Presidential Young Investigator Award: 2-D and 3-D Interactive Computer Modeling Systems

一项交互式计算机建模的研究计划正在启动。 本研究集中在曲线和 几何造型中曲面表示及其实现 系统. 许多理论和实践问题进行了探讨，包括 允许局部形状参数，在更高程度上泛化， 确定差分公式，推导递推关系， 开发细分技术和设计渲染算法。 所有这些主题的研究都使用符号计算工具，例如 Vaxima来处理正式的计算。 这项工作是追求双方 因为它内在的数学兴趣和它在 计算机图形学和计算机辅助几何设计。 希望 学习数学理论是为了满足 应用领域将产生更好的基本理解， 提供计算机图形学领域的有用技术， 计算机辅助几何设计

A research program in interactive computer modeling is being initiated. This research concentrates on mathematical techniques for curve and surface representation and their implementation in geometric modeling systems. Many theoretical and practical issues are explored, including allowing local shape parameters, generalizing in higher degree, determining divided-difference formulas, deriving recurrence relations, developing subdivision techniques, and designing rendering algorithms. Research in all these topics uses symbolic computation tools such as Vaxima to handle the formal calculations. This work is pursued both for its intrinsic mathematical interest and its potential use in computer graphics and computer-aided geometric design. It is hoped that studying the mathematical theory in response to the needs of the application area will engender a better fundamental understanding and provide useful techniques in the fields of computer graphics and computer-aided geometric design.