2 replies to this topic

[Dreamchaser]

Hi, I have a problem here. And I need advice :)

This is the input:
I have a sheet of steel, sized 2 x 3 m. Fixed.
And I also have a list (around 30 items) of rectangles with variable sizes. Yes, just rectangles.

The need:
I need to know how I should cut that sheet of steel, so that it can be used as efficient as it can be, leaving the least unused space from the sheet.

The output:
The design of how I should cut the sheet, picturing which rectangles are put in certain places. It is very possible that within a sheet, I can only put several items out of those 30 listed so that the sheet is cut efficiently, so that I will have to use additional sheet.

The question:
What's the algorithm used to solve this kind of problem? There will be more variations later, though, with other shapes like triangles, circles, etc. Not just rectangles. But for now, this is what I need to find out.

Any idea?
Thanks in advance :)

[WingedPanther]

In the case of circles, it is a sphere-packing problem (I know circle != sphere, but mathematicians don't care to much about the precise number of dimensions).
Here and here are two resources that may help.

[Dreamchaser]

Never thought that even wikipedia includes this issue as well.
Thank you for the references :)