“Integrated analytic spatial and temporal anti-aliasing for polyhedra in 4-space” by Grant

  • ©Charles W. Grant




    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.


    1. Catmull, Edwin, “‘A Hidden Surface Algorithm with Anti- Aliasing” Computer Graphics 12(3), August 1978, pp. 6-11.
    2. Catmull, Edwin, “An Analytic Visible Surface Algorithm for Independent Pixel Processing” Computer Graphics 18(3), july 1984, pp. 109-115.
    3. Cook, Robert L., Thomas Porter, Loren Carpenter, “Distributed Ray-Tracing” Computer Graphics 18(3), July 1984, pp. 137-145.
    4. Feibush, Eliot A., Marc Levoy, Robert L Cook, “Synthetic Texturing Using Digital Filtering” Computer Graphics 14(3), July 1980, pp. 294-301.
    5. Korein, Jonathan, Norman Badler, “‘Temporal Anti-Aliasing in Computer Generated Animations” Computer Graphics 17(3), July 1983, pp. 377-388.
    6. Lien~Sheue-ling James T. Kajiya, “‘A Symbolic Method for Calculating the Integral Properties of Arbitrary Nonconvex Polyhedra” IEEE Computer Graphics and Applications 4(10), October 1984, pp. 35-41.
    7. Max, Nelson, Doug Lerner, “A Two and a Half D Motion Blur Algorithm”, Computer Graphics 19(3), July 1985, pp.
    8. Norton, Alan, Alyn P. Rockwood, Philip T. Skolmoski, “Clamping a Method of Anti-Aliasing Textured Surfaces by Bandwidth Limiting in Object Space” Computer Graphics 16(3), July 1982, pp. 1-8.
    9. Porter, Thomas, “Motion Blur” in SIGGRAPH 84 “State-ofthe-Art in image Synthesis course notes”, July 1984.
    10. Potmesil, Michael, Indranil Chakravarty, “‘Modeling Motion Blur in Computer Generated images” Computer Graphics 17(3), July 1983, pp. 389-399.
    11. Reeves, William T., “Particle Systems – A Technique for Modeling a Class of Fuzzy Objects” Computer Graphics 17(3), July |983, pp. 359-376.
    12. Sutherland, Ivan E., Gary W. Hodgman, “Reentrant Polygon Clipping” Comm. ACM 17(1), January 1974, pp. 32-42.
    13. Sutherland, Ivan E., Robert E Sproull, Robert A. Schumacher, “‘A Characterization of Ten Hidden Surface Algorithms” ACM Computing Surveys 6(1), March 1974, pp. 1-55.
    14. Szabo, Nicholas S., “Digital Image Anomalies; Static and Dynamic” in “‘Computer Image Generation” Ed. Bruce J. Schachter, John Wiley and Sons, Inc., New York, 1983.
    15. Whitted, Turner, “An Improved Illumination Model for Shaded Display” Comm. ACM 23(6), June 1980, pp. 343-349.

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