The Power of Geometric Algebra Computing

For Engineering and Quantum Computing
1. Auflage 2023
ISBN: 978-0-367-68775-5
Verlag: Chapman and Hall/CRC

Buch, Englisch, 202 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 301 g

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 from a computing perspective in presenting the power of Geometric Algebra Computing for engineering applications and quantum computing.

The Power of Geometric Algebra Computing is based on GAALOPWeb, a new user-friendly, web-based tool for the generation of optimized code for different programming languages as well as for the visualization of Geometric Algebra algorithms for a wide range of engineering applications.

Key Features:

- Introduces a new web-based optimizer for Geometric Algebra algorithms

- Supports many programming languages as well as hardware

- Covers the advantages of high-dimensional algebras

- Includes geometrically intuitive support of quantum computing

This book includes applications from the fields of computer graphics, robotics and quantum computing and will help students, engineers and researchers interested in really computing with Geometric Algebra.

Autoren/Hrsg.

Hildenbrand, Dietmar

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Spiele-Programmierung, Rendering, Animation
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Computer Vision
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Robotik
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Mustererkennung, Biometrik

Inhaltsverzeichnis

Foreword

Preface

Acknowledgements

Introduction
1.1 GEOMETRIC ALGEBRA
1.2 GEOMETRIC ALGEBRA COMPUTING
1.3 OUTLINE

Geometric Algebras for Engineering
2.1 THE BASICS OF GEOMETRIC ALGEBRA
2.2 CONFORMAL GEOMETRIC ALGEBRA (CGA)
2.2.1 Geometric Objects of Conformal Geometric Algebra
2.2.2 Angles and Distances in 3D
2.2.3 3D Transformations
2.3 COMPASS RULER ALGEBRA (CRA)
2.3.1 Geometric objects
2.3.2 Angles and Distances
2.3.3 Transformations
2.4 PROJECTIVE GEOMETRIC ALGEBRA (PGA) WITH GANJA
2.4.1 2D PGA
2.4.2 3D PGA

GAALOP
3.1 INSTALLATION 26
3.2 GAALOPSCRIPT 28
3.2.1 The main notations 28
3.2.2 Macros and Pragmas 28
3.2.3 Bisector Example 29
3.2.4 Line-Sphere Example 30

GAALOPWeb
4.1 THE WEB INTERFACE
4.2 THE WORKFLOW
4.3 GAALOPWEB VISUALIZATIONS
4.3.1 Visualization of the Bisector Example
4.3.2 Visualization of the Rotation of a Circle
4.3.3 Visualization of the Line-Sphere Example
4.3.4 Visualization of a Sphere Of Four Points
4.3.5 Sliders

GAALOPWeb for C/C++
5.1 GAALOPWEB HANDLING
5.2 CODE GENERATION AND RUNTIME PERFORMANCE
BASED ON GAALOPWEB

GAALOPWeb for Python
6.1 THE WEB INTERFACE
6.2 THE PYTHON CONNECTOR FOR GAALOPWEB
6.3 CLIFFORD/PYGANJA
6.4 GAALOPWEB INTEGRATION INTO CLIFFORD/PYGANJA
6.5 USING PYTHON TO GENERATE CODE NOT SUPPORTED BY GAALOPWEB

Molecular Distance Application using GAALOPWeb
for Mathematica
7.1 DISTANCE GEOMETRY EXAMPLE
7.2 GAALOPWEB FOR MATHEMATICA
7.2.1 Mathematica code generation
7.2.2 The Web-Interface
7.3 COMPUTATIONAL RESULTS

Robot Kinematics based on GAALOPWeb for Matlab
8.1 THE MANIPULATOR MODEL
8.2 KINEMATICS OF A SERIAL ROBOT ARM
8

Über Autor(innen)

Dietmar Hildenbrand is a lecturer in Geometric Algebra at TU Darmstadt.