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From: ph@pixar.UUCP
Newsgroups: comp.graphics,sci.math
Subject: Re: Can You Transform Quadric Surfaces With 4x4 Matrices?
Message-ID: <512@pixar.UUCP>
Date: Sat, 31-Jan-87 04:20:00 EST
Article-I.D.: pixar.512
Posted: Sat Jan 31 04:20:00 1987
Date-Received: Sat, 31-Jan-87 16:18:10 EST
References: <255@onion.cs.reading.ac.uk> <511@pixar.UUCP>
Organization: Pixar -- Marin County, California
Lines: 9
Summary: minor correction
Xref: watmath comp.graphics:225 sci.math:416

Correction to a typo in my previous posting:  to transform a plane N
by matrix T: N' = T^-1*N, not N' = T*N.
It makes perfect sense if you remember the correspondence between
plane equations in the two coordinate systems:  P'*N'=0 <==> P*N=0 :

	P'*N' = (P*T)*(T^-1*N) = P*(T*T^-1)*N = P*N

Interesting note: some computer graphicists mistakenly transform normals
(planes) using N' = T^t*N, but this is correct only for rotations.