“Efficient alias-free rendering using bit-masks and look-up tables” by Whitted, Westover and Abram

We demonstrate an efficient method of rendering alias-free synthetic images using precomputed convolution integrals. The method is based on the observation that a visible polygon fragment’s contribution to an image is solely a function of its position and shape, and that within a reasonable level of accuracy, a limited number of shapes represent the majority of cases encountered in images commonly rendered.The convolution integral is precomputed for all pixels affected by the polygon fragment and is stored in a table. Completely visible fragments which are either triangular or trapezoidal produce two indices into the table. Most other fragments which are represented as differences of simple fragments. The remaining cases are characterized by a bit-mask for which each bit has a corresponding set of look up tables.The basic technique has been applied to several fundamentally different rendering algorithms. In addition, we illustrate a version of the newly introduced nonuniform sampling technique implemented in the same program, but with different table values.

1. Abram, G.D., forthcoming PhD dissertation.
2. Carpenter, L.C., “The A-buffer, an Antialiased Hidden Surface Method,” Computer Graphics, 18, 3, SIGGRAPH ACM, Jul. 1984.
3. Catmull, E., “A Hidden-Surface Algorithm with Anti-Aliasing,” Computer Graphics, 12, 3, SIG- GRAPH ACM, Aug. 1978.
4. Catmull, E., “An Analytic Visible Surface Algorithm for Independent Pixel Processing,” Computer Graphics, 18, 3, SIGGRAPH ACM, Jul. 1984.
5. Cook, R.L., T. Porter, and L. Carpenter, “Distributed Ray Tracing,” Computer Graphics, 18, 3, SIC- GRAPH ACM, Jul. 1984.
6. Crow, F.C., “The Aliasing Problem in Computer- Generated Shaded Images,” Comm. of the A CM, 20, 11, Nov. 1977.
7. Crow, F.C., “A Comparison of Antialiasing Techniques,” IEEE Computer Graphics and Applications, 1, 1, Jan. 1981.
8. Feibush, Eliot, Marc Levoy, and Robert L. Cook, “Synthetic Texturing Using Digital Filters,” Computer Graphics, 14, 3, SIGGRAPH ACM, Jul. 1980.
9. Fiume, E., and A. Fournier, “A Parallel Scan Conversion Algorithm with Anti-Alia.sing for a General-Purpose Ultraeomputer,” Computer Graphics, 17, 3, SIGGRAPH ACM, Jul. 1983.
10. Fuchs, Henry, John Poulton, AI Paeth, and Alan Bell, “Developing Pixel Planes, a Smart Memory- Based Raster Graphics System”, Proceedings of the 1982 MIT Conference on Advanced Research in VLSI.
11. Fuchs, Henry, Jack Goldfeather, Jeff P. Hultquist, Susan Spach, and John D. Austin, John G. Eyles, and John Poulton, “Fast Spheres, Shadows, Textures, Transparencies, and Image Enhancements in Pixel-Planes,” Proceedings of Siggraph ’85.
12. Mitchell, Don P., “Antialiased Ray Tracing By Nonuniform Sampling,” AT&T Bell Labs., unpublished report, Dec. 1984.
13. Jerri, A.J., “The Shannon Sampling Theorem- Its Various Extensions and Applications: A Tutorial Review,” Proc. IEEE, 66, 11, Nov. 1977.
14. Robinson, John, tutorial notes for State of the Art in Imase Synthesis Seminar, SIGGRAPH ’81.
15. Shapiro, H.S., and R.A. Silverman, “Alias Free Samplin~ of Random Noise,” J. SIAM, 8, Jun. 1960.
16. Weiler, Kevin J., and Peter A. Atherton, “Hidden Surface Removal using Polygon Area Sorting,” Computer Graphics, 11, 3, SIGGRAPH ACM, Jul. 1977.
17. Whitted, T., and David M. Weimer, “A Software Testbed for the Development of 3D Raster Graphics Systems,” A CM Trans. Graphics, 1, 1, Jan. 1982.
18. Whitted, T., “Anti-aliased Line Drawing using Brush Extrusion,” Computer Graphics, 17, 3, SIGGRAPH ACM, July 1983.