Optimal Static 2-Dimensional Screen Subdivision for Parallel Rasterization Architectures

Designers of computer graphics hardware have used increasing device counts available from IC manufacturers to increase parallelism using techniques such as putting a longer pipeline of data path elements on integrated circuits. or developing designs which use an array of processors. Pixel-Planes 1-5 and PixelFIow l are examples of architectures which use an array of pixel processors for rasterization. Early generations of Pixel Planes attempted to make these arrays as large as the display providing one processor for each display pixel. Later generations improved performance by grouping processors into multiple smaller arrays, subdividing the screen into sections of a corresponding size and having the arrays independently process the screen subdivisions. This paper describes'simulations which were performed to determine the optimum size subdivision for a graphics computer which uses Pixel-Planes type parallelism. i.e. •.st~tjc. tv.:0 dimensional screen subdivision parallel polygon rastenzatJon. We then develop a mathematical approach to determining the optimal subdivision size and show that it agrees well with the experimental data. For special purpose architectures we show that the optimal size depends nOI only on the polygon size bUI also on the silicon area consumed by the rasterizer overhead. The mathematical approach can be directly applied to special purpose architectures. and we show how it can be modified for use in analyzing algorithms developed for general purpose architectures such as the Intel Touchstone or Paragon. or the Thinking Machines CM-5.