Geometric algebra: A computational framework for geometrical applications (Part I: Algebra)
Geometric algebra: A computational framework for geometrical applications (Part I: Algebra)
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DOI：
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发表时间：
2002
影响因子：
1.8
通讯作者：
L. Dorst;Stephen Mann
中科院分区：
文献类型：
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作者：
L. Dorst;Stephen Mann
几何代数是定义几何基元及其关系的一致计算框架。这种代数方法包含所有几何运算符，并允许以无坐标的方式指定结构。因此，几何代数的思想对于CAD系统的开发者来说是重要的。本文介绍了几何代数的元素，它包含任意维(而不仅仅是向量)的基元，并介绍了几何代数的三个乘积：几何积、内积和外积。这些积通过用它们来解决简单的几何问题来说明。
Geometric algebra is a consistent computational framework in which to define geometric primitives and their relationships. This algebraic approach contains all geometric operators and permits specification of constructions in a coordinate-free manner. Thus, the ideas of geometric algebra are important for developers of CAD systems. This paper gives an introduction to the elements of geometric algebra, which contains primitives of any dimensionality (rather than just vectors), and an introduction to three of the products of geometric algebra, the geometric product, the inner product, and the outer product. These products are illustrated by using them to solve simple geometric problems.