Compatible TOSets with POSets: An Application to Additive Manufacturing

Abstract

Additive manufacturing (AM) has become a widely used technique in 3D printing, but it has proven to be a very costly process, even when optimizing parameters in existing models. Due to the characteristics of AM, and in order to optimize its process, a new approach is introduced to the problem: the discretization of each layer to be printed. This involves establishing an order relation based on the sequence in which the layers should be printed. The valid orders for the execution of the process, referred to as compatible with the order relation, will be characterized. Additionally, algorithms will be provided to obtain newcompatible orders from others that were already compatible, and strategies will be presented to optimally and efficiently reorder non-compatible orders, converting them into compatible ones.