Path: utzoo!attcan!uunet!lll-winken!lll-tis!ames!elroy!mahendo!wlbr!etn-rad!shaw
From: shaw@etn-rad.UUCP (Howard Shaw)
Newsgroups: comp.graphics
Subject: Projective transformations
Summary: How to do them.
Message-ID: <559@etn-rad.UUCP>
Date: 25 Jul 88 22:31:28 GMT
Reply-To: shaw@etn-rad.UUCP (Howard Shaw)
Organization: Eaton Inc. IMSD, Westlake Village, CA
Lines: 22

Help!!  I have a problem which is a special case of a problem which has
no doubt been solved before, but it's new to me, and I sure could use
a hand, suggestions, pointers, etc.

I have a digitized map, or equivalently, a digitized image of a piece of 
the earth's surface taken from the vertical, far above it.  Let's assume 
that the earth is flat (at sea-level, no hills, not even earth curvature).
I wish to (perspectively) transform the image so that it appears as it 
would from an arbitrary point in space "nearby".  I am given the viewing
point (Lat, Long, and Alt, relative to the assumed to be known Lat/Long 
for some points on the original image), and the viewing angles (degrees 
clockwise from North, and degrees down from the local horizontal).

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