On the priority approach to hidden-surface algorithms

The task of eliminating invisible parts when generating an image is one of the central problems in computer graphics. One approach achieves the desired obscuring effect by assigning priority numbers to the faces of an object. Image generation can be speeded up significantly in these priority schemes if priority information of the faces can be partly computed in advance, before a viewing position is specified. These observations were first made by Schumacker and are utilized to advantage in simulation applications. However, the priority calculations are usually done manually, for lack of an adequate theoretical understanding. In this paper we study the underlying mathematical structure of these priority orders, and present efficient algorithms for handling some special classes of geometrical configurations.