Determining the Preferred Viewpoint in Linear Perspective

The basic theory of linear perspective is reviewed, and it is shown that a perspective picture implies the existence of a unique point in space which is, on optical grounds, the preferred viewpoint of the picture. The concepts of the visible, terrestrial, and sensible horizons are then compared, and it is found that the horizon in a picture can give the vertical position of the viewpoint. The outside knowledge or assumptions which are necessary in order completely to determine the preferred viewpoint are then considered. The assumptions used here are based on common knowledge of the three-dimensional shapes and orientations of pictured objects and knowledge of the picture-making processes. A step-by-step procedure is then given for finding the location of the preferred viewpoints of one-, two- and three-point perspectives. It is found that a three-point perspective provides more information about the viewpoint, with fewer assumptions, than either of the other two cases. Finally, the reasons why alternate viewpoints may be just as acceptable as the optically preferred one are discussed.