Computational geometry and data analysis

点击翻译按钮获取中文摘要

I study the geometry in problems with the intent of producing correct and efficient computer programs. Applications such as computer graphics, computer vision, optical character recognition, robotics, computer-aided design, and computer-aided manufacturing, network design, and data analysis all have some geometric component. My work focuses on the geometric structure or geometric patterns that can be used to solve these types of problems. The nature of my research is primarily theoretical in the sense that general methods and techniques are given. These results may not immediately apply to a particular problem. However, with the appropriate modifications, these results will be used for a variety of applications. Furthermore, these results are not based on any existing computer hardware or operating system. Thus the results have the added advantage of being useful in the future on some currently unimaginable machine.