Rotating images: how does it work?

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I have to make dissertation for mathematics this schoolyear. I'm studying the link between mathematics and photography. Now I want to know how images are rotated in Photoshop or other photo software. I found out that it has to do with complex numbers because you can rotate every pixel in the complex plane, but I can't find any source that explains how this mathematical theory is implemented in the software.

Does anyone know how they do it?

I really want to find out how it actually works, so I can make a good dissertation.
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Bert M

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Posted 6 years ago

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Rory Hill

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Back in the day when I was playing with image processing I used the 3 shear method.

Shear 1: x' = x - tan (theta/2) * y
Shear 2: y' = y + sin(theta) * x
Shear 3: x' = x - tan (theta/2) * y

You can google this to get more info.

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Rob Cole

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Crop rotation in Lightroom:

x' = x * Cos(theta) - y * Sin(theta) + a
y' = x * Sin(theta) + y * Cos(theta) + b

(formula originally provided by Steve Sprengel)


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Chris Cox

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here's the book on warping, rotations, etc.

Basic computer graphics texts will also provide simpler explanations:

Most colleges will have copies of these books (or earlier editions).