Mathematical model and efficient algorithms for object packing problem

Authors:
N. Chernov;Yu. Stoyan;T. Romanova
Affiliations:
Department of Mathematics, University of Alabama at Birmingham, AL 35294, United States;Department of Mathematical Modeling, Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov, Ukraine;Department of Mathematical Modeling, Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov, Ukraine
Venue:
Computational Geometry: Theory and Applications
Year:
2010

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Abstract

The article is devoted to mathematical models and practical algorithms for solving the cutting and packing (C&P) problem. We review and further enhance the main tool of our studies - phi-functions. Those are constructed here for 2D and 3D objects (unlike other standard tools, such as No-Fit Polygons, which are restricted to the 2D geometry). We also demonstrate that in many realistic cases the phi-functions can be described by quite simple formulas without radicals and other complications. Lastly, a general solution strategy using the phi-functions is outlined and illustrated by several 2D and 3D examples.