Question

Ive got a bunch of rectangular objects which I need to pack into the smallest space possible (the dimensions of this space should be powers of two).

I’m aware of various packing algorithms that will pack the items as well as possible into a given space, however in this case I need the algorithm to work out how large that space should be as well.

Eg say Ive got the following rectangles

• 128*32
• 128*64
• 64*32
• 64*32

They can be packed into a 128*128 space

 _________________
|128*32          |
|________________|
|128*64          |
|                |
|                |
|________________|
|64*32  |64*32   |
|_______|________|

However if there was also a 160*32 and a 64*64 one it would need a 256*128 space

 ________________________________
|128*32          |64*64  |64*32  |
|________________|       |_______|
|128*64          |       |64*32  |
|                |_______|_______|
|                |               |
|________________|___            |
|160*32              |           |
|____________________|___________|

What algorithms are there that are able to pack a bunch of rectangles and determine the required size for the container (to a power of 2, and within a given maximum size for each dimension)?

Answer 1

The quick and dirty first pass solution is always a great one to start with, as a comparison if nothing else.

Greedy placement from large to small.

Put the largest rectangle remaining into your packed area. If it can’t fit anywhere, place it in a place that extends the pack region as little as possible. Repeat until you finish with the smallest rectangle.

It’s not perfect at all but it’s easy and a nice baseline. It would still pack your original example perfectly, and give you an equivalent answer for the second as well.