METHODS FOR SEARCHING FOR ARRANGEMENTS OF SHAPES SUBJECT TO BOUNDARY DISTANCE CONSTRAINTS AMONG THOSE SHAPES

摘要

This disclosure describes methods to manufacture one or more articles of manufacture that searches for an arrangement of shapes that satisfy exact or approximate analytical representations of boundary distance constraints. The disclosed methods include the execution of the following steps: step (a) constructing functions for one or more boundary distance constraints; step (b) constructing an analytical optimization problem which incorporates the constraint functions of step (a); step (c) selecting the initial values of one or more optimization variables; step (d) solving the optimization problem constructed in step (b) using one or more analytical optimization methods and one or more of the initial values of step (c).