Multidimensional Computations: Design Theory and VLSI Prototyping

本研究的重点是栅格化理论的理论研究和所开发的栅格化结构的原型设计。实时栅格化结构正在开发中。在这种新架构中，所需的计算在两个相邻像素到达之间的时间间隔内执行，而无需大量缓冲和重新格式化数据。这是通过将多维计算转换为一维计算并处理转换后的数据来实现的。光栅化理论正在发展，它提供了一个数学基础，将许多多维计算，限制在利用实时扫描线数据，到他们等效的一维计算。许多计算需要全球数据通信以及对大量数据的实时评估。计算架构经常受到输入数据可用格式的限制，即光栅扫描格式。然而，要执行的操作在本质上通常是全局的。如果没有大量缓冲和重新格式化输入/输出数据，这种输入/输出格式约束将阻碍并行性的充分利用。本研究开发了必要的计算模型，使设计计算和输入/输出的平衡结构成为可能。

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.