Assembly: Squid.Core (in Squid.Core.dll)
Original code by Javier Arevalo (jare at iguanademos dot com). Rewritten to C# / .NET by Markus Ewald (cygon at nuclex dot org). The following comments were written by the original author when he published his algorithm.
You have a bunch of rectangular pieces. You need to arrange them in a rectangular surface so that they don't overlap, keeping the total area of the rectangle as small as possible. This is fairly common when arranging characters in a bitmapped font, lightmaps for a 3D engine, and I guess other situations as well.
The idea of this algorithm is that, as we add rectangles, we can pre-select "interesting" places where we can try to add the next rectangles. For optimal results, the rectangles should be added in order. I initially tried using area as a sorting criteria, but it didn't work well with very tall or very flat rectangles. I then tried using the longest dimension as a selector, and it worked much better. So much for intuition...
These "interesting" places are just to the right and just below the currently added rectangle. The first rectangle, obviously, goes at the top left, the next one would go either to the right or below this one, and so on. It is a weird way to do it, but it seems to work very nicely.
The way we search here is fairly brute-force, the fact being that for most offline purposes the performance seems more than adequate. I have generated a japanese font with around 8500 characters and all the time was spent generating the bitmaps.
Also, for all we care, we could grow the parent rectangle in a different way than power of two. It just happens that power of 2 is very convenient for graphics hardware textures.
I'd be interested in hearing of other approaches to this problem. Make sure to post them on http://www.flipcode.com