Path: utzoo!mnetor!uunet!husc6!bbn!rochester!ur-tut!sunybcs!lively
From: lively@sunybcs.uucp (Richard S. Lively)
Newsgroups: comp.graphics
Subject: Re: Shear with "basic" transformations
Message-ID: <10030@sunybcs.UUCP>
Date: 8 Apr 88 14:02:19 GMT
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Reply-To: lively@sunybcs.UUCP (Richard S. Lively)
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Organization: SUNY/Buffalo Computer Science
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The question was to represent a shearing transformation as a
sequence of "basic" transformations, not just as single rotation
and a single scale.  A sequence that will give the matrix:

                     (1   0)
                     (a   1)

is as follows:

R(-PI/4) S(sqrt((1-a)/(1+a)), 1) R(sqrt(1-a), sqrt(1+a))
S((1-a)/sqrt(2(1-a)), 1/sqrt(2(1+a)))

where the notation R(x,y) is a rotation by angle theta with
cos(theta) = x and sin(theta) = y.