Efficient nesting of congruent convex figures

Abstract

Optimal nesting is the arrangement of two- dimensional polygons within a rectangular board so that waste is minimized. Our approach follows a top-down, stepwise refinement of the original problem into simpler subproblems; the combined solution of all of the problems permits the solution of the original problem. We first show that the original problem can be decomposed into two subproblems--one consisting of finding all convex paver polygons and the other of optimal (minimal waste) circumscription of the original figure in the most appropriate paver polygon.