Affine Transformations are Here
by Jiang on Aug.16, 2007, under General
What operation allows you to translate, scale, shear, and rotate your picture all at once? You guessed it… it’s the affine transformation.
What’s an affine transformation? Also known as an affinity, an affine transformation maps points (x,y) to (x’,y’) such that collinearity and distance ratios are preserved. This means that all points lying on a line before transformation still lie on a line after transformation, and proportion and betweenness are preserved along lines. An affinity does not preserve angles or lengths.
But we know that graphic designers can’t be bothered with all this math stuff, so we’ve put all the juicy affine goodies into a neat little package called… well, the Affine Transformation. At the core of this package is a matrix operator that does all sorts of things to your image, but all you have to know is that your picture comes out looking nice and pretty. Now, how exactly do you use this tool?
The Affine Transformation tool can be located in the Filter menu. The central operation is rotation — just specify an angle in degrees and your image will be rotated clockwise by that much. To rotate counterclockwise, just input a negative angle. Now, you can also scale your image horizontally and vertically before you rotate by specifying the Presize fields. To scale after you rotate, just specify the Size fields. Not only that, but you can also shear your image using the Preshear and Shear fields. What does shearing do? Well… just imagine taking two opposite vertices of your picture and stretching them out or pushing them in; you end up with a parallelogram, and that’s exactly what the shear operation does.
Why stick the transformations together? Why not have the rotation, shearing, and scaling operators by themselves? While this is definitely going to be done in addition to the combined operator, the combined operator is here to stay. See, every time you transform your image, you lose some quality. This is because while you’re stretching it out in all sorts of ways, it has to end up back on a boring old two-dimensional array of pixels. So doing everything in one go actually reduces quality loss, as opposed to doing the operations separately.
The affinity operator will be improved, allowing proportion constraints, absolute measurements, and so on. Anyway, I have to go to work now, so hang on!
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