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Topic: One-point perspective and vector geometry
Replies: 6   Last Post: Jun 5, 1998 12:31 PM

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Heidi Burgiel

Posts: 44
Registered: 12/3/04
Re: One-point perspective and vector geometry
Posted: Jan 26, 1995 10:38 AM
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I'm sure there are many books containing the information you need.
Unfortunately, I don't know any offhand. Try looking in your library
for books combining the subjects of math and art.

I do know that the problem can be solved using matrix multiplication.
If you multiply your three dimensional vector (a 1 by 3 matrix) by a 3
by 2 matrix, you will get a two dimensional vector (a 1 by 2 matrix).
You can use this to transform from real-world coordinates to computer
screen coordinates.

To do a parallel projection (no perspective), you would use a 3 by 2
matrix that removed, say, the y coordinate from your vector. E.g.:

(3 3 2) ( 1 0 ) = (3 2)
( 0 0 )
( 0 1 )

I forget the exact technique for perspective projections, but I'd
guess you want to dilate your x and z coordinates by some factor of
your y coordinate. You know that the end result should be linear, and
that when the y coordinate is infinite you get the vanishing point.

It's been several years since I worked on this problem; maybe someone
else will have some better advice.

Good luck!

Heidi B.

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