Deconstructing affine transformations into rotation, scale, skew
- From: no_spam@xxxxxxxxxxxxxxxxxx (Spud Demon)
- Date: 30 Jun 2008 22:10:34 GMT
Given a 2-dimensional affine transform (6 coefficients as defined at
http://java.sun.com/j2se/1.5.0/docs/api/java/awt/geom/AffineTransform.html )
[ x'] [ m00 m01 m02 ] [ x ] [ m00x + m01y + m02 ]
[ y'] = [ m10 m11 m12 ] [ y ] = [ m10x + m11y + m12 ]
[ 1 ] [ 0 0 1 ] [ 1 ] [ 1 ]
How can I separate this transformation into its components?
The translation vector is obviously <m02,m12>, but after that it's not so
trivial. I would like to come up with:
* Rotation (scalar)
* Scaling or dilation (scalar or 2-D vector)
* Indication of whether the transform flips the image (bit)
* Skew (2-D vector?)
Pointers to info or even just the "right" terms to use in my web search
will be greatly appreciated!
--Spud Demon
.
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