Inferring the relative three-dimensional positions of two moving points

We show that four orthographic projections of two rigidly linked points are compatible with at most four interpretations of the relative three-dimensional positions of the points if the points rotate about a fixed axis--even when the points as a system undergo arbitrary rigid translations. A fifth view (projection) yields a unique interpretation and makes zero the probability that randomly chosen image points will receive a three-dimensional interpretation. Assuming that the points rotate at a constant angular velocity, instead of adding a fifth view, also yields a unique interpretation and makes zero the probability that randomly chosen image points will receive a three-dimensional interpretation.