Computer-Aided Geometric Design and Computational Geometry of Geometric Constructs Defined by Line Geometry

计算机辅助几何设计和线几何定义的几何构造的计算几何

• 批准号: 8619165
• 负责人: Bahram Ravani
• 金额: $ 6.4万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-01 至 1987-10-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8619165&HistoricalAwards=false
• 关键词: Computer; Aided; Geometric; Design; Computational

Most computer-aided design systems define surfaces as doubly infinite families of points. Using point geometry allows only two geometric constructs: curves and surfaces. Using lines as the basic building block of space is more flexible for shape generation and design since line geometry allows the definition of three types of geometric constructions. This research focuses on the development of the mathematical foundation for computer-aided design of products based online geometry. The fundamental idea is to use lines, rather thanpoints, as the fundamental building block of geometric shapes. The three geometric constructs defined in a line geometry are ruled surfaces, line congruences, and line complexes which are one, two, and three parameter families of lines respectively. This research will study the computational geometry of these three geometric constructs and,in addition, develop a general framework for computer-aided design based on line geometry.

大多数计算机辅助设计系统将曲面定义为无限倍的点族。使用点几何只允许两种几何结构：曲线和曲面。使用线条作为空间的基本构建块对于形状的生成和设计更加灵活，因为线条几何允许定义三种类型的几何结构。本研究的重点是基于在线几何的产品计算机辅助设计的数学基础的开发。其基本思想是使用线，而不是点，作为几何形状的基本组成部分。在直线几何中定义的三种几何结构是直纹面、线同余和线复合体，它们分别是直线的一个、两个和三个参数族。本研究将研究这三种几何结构的计算几何，此外，开发基于线几何的计算机辅助设计的一般框架。