论文标题
课程注释计算机图形的几何代数，Siggraph 2019
Course notes Geometric Algebra for Computer Graphics, SIGGRAPH 2019
论文作者
论文摘要
在计算机上进行欧几里得几何形状的最佳表示是什么？这些注释来自Siggraph 2019的短期课程，标题为“计算机图形的几何代数”，将投影性几何代数（PGA）引入了这项任务的现代框架。 PGA特征：点，线和平面的均匀表示；强大的，平行安全的加入并满足操作；欧几里得公式和结构的紧凑，多态性语法；同量法的单个直观三明治形式；对自动差异的本地支持；以及运动学和刚体力学的紧密整合。 PGA包括矢量，四元组，双重四基因和外部代数为子代数，简化了经验丰富的从业者的学习曲线和过渡路径。从实际方面来说，它可以有效地实施，而其丰富的语法可以提高编程生产率。基本思想是在2D上下文中引入的，并为3D选择性开发。最终，在表格中收集了传统方法的优势。该文章旨在成为欧几里得几何学从业者的独立介绍，并包括许多例子，公式，图形和表格。
What is the best representation for doing euclidean geometry on computers? These notes from a SIGGRAPH 2019 short course entitled "Geometric algebra for computer graphics" introduce projective geometric algebra (PGA) as a modern framework for this task. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet operations; compact, polymorphic syntax for euclidean formulas and constructions; a single intuitive sandwich form for isometries; native support for automatic differentiation; and tight integration of kinematics and rigid body mechanics. PGA includes vector, quaternion, dual quaternion, and exterior algebras as sub-algebras, simplifying the learning curve and transition path for experienced practitioners. On the practical side, it can be efficiently implemented, while its rich syntax enhances programming productivity. The basic ideas are introduced in the 2D context and developed selectively for 3D. Advantages to traditional approaches are collected in a table at the end. The article aims to be a self-contained introduction for practitioners of euclidean geometry and includes numerous examples, formulas, figures, and tables.
