Introduction to Geometric Algebra Computing (Computer Vision)

From the Foreword:

"Dietmar Hildenbrand's new book, Introduction to Geometric Algebra Computing, in my view, fills an important gap in Clifford's geometric algebra literature…I can only congratulate the author for the daring simplicity of his novel educational approach taken in this book, consequently combined with hands on computer based exploration. Without noticing, the active reader will thus educate himself in elementary geometric algebra algorithm development, geometrically intuitive, highly comprehensible, and fully optimized."

--Eckhard Hitzer, International Christian University, Tokyo, Japan

Geometric Algebra is a very powerful mathematical system for an easy and intuitive treatment of geometry, but the community working with it is still very small. The main goal of this book is to close this gap with an introduction to Geometric Algebra from an engineering/computing perspective.

This book is intended to give a rapid introduction to computing with Geometric Algebra and its

power for geometric modeling. From the geometric objects point of view, it focuses on the most basic ones, namely points, lines and circles. This algebra is called Compass Ruler Algebra, since it is comparable to working with a compass and ruler. The book explores how to compute with these geometric objects, and their geometric operations and transformations, in a very intuitive way.

The book follows a top-down approach, and while it focuses on 2D, it is also easily expandable to 3D computations. Algebra in engineering applications such as computer graphics, computer vision and robotics are also covered.

從前言中：

「Dietmar Hildenbrand的新書《Introduction to Geometric Algebra Computing》填補了Clifford幾何代數文獻中的一個重要空白...我只能對作者在這本書中採取的大膽簡潔的教育方法表示祝賀，並結合了基於電腦的實踐探索。在不知不覺中，積極的讀者將在基礎幾何代數算法開發方面自我教育，具有幾何直觀性、高度可理解性和完全優化。」

- Eckhard Hitzer, 國際基督教大學, 東京, 日本

幾何代數是一個非常強大的數學系統，用於對幾何學進行簡單直觀的處理，但使用它的社群仍然非常小。本書的主要目標是從工程/計算的角度介紹幾何代數，以填補這一空白。

本書旨在快速介紹如何使用幾何代數進行計算，以及其在幾何建模中的應用。從幾何物體的角度來看，它主要關注最基本的幾何物體，即點、線和圓。這種代數被稱為Compass Ruler Algebra，因為它類似於使用指南針和尺子進行操作。本書探討了如何以非常直觀的方式計算這些幾何物體及其幾何操作和變換。

本書採用自上而下的方法，雖然重點是2D，但也很容易擴展到3D計算。還介紹了在計算機圖形學、計算機視覺和機器人等工程應用中的代數。