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A QuickDraw GX mapping, being a 3-by-3 matrix, can specify any 2D linear
transformation. It is easy enough to build up such a transformation from a
sequence of primitive transformations, namely translations, scalings,
rotations, skews and perspective distortions -- GX provides calls to construct
nearly all of these components (the exception is perspective, for which there
is library code in the GX SDK). Sometimes there is a need to go the other way:
given an arbitrary linear transformation, can you break it into a sequence of
pure translations, scalings, skews and perspective distortions? This Technote
will show you how.
This Technote is aimed at those who already have some basic understanding of
QuickDraw GX graphics, including how to make use of GX mappings. The exposition
will take more of an intuitive, hand-waving approach, with little pretense at
rigorous derivation.
This Technote is heavily dependent upon mathematical derivation, which HTML
does not yet adequately support. In order to ensure the mathematical integrity
of the text, we are not publishing the body of the Technote as an HTML file.
You can download the Technote, in its entirety, as an Adobe Acrobat document
by clicking
here.
Updated: [July 1 1996]
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