Multidimensional Computations: Design Theory and VLSI Prototyping

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This research focuses on the theoretical study of rasterization theory and the prototyping of the developed rasterized structure. A real-time rasterized structure is being developed. In this new architecture, the desired computations are performed in the time interval between the arrivals of two neighboring pixels without extensive buffering and reformatting of the data. This is achieved by transforming a multidimensional computation into a one dimensional one and by processing the transformed data. A rasterization theory is being developed which provides a mathematical basis for translating many multidimensional computations, constrained to utilizing scan-line data in real time, into their equivalent one-dimensional computation. Many computations require global data communication as well as the real-time evaluation of large quantities of data. Computational architectures are often constrained by the format in which the input data is available, namely, raster-scan format. However, the operations to be performed are often global in nature. This input/output format constraint would hinder full utilization of parallelism without extensive buffering and reformatting of input/output data. This research develops the necessary computational model, which makes possible the design of a balanced structure of computations and inputs/outputs.