Re: Help with understanding matrices
Re: Help with understanding matrices
- Subject: Re: Help with understanding matrices
- From: Simon Topliss <email@hidden>
- Date: Fri, 15 Feb 2008 14:49:18 +0000
On 15 Feb 2008, at 14:30, Mark J. Reed wrote:
Skew (a.k.a. "shear" outside of Adobe) and rotation and scaling are
not independent values. They're all combined together in the matrix.
And you don't have enough information to separate them all back out.
Consider each of the components:
horizontal skew
vertical skew
horizontal scale
vertical scale
rotation angle
That's five variables. You only have four relevant values from the
matrix.
And there's no difference in the effect on an image, whether you start
out by saying you're going to rotate it so many degrees and then scale
it, or by saying you're going to skew it so much along each axis.
You can use the matrix to reconstruct what the image is like in an
untransformed state, but if you want to represent the transformation
itself - as something other than the matrix -, you have to pick your
representation. It makes sense to include either rotation or skew in
that representation, but not both.
OK. Thanks for all your help, Mark.
Simon
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