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How does the programming behind transforming a picture work?

4 points by dmak ↗ HN
I'm interested in what happens when you "Free Transform" an image in photoshop. It allows you to skew the image into a perspective, resize, rotate, and so on. How does the programming behind that work?

4 comments

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wtracy
If you're mathematically inclined, look at: http://en.wikipedia.org/wiki/Transformation_matrix

For a less technical description: The pixel values in the transformed image are generated as a function of the pixel values in the input image. Once you have the transformation function figured out, the rest is basic algebra.

If you want to get an idea of what these functions look like, flip to the "Examples in 2D graphics" section in the above Wikipedia link. There's examples there for rotation, resizing, shearing, and others.

dmak
I never thought that learning Linear Algebra would be useful until today.
wtracy
Computer animation is just about the only thing I've used calculus for outside of school. So yeah, I hear you. :-)
kombinatorics
Wow, thanks for the info. I always liked proof based math more than the applied math. Linear Algebra is going to be a lot more interesting now.