A three-dimensional algorithm using two-dimensional slice data for building multiple parts in layered manufacturing

Abstract

In a rapid prototyping process, the time required to build multiple prototype parts can be reduced by building several parts simultaneously in a work volume. Interactive arrangement of the multiple parts, called three-dimensional nesting, is a tedious process and does not guarantee the optimal placement of all the parts. The three-dimensional nesting is well known as a problem requiring intense computation. Thus, an efficient algorithm to solve this problem is still under investigation. This paper presumes that the three-dimensional packing problem can be simplified into a set of two-dimensional irregular polygon nesting problems for each layer to take advantage of the characteristic of a rapid prototyping process, i.e. the process eventually uses two-dimensional slicing data of the STL file. The proposed algorithm uses a no-fit polygon (NFP) to calculate the allowable locations of each slice of a part such that it does not overlap other existing slices in the same z level. Then the allowable position of the part with respect to other parts already located in a work volume can be determined by obtaining the union of all NFPs that are obtained from each slice of the part. Additionally, a genetic algorithm is used to try and determine the various orders of the placement of the part and the various orientations of each part for efficient packing. Various orientations of a part are examined by rotating it about the normal vector of the slice in finite angles and by inversion. The proposed algorithm can be applied to a rapid prototyping process that does not use support structures.