Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: Onepoint perspective and vector geometry
Posted:
Jan 26, 1995 10:38 AM


Hi!
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 realworld 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.



