Path: utzoo!attcan!uunet!wuarchive!udel!princeton!phoenix!gauss!markv
From: markv@gauss.Princeton.EDU (Mark VandeWettering)
Newsgroups: comp.graphics
Subject: Re: Looking for a word
Message-ID: <12899@phoenix.Princeton.EDU>
Date: 13 Jan 90 20:09:38 GMT
References: <447@fsu.scri.fsu.edu>
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Reply-To: markv@gauss.Princeton.EDU (Mark VandeWettering)
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In article <447@fsu.scri.fsu.edu> pepke@scri1.scri.fsu.edu (Eric Pepke) writes:

>Consider transformation of 2-d images.  In that case, n is 2.  If a 
>transformation had this property, then the transformed Y value would only 
>depend on the original Y value, likewise for X.  If the transformation did not
>have this property, the transformed Y could depend on both the original X and
>Y.  With this property, a mapping (X1, Y1) -> (X2, Y2) could be decomposed
>into two mappings: X1 -> X2 and Y1 -> Y2.  Without this property, no such
>decomposition would be feasible.

>Uniform scaling and stretching along one axis, even if nonlinear, would have
>this property. Skewing and rotation would not. 

Hmmm.  Very interesting question, and it even brings a few questions into my
head.  The term originally thought of by myself is "separable", but that 
has typically been used to say that only one coordinate is modified during 
a pass, not that it was the only one used to specify the transformation.

Without knowing the precise use that you intend, this may be enough to 
describe the algorithms you intend.  Alvy Ray Smith and Edwin Catmull 
published a paper called "3-D transformation in scanline order" which outlines
the basic method of image transformation composed as a series of seperable 
(1-D) transformations.  Their work has been followed up by a number of articles
dealing with image warping.  Fant had a much less general, but possibly
easier to follow paper in IEEE CG&A.  

If your usage of "decomposeable" is consistent with the terms separable, 
then I would advise using the already existing terminology.  Otherwise,
its up to somebody else to make a suggestion.

Mark