Optimal 3-D Packing using 2-D Slice Data for Multiple Parts Layout in Rapid Prototyping

신속시작작업에서 2차원 단면데이터를 이용한 3차원 물체의 최적자동배치를 위한 알고리즘의 개발

In Rapid Prototyping process, the time required to build multiple prototype parts can be reduced by packing several parts optimally in a work volume. Interactive arrangement of the multiple parts is a tedious process and does not guarantee the optimal placement of all the parts. In this case, packing is a kind of 3-D nesting problem because parts are represented by STL files with 3-D information. 3-D nesting is well known to be a problem requiring an intense computation and an efficient algorithm to solve the problem is still under investigation. This paper proposes that packing 3-D parts can be simplified into a 2-D irregular polygon nesting problem by using the characteristic of rapid prototyping process that the process uses 2-dimensional slicing data of the parts and that slice of the STL parts are composed of polygons. Our algorithm uses no-fit-polygon (NFP) to place each slice without overlapping other slices in the same z-level. The allowable position of one part at a fixed orientation for given parts already packed can be determined by obtaining the union of all NFP's that are obtained from each slice of the part. Genetic algorithm is used to determine the order of parts to be placed and orientations of each part for the optimal packing. Optimal orientation of a part is determined while rotating it about the axis normal to the slice by finite angles and flipping upside down. This algorithm can be applied to any rapid prototyping process that does not need support structures.