1. A method for preventing interference between two physical tooth models coupled to a base about one or more pins so as to form a physical model of an arrangement of teeth, the method comprising: digitally representing surfaces of each of the two physical tooth models, thereby providing digital representations of the two physical tooth models; receiving a digital dental arch model configuration defining a positioning of the digital representations of two physical tooth models, wherein the digital representations of each of the two physical tooth models as positioned in the arch model intersect to form an overlapping portion; using the overlapping portion between the digital representations to determine a predicted interference of the two physical tooth models; and selecting an adjusted pin configuration for a physical model of an arrangement of teeth so as to avoid the predicted interference.