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

大多数计算机辅助设计系统将表面定义为双重 无穷多个点 使用点几何只允许两个 几何构造：曲线和曲面。 以线条为基础 空间的构建块对于形状生成更灵活， 设计，因为线几何允许定义三种类型的 几何构造 本研究的重点是发展 计算机辅助产品设计的数学基础 在线几何学 基本的想法是使用线条，而不是 thanpoints，作为几何形状的基本构建块。 线几何中定义的三个几何构造是直纹的 曲面、线同余和线复形，它们是一个，两个， 和三个参数线族。 本研究 将研究这三个几何的计算几何， 构建，并制定一个总体框架， 基于直线几何学的计算机辅助设计。

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.