Visual nesting system for irregular cutting-stock problem based on rubber band packing algorithm

This article deals with the packing problem of irregular items allocated into a rectangular sheet to minimize the waste. Conventional solution is not visual during the packing process. It obtains a reasonable and relatively satisfactory solution between the nesting time and nesting solution. This article adopts a physical method that uses rubber band packing algorithm to simulate a rubber band wrapping those packing irregular items. The simulation shows a visual and fast packing process. The resultant rubber band force is applied in the packing items to translate, rotate, and slide them to make the area decrease and obtain a high packing density. An improved analogy QuickHull algorithm is presented to obtain extreme points of rubber band convex hull. An adaptive module could set a variable rubber band force and a variable time step to make a proper convergence and no intersection. A quick convex decomposition method is used to solve the problem of concave polygon. A plural vector expression approach is adopted to calculate the resultant vector of the rubber band force. Several cases are compared with the benchmark problems to prove rubber band packing algorithm performance.