens if the sight lines don't have the correct angles 
between them?  What's the diff?  There is no difference if 
everything in the scene is far, far away but a problem arises if 
some object is up close.  

And here's the problem.  If something is up close, it appears 
bigger than something which is farther away even though it's the 
same size.  If you move far away from both objects, both objects 
appear about the same size.  So if you take a picture with one 
object up close and then view from far away, your brain sees the 
closer object as being bigger because it is far away like the far 
object yet it is bigger.  I guess this makes no sense without some 
math but I won't brutalize you with math.  8-)

John B


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