Introduction to Geometric Algebra Computing
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.
Table of Contents
1 Introduction I Tutorial 2 Compass Ruler Algebra in a Nutshell 3 GAALOP Tutorial for Compass Ruler Algebra II Mathematical Foundations 4 Mathematical Basics and 2D Euclidean Geometric Algebra 5 Compass Ruler Algebra and its Geometric Objects 6 Intersections in Compass Ruler Algebra 7 Distances and Angles in Compass Ruler Algebra 8 Transformations of Objects in Compass Ruler Algebra III Applications 9 Robot Kinematics using GAALOP 10 Detection of Circles and Lines in Images using GAALOP 11 Visibility Application in 2D using GAALOP 12 RuntimePerformance using GAALOP 13 Fitting of Lines or Circles into Sets of Points 14 CRAbased Robotic Snake Control 15 Expansion to 3D Computations IV Geometric Algebra at School 16 Geometric Algebra for Mathematical Education 17 SpaceTime Algebra in School and Application
Dietmar Hildenbrand is a lecturer in Geometric Algebra at TU Darmstadt.