Interactive Computer Graphics for the Geometry of Surfaces in 3- and 4-Space

3 空间和 4 空间曲面几何的交互式计算机图形学

• 批准号: 9105166
• 负责人: Thomas Banchoff
• 金额: $ 12万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1995-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9105166&HistoricalAwards=false
• 关键词: Interactive; Computer; Graphics; Geometry; Surfaces

During the past two years, the PI's NSF grant has made it possible to generate a new collection of computer graphics programs for the geometry of smooth and polyhedral submanifolds in euclidean 3- and 4-space. This ongoing work has been the result of collaborations with undergraduate and graduate students. It has been applied in the proposer's research on the geometry of piecewise circular curves and on highly symmetric combinatorial structures on the complex projective plane. Preliminary versions of this research program have been used to provide the illustrations for proposer's Scientific American Library book and several articles, as well as the images used for Mathematics Awareness Week. The P.I. and his assistants intend to continue the development of this system, and to apply it to extensions of the problems, as well as other problems in the geometry of submanifolds. The work of the P.I. has interest to the mathematical Sciences community at large, as well as to mathematics educators.

在过去的两年里，PI 的 NSF 资助使得生成一系列新的计算机图形程序成为可能，用于欧几里得 3 空间和 4 空间中的光滑和多面体子流形的几何形状。 这项正在进行的工作是与本科生和研究生合作的结果。 它已被应用于提出者对分段圆曲线几何和复射影平面上高度对称组合结构的研究。 该研究计划的初步版本已用于为提案者的《科学美国图书馆》书籍和几篇文章提供插图，以及用于数学意识周的图像。 P.I.他和他的助手打算继续开发这个系统，并将其应用于问题的扩展以及子流形几何中的其他问题。 P.I. 的工作整个数学科学界以及数学教育工作者都感兴趣。