In article <l7k3s3thj9ahjdpdif14fpg814trv6l2tm@[EMAIL PROTECTED]
>, Wildepad
<noreplies@[EMAIL PROTECTED]
> writes
>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 ship them somewhere is not really an
>option -- glass is heavy, driving up the cost.
>--
I would make scale models in cardboard and play with them. I suspect
that setting this up on the computer will turn it into a hard problem. A
lot of work has been put into the problem of laying out shapes on a 2-D
plane, e.g. for manufacturers who want to cut out clothes from large
sheets of fabric with as little waste as possible. Simple schemes don't
work too badly (e.g. arrange them in order starting from the largest
first, hoping to pack the smaller items in the gaps between the larger
ones) but finding the absolute best answers can take a lot of computer
time - "Even the most elementary-sounding bin-packing problems are NP-
complete" says Skiena in "The algorithm design manual."
--
A.G.McDowell
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