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
Biography
Dietmar Hildenbrand is a lecturer in Geometric Algebra at TU Darmstadt.
"This book is a hands-on introduction to conformal geometric algebra (CGA) using the GAALOP (Geometric Algebra Algorithms Optimizer) software. It aims at quickly enabling the reader to use CGA and GAALOP for constructions with and transformations of elementary 2D geometric entities (points, lines, circles, and point pairs). Only cursory information on the underlying theory is given. Instead we ¿nd numerous code listings and ¿gures (unfortunately also some of unsatisfactory quality). Readers who are interested in more background information to CGA computing are referred to [D. Hildenbrand, Foundations of geometric algebra computing. Berlin: Springer (2013; Zbl 1268.65038)].
Section I is a tutorial on 2D CGA (here also called “Compass Ruler Algebra”) and GAALOP. Section II introduces more mathematical concepts and provides geometric interpretations of diverse CGA objects and products. In Section III the author gives application examples of CGA in robotics, image processing, or computational geometry. Even if drawing from serious scienti¿c publications, the presentation remains at an elementary level. The end of this section also features a brief introduction to 3D CGA. The ¿nal Section IV contains thoughts on the educational values of CGA at high-school level and a reference to D. Hestenes’ pioneering work on application of CGA in physics and its didactics [Space-time algebra. New York-London-Paris: Gordon and Breach Science Publishers (1966; Zbl 183.28901)].
The target audience of this book is readers who want to familiarize themselves quickly with basic concepts of CGA and the GAALOP software and don’t require too much theoretical background. The provided information is su¿cient for constructions and computations in elementary geometry but also for educational purposes and certain applications in engineering and computer science."
-Hans-Peter Schr¨ocker (Innsbruck) - Zentralblatt MATH 1397 — 1
