Notes on the Mathematics of the PHIGS Viewing Pipeline

It is well known that homogeneous linear matrix transformations of the projective space may be efficiently used for the representation and the execution of common geometrical transformations but the general class of such transformations include also matrices which may cause numerical problems by transforming certain finite geometrical objects to infinity Different methods have been developed for handling such cases and this paper presents a new one called'UW clipping'which is based on some interesting properties of projective transformations. Furthermore the paper introduces die concept of 'conic sectors' as a generalisation to half-planes and halfspaces respectively, with the invariance property that such sectors are mapped onto other such sectors by projective transformations, and thus enable the transformation of clipping halfplanes and halfspaces. Finally the possibility of transforming die rectangular clipping box into the object space is investigated.