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From: pepke@loligo.cc.fsu.edu (Eric Pepke)
Newsgroups: comp.graphics
Subject: Looking for a word
Message-ID: <447@fsu.scri.fsu.edu>
Date: 12 Jan 90 21:31:07 GMT
Sender: news@fsu.scri.fsu.edu
Reply-To: pepke@scri1.scri.fsu.edu (Eric Pepke)
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Organization: Supercomputer Computations Research Institute
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I am looking for a word to describe a property of transformations and other
mappings.  The property is this:  Say I have a mapping from R(n) to R(n)
where n is greater than one.  Call the independent variable in the dimension
k where 1 <= k <= n a(k) and the dependent variable b(k).  If the mapping
has this property for which I need a name, b(i) is not dependent on a(j)
when i is not equal to j.

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. 

This is a very elementary and important property and is basic to algorithm 
design, but I can't for the life of me think of the word for it!  I looked
up all the words in Webster's that begin with "ortho" but to no avail.  I
could call the individual component mappings independent from each other,
or I could say that the composite mapping was decomposable, but there must
be a better and more specific term.  Does this ring anybody's bell?

Eric Pepke                                     INTERNET: pepke@gw.scri.fsu.edu
Supercomputer Computations Research Institute  MFENET:   pepke@fsu
Florida State University                       SPAN:     scri::pepke
Tallahassee, FL 32306-4052                     BITNET:   pepke@fsu

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