Computer tool for maximizing the placement of congruent polyhedra

• Main Author: Gaspar, M.
• Publication Date: 2015
• Other Authors: Alves, N., Mateus, A., Martins-Ferreira, N.
• Format: Article
• Language: eng
• Source: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Download full: http://hdl.handle.net/10400.8/1419
• topic: Rapid Prototyping; Stereolithography; Containment; Packing; Optimization

Given multiple identical polyhedral objects and a parallelepiped container, how should one place the objects so that the largest number fits inside the container? This simple question is important in many applications, yet the answer is elusive. In fact, we know of no published solution for this very general formulation. Still, in many circumstances, further restrictions apply, resulting in a large number of variations requiring different algorithmic strategies. This paper is the continuation of [12] and focus on the fundamental concepts and tools that are used for this kind of problem, such as the no-fit polygon. We also present some of its many variations, giving in particular one that applies to the stereolithographic rapid prototyping technology.