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From: saponara@batcomputer.tn.cornell.edu (John Saponara)
Newsgroups: comp.graphics
Subject: Re: Transforming Quadric Surfaces ( HELP!!!! )
Message-ID: <6466@batcomputer.tn.cornell.edu>
Date: 5 Oct 88 13:02:34 GMT
References: <511@uvicctr.UUCP>
Reply-To: saponara@tcgould.tn.cornell.edu (John Saponara)
Distribution: na
Organization: Cornell Theory Center, Cornell University, Ithaca NY
Lines: 37

In article <511@uvicctr.UUCP> bcorrie@uvicctr.UUCP (Brian Corrie) writes:
>Imagine a surface, a quadric surface, caught in ( du du du du du du du du )
>                        THE TWILIGHT ZONE
 
>  My problem is that I need to translate and rotate this quadric by a standard
>  3D translation. ( eg. Translate its center to origin ). It is my
>  understanding that this can be done by using a standard 4x4 3D homogenous
>  transformation matrix and its transpose or its inverse. It is done
>  something like this
>
>      Q' = T Q T' where Q is the quadratic matrix, Q' is the translated
>  quadratic matrix, T and T' are the translation matrix and its transpose.
>
>  So what is wrong???? I don't know whether to use T and its transpose, or
>  T and its inverse. For a pure translation, I get a correct result if I use
>  the inverse of T and the transpose of the inverse of T. Is this correct??
>  I need some confirmation or pointers.

From Jim Blinn's "The Algebraic Properties of Homogeneous Second Order
Surfaces":

		Q' = T* Q T*t

	[where T* is the adjoint (or inverse) of the transformation matrix,
	T*t the transpose of the adjoint]

	That is, to transform a quadric curve, multiply on the left by the
	adjoint (i.e. generalized inverse) of the point transformation and on
	the right by the transpose of the adjoint.

By the way, does anyone know if this Blinn article has been reprinted anywhere
but SIGGRAPH class notes (i.e. someplace more accessible)?  If not, why not?

Eric Haines (who does not walk and talk like John Saponara - I don't know why
	the computer thinks I'm him)

NOTE: this account goes away soon, so write me at hpfcla!hpfcrs!eye!erich