On Feb 24, 3:56=A0pm, Wildepad <noreplies> wrote:
> I have 126 glass panes which range in size from (all measurements in
> inches) 9x5 to 24x16. (It is not a uniform distribution -- almost 1/4
> of them are 16x12.)
>
> I want to mount them in frameworks to form decorative screens. The
> size of the panels can be from 14 to 28 inches wide and from 60 to 84
> inches tall, but there have to be several (2 to 6) panels of each
> finished size to assemble them into a screen.
>
> They cannot reasonably be cut [1], and a uniform pane size is not
> desirable anyway (if you're familiar with art deco room dividers,
> you'll know the look I'm after).
>
> I could just mark out suitable dimensions on the floor, start grabbing
> panes, and try to figure out a pattern, but that would be long,
> frustrating, and tedious. (It would also be too much like work for my
> taste.)
>
> I could use a CAD program, making a rectangle to represent each piece,
> and try to fit them into a suitable pattern, but that would also take
> a long time, and I'm supposed to be cutting back on the hours spent at
> the computer.
>
> It strikes me, however, that there could be a parallel in some branch
> of science, some method of determining arrangements of randomly sized
> objects to form regular shapes.
>
> But I don't have a clue as to where to start looking.
>
> Any help appreciated.
>
> [1] They are molded glass panels and many are tempered. They cannot be
> cut by the usual 'score and snap' method. The only local that could
> cut them charges $30 per setup plus a dollar an inch, with no
> guarantee against breakage. To ****p them somewhere is not really an
> option -- glass is heavy, driving up the cost.
> --
I can't guarentee that it'll give a disirable solution, but this
is similar to a 2D bin packing problem.
http://en.wikipedia.org/wiki/Bin_packing_problem
which is a subset of what are called 'knapsack problems'
Getting the maximal packing is NP-hard, and probably won't
give you an aesthetic result.
Peter Trei
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