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Calculating possible solutions

Posted 11 years ago
So I was wondering if it's possible to use Mathematica for the following:

I have an arbitrary shape that I would like to cut out from a big piece of square material of fixed dimension.

I was wondering if Mathematica can help to calculate the number of such arbitrary shapes whose dimensions I will specify that can be cut out from the bigger piece of material?
POSTED BY: jtherlio
4 Replies
Posted 11 years ago
It sounds like you are interested in polygon tesselation.

You might look at , then think about how to translate your problem into a mathematical formulation that answers the question you need to answer, then the final step is to translate your math into Mathematica commands.

Here is a tiling demonstration
Posted 11 years ago
Especially if you have just one rectangular shape, problem gets considerably simpler. There are probably still arrangements whose optimality not entirely obvious.

Unfortunately this is not my field of expertise...
POSTED BY: Jari Kirma
Posted 11 years ago
This problem equivalent to problem called "the nesting problem." It is a practical problem and active subject of operations research. Optimal solutions for arbitrary shapes are unfortunately computationally complex.

Certainly methods solving this problem can be implemented in Mathematica, but I can't provide you one.
POSTED BY: Jari Kirma
Posted 11 years ago
Hi Jari, thanks.

What if it were in 2D and my arbitrary shape is just a rectangle of variable dimensions?
POSTED BY: jtherlio
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