Computational geometry and data analysis

我研究问题中的几何，目的是编写正确而高效的计算机程序。诸如计算机图形学、计算机视觉、光学字符识别、机器人技术、计算机辅助设计、计算机辅助制造、网络设计和数据分析等应用程序都有一些几何成分。我的工作重点是几何结构或几何图案，可以用来解决这些类型的问题。我的研究本质上主要是理论性的，因为我给出了一般的方法和技术。这些结果可能不会立即适用于特定问题。但是，通过适当的修改，这些结果将用于各种应用程序。此外，这些结果不是基于任何现有的计算机硬件或操作系统。因此，这些结果还有一个额外的优点，那就是将来在一些目前无法想象的机器上很有用。

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.