Integrated analytic spatial and temporal anti-aliasing for polyhedra in 4-space

A visible surface algorithm with integrated analytic spatial and temporal anti-aliasing is presented. This algorithm models moving polygons as four dimensional (X,Y,Z,T) image space polyhedra, where time (T) is treated as an additional spatial dimension. The linearity of these primitives allows simplification of the analytic algorithms. The algorithm is exact for non-intersecting primitives, and exact for the class of intersecting primitives generated by translation and scaling of 3-d (X,Y,Z) polygons in image space. This algorithm is an extension of Catmull's analytic visible surface algorithm for independent pixel processing, based on the outline of integrated spatial and temporal anti-aliasing given by Korien and Badler. An analytic solution requires that the visible surface calculations produce a continuous representation of visible primitives in the time and space dimensions. Visible surface algorithm, graphical primitives, and filtering algorithm, (by Feibush, Levoy and Cook) are extended to include continuous representation of the additional dimension of time. A performance analysis of the algorithm contrasted with a non-temporally anti-aliased version is given.