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

Abstract

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 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. 3-d (X, Y,Z) polygons in image space. This algorithm is an extension of Catmull3 analytic visible surface algorithm for independent pixel processing, based on the outline for integrated spatial and temporal antialiasing given by Korien and Badler. An analytic solution requires that the visible su~ace calculations produce a continuous representation of visible primitives in the time and space dimensions. Visible su~ace

Real-Time Motion Blur Using Triangular Motion Paths

“…Analytical methods: Our research is inspired by the analytical visibility approaches described by Korein and Badler [9], Newell et al [15], and Grant [16]. Korein and Badler [9] compute a covering interval of each geometry for a given pixel.…”

“…We similarly find a time interval of each moving triangle by exploiting the standard rasterization then removing occluded intervals using a sorting in the depth-time dimensions and bitwise operations. Our sorting algorithm is analogous to a method described by Newell et al [15] and polyhedron clipper described by Grant [16].…”

Temporal Issues of Animate Response

“…From this it is concluded that the human vision system can trade off temporal resolution against spatial resolution. A number of papers present methods to generate motion blur (also known as temporal antialiasing) [Korein, 1983;Potmesil, 1983;Max, 1985;Grant, 1985], but arguments why it is needed do not go any further than "animation which simulates motion blur feels more natural" or "it smooths out jerkiness". A more theoretical foundation of why and to what extend motion blur is needed can be found in E.H. Blake's PhD thesis on computing adaptive detail [Blake, 1989].…”

“…If we analyze the methods presented in [Korein, 1983;Potmesil, 1983;Grant, 1985] we see that these methods are basically supersampling techniques, due to which the computational cost of one anti-aliased frame is much more than the cost of an aliased frame. Also the more efficient method presented in [Max, 1985] adds computation cost to each frame.…”

Realism in Computer Graphics: A Survey

“…Catmull 27 used a simplification that projected the temporal problem into the spatial domain by distorting the 2-D filter to account for the velocity of objects. Grant 28 proposed an analytic solution by modeling moving polygons as 4 dimensional polyhedra. It unfortunately is an expensive and very involved procedure that does not look promising.…”