A part feeder is a mechanism that receives a stream of identical parts in arbitrary orientations and outputs them oriented the same way. Various sensorless part feeders have been proposed in the literature. The feeder we consider consists of a sequence of fences that extend partway across a conveyor belt; a polygonal part P carried by the belt is reoriented by each fence it encounters. We present an O(m + n² log³n)-time algorithm to compute a sequence of fences that uniquely orients P, if one exists, where m is the total number of vertices and n is the number of stable edges of P. We reduce the problem to searching for a path in a state graph that has O(n³) edges. By exploiting various geometric properties of this graph, we show that it can be represented implicitly and that a desired path can be computed in O(m + n² log³n) time. We believe that our technique is quite general and could be applicable to other part-manipulation problems as well.