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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?
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Posted 11 years ago
 It sounds like you are interested in polygon tesselation.You might look at http://mathworld.wolfram.com/Tessellation.html , 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 http://demonstrations.wolfram.com/PentagonTilings/
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 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 11 years ago
 Hi Jari, thanks.What if it were in 2D and my arbitrary shape is just a rectangle of variable dimensions?