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From: steve@thumper.UUCP
Newsgroups: comp.graphics
Subject: Re: Can You Transform Quadric Surfaces With 4x4 Matrices?
Message-ID: <373@thumper.UUCP>
Date: Fri, 30-Jan-87 18:31:00 EST
Article-I.D.: thumper.373
Posted: Fri Jan 30 18:31:00 1987
Date-Received: Sat, 31-Jan-87 15:00:36 EST
Distribution: net
Organization: The Fantasy Factory
Lines: 18

>So, how do we map a quadratic surface Q by a map M?  We want a surface K
>such that p is on Q if and only if (p M) is on K; that is, we want a matrix
>K such that 
>
>  p Q p' = 0  iff   (p M) K (p M)' = 0
>  
>Since (p M)' = M' p', we conclude that 
>
> K = M~ Q  M~'
>  
>will do the trick, where M~ is the inverse of M, and M~' its transpose.

This will also work if M~ is replaced by M* (the adjoint of M), which
always exists (the inverse doesn't), and is slightly cheaper to compute.

BTW: A very nice description of some complicated stuff!

	-Steve Miller ihnp4!bellcore!thumper!steve