应数学系应用数学研究所的邀请，美国莱斯大学（Rice University）的Ronald Goldman教授将于2015年7月16日到7月22日来公司进行交流访问，并于7月17日下午做学术报告，欢迎感兴趣的师生参加！

报告时间：2015年7月17日，16:00--17:30

报告地点：正心楼42教室

报告题目: Algebraic and Geometric Extensions of The Lane-Riesenfeld Subdivision Algorithm

报告摘要: Subdivision is a contemporary, computer aided tool for generating smooth shapes from course data. The Lane-Riesenfeld algorithm is a classical subdivision procedure based on the standard split and average paradigm, which generates uniform B-spline (i.e. piecewise polynomial) curves and surfaces. We begin by investigating algebraic variants of the Lane-Riesenfeld Algorithm, using more wide-ranging averaging rules in order to generate more general functions. We go on to discuss geometric variations of the Lane-Riesenfeld algorithm in order to develop subdivision schemes with additional shape control. Instead of treating each component of a curve independently, we treat the control polygons as geometric entities, where the components do not have independent geometric meanings. The split and averaging paradigm of the Lane-Riesenfeld algorithm is mimicked, but midpoint averaging is replaced by different notions of geometric averaging. Extensions of these ideas to the complex plane are also investigated. We discuss what is currently known, conjectured, and not known about the convergence, continuity, and smoothness of these algebraic and geometric extensions of the Lane-Riesenfeld subdivision algorithm.

报告人简介：Ronald Goldman 教授1968年毕业于MIT数学系, 1973年获John-Hopkins大学数学博士学位，毕业后到福特汽车公司工作，负责图形与几何设计软件的开发工作。1987年任Waterloo大学计算机系副教授，1990年起任Rice大学计算机系教授。Ron Goldman教授是几何设计与计算领域的国际著名专家，是Advances in Computational Mathematics, Computer-Aided Design及Computer-Aided Geometric Design等国际著名专业杂志编委，多次担任国际专业会议主席及在重要会议（包括Pacific Graphics, Geometric Modeling and Processing等）作特邀报告，主持美国NSF基金项目20余项，发表学术论文150余篇，出版专著6本，2005年获得John Gregory Memorial Award，是目前几何设计领域最高奖项。