Path: utzoo!attcan!uunet!husc6!think!ames!pasteur!agate!eos!jbm
From: jbm@eos.UUCP (Jeffrey Mulligan)
Newsgroups: comp.graphics
Subject: Re: Projective transformations
Message-ID: <1161@eos.UUCP>
Date: 26 Jul 88 18:05:09 GMT
References: <559@etn-rad.UUCP>
Organization: NASA Ames Research Center, California
Lines: 24

From article <559@etn-rad.UUCP>, by shaw@etn-rad.UUCP (Howard Shaw):

< I believe the mapping from the original image space to the new image 
< space is a bilinear fractional transformation:
< 
<         a*x + b*y + c                     f*x + g*y + h
<     X = -------------                 Y = --------------
<         d*x + e*y + 1                     d*x + e*y + 1
< 
< Any known easy way to get the coefficients a,b,...?  Even if I could
< only get four (x,y) <-> (X,Y) pairs, I could get the coefficients by
< curve-fitting.  Any help would be greatly appreciated.   -HS

If you have four points, the transformation is determined;  8 equations,
8 unknowns.  Set up an 8 by 8 matrix which operates on the vector
of coefficients, then invert this matrix.  I have written program
which does this, but it doesn't handle special cases very nicely
right now.

-- 

	Jeff Mulligan (jbm@aurora.arc.nasa.gov)
	NASA/Ames Research Ctr., Mail Stop 239-3, Moffet Field CA, 94035
	(415) 694-6290