Computational Geometry and Applications

计算几何及其应用

• 批准号: RGPIN-2015-06662
• 负责人: Rappaport, David
• 金额: $ 1.75万
• 依托单位: Queen's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=614285
• 关键词: Computational; Geometry; Applications

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.

我研究几何方面的计算问题的目的是产生正确和有效的算法。我的工作应用包括计算机图形学，计算机视觉，光学字符识别，机器人，计算机辅助设计和制造（CAD/CAM），网络设计和数据分析。 我的研究的一个重要部分是理论的，在这个意义上，一般的方法和技术是为解决一系列假设问题而开发的。我的工作也有一个方面是应用驱动的。我一直在与博物馆服务领域的全球领导者Research Casting International（RCI）公司合作，为他们的业务数字化提供软件解决方案。我还与同事合作，共同监督从事计算机视觉和计算机图形学研究的博士生。 我研究的理论方面是好奇心驱动的，重点是几何结构和几何对象如何相互作用的组合学。我的重点是与“可见性”有关的问题，即域中几何实体之间的关系。可见性可以构成从一个对象到另一个对象的直线无障碍路径，但也可以采取相邻对象的形式，或者满足物理和几何特性的组合的对象。我最感兴趣的是优化算法及其应用。我曾经研究过的一些主题包括音乐相似性度量、图形绘制和三角测量。 我的理论研究和我的博士生的工作可能会以今天没有预料到的方式具有长期价值。我们的应用研究对计算机视觉和计算机图形学领域产生了更直接的影响，包括为RCI解决问题的技术转让。我们为RCI提供了定制的软件，用于增强他们的工作流程，并为他们赢得利润丰厚的合同提供竞争优势。 我所有的工作都有一个重要的培训部分。我现在和将来都将与高中生、本科生、硕士生、博士生和博士后合作。