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

Subdivision Algorithm

报告人： Ron Goldman, Department of Computer Science, Rice University

报告时间：4.26（周三）上午：9.45-10:45

地点：1218

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.