Computational Geometry and Applications

点击翻译按钮获取中文摘要

I study geometric aspects of computational problems with the intent of producing correct and efficient algorithms. Applications of my work include computer graphics, computer vision, optical character recognition, robotics, computer-aided design and manufacturing (CAD/CAM), network design, and data analysis.***A significant part of my research is theoretical in the sense that general methods and techniques are developed for solving a range of hypothetical problems. There is also a side of my work that is application driven. I have been collaborating with the firm Research Casting International (RCI), a world leader in museum services, by providing them with software solutions for the digital element of their business. I also collaborate with colleagues through joint supervision of PhD students who work in computer vision, and computer graphics.***The theoretical side of my research is curiosity driven and focuses on geometric structure and the combinatorics of how geometric objects interact. My focus is on problems that are related to "visibility", that is, the relationship between geometric entities in a domain. The visibility could constitute a straight line unobstructed path from one object to another, but could also take the form of objects being adjacent, or objects satisfying a combination of physical and geometric properties. I am most interested in optimization algorithms and their applications. Some of the topics that I have worked on include, music similarity measures, graph drawing, and triangulations. ***My theoretical research and the work of my PhD students may have long term value in ways that are not anticipated today. Our applications research has a more immediate impact to the fields of computer vision and computer graphics, including technology transfer to solve problems for RCI. We have provided customized software to RCI used to enhance their workflow and provide them with the competitive edge at winning lucrative contracts. ***All of my work has a significant training component. I am, and will be, collaborating with high school students, undergraduates, Master's students, PhD students, and post docs. **