NetNews Usenet Archive 1992 #19/NN_1992_19.iso/spool/sci/math/10851

Internet Message Format | 1992-09-01 | 1.8 KB

Path: sparky!uunet!cis.ohio-state.edu!pacific.mps.ohio-state.edu!linac!att!cbnewsm!cbnewsk!att-out!oucsboss!oucsace!bwhite
From: [e-mail] (William E. White )
Newsgroups: sci.math
Subject: Need help on convex 4-gon to convex 4-gon xform algorithm
Message-ID: <[e-mail]>
Date: 2 Sep 92 07:00:41 GMT
Distribution: usa
Organization: O.U., Harvard on the Hocking, Berkeley in the Boondocks!
Lines: 23

Where I work we need to transform an arbitrary convex four-sided polygon
to another arbitrary convex four-sided polygon (well actually we know the
coordinates of the source and destination 4-gon; what we want is to find
a mapping that goes from one to the other).  In the end, we should be
able to apply this mapping to, say, a grid of lines within the source 4-gon
and have a similar (but "squashed") grid appear on the other 4-gon.

The only thing I could think of off hand was using two affine mappings and
dividing the 4-gon into two triangles; this works for our original needs
(which was that the transform would only be used on points on the sides of
the 4-gon itself), but now we need to be able to transform any point, inside
or outside of the original 4-gon.  I know there's a way to do this but I'm
having enough trouble with linear algebra as it is.

Please email all responses.  This is going into software; exact answers take
precedence over computational time.  I have code to invert a matrix if the
solution can be expressed as a linear equation.

William White                        [e-mail]
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