## Fitting a Rectangle Inside a Rectangle

*January 18, 2016 by Chris Johnson. Filed under algorithms, graphics, public.*

A common problem in computer graphics and user interfaces is scaling one rectangle to fit inside another—preserving the rectangle’s aspect ratio. For example, I’ve encountered this problem in the following situations:

- Placing an image of arbitrary size on a button of fixed size.
- Overlay a map on a corner of a game scene.
- Squeezing an image to fit on a mobile phone screen.

When I first encountered the problem, I just hacked away until I found some scale factors and logic that did the trick. But now that I’ve solved it N times, I need a little more certainty that I am doing the right thing. So, I sat down to prove to myself that my solution works.

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