**Foundations of Geometric Algebra Computing**

by Dietmar Hildenbrand [Technische Universität Darmstadt]

Springer Series: Geometry and Computing

ISBN 978-3-642-31793-4, 49.95 Euros, 69.95 USD, ca. 240 pp., ca. 09/12

**Outline**

The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, com-puter graphics, and robotics.

This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific lan-guage in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and appli-cations.

The book is suitable for students, engineers, and researchers in computer science, computational engineer-ing, and mathematics.

**Table of Contents**

• Introduction

Part I – Mathematical Foundations

• Mathematical Introduction

• Conformal Geometric Algebra

• Maple and the Identification of Quaternions and Other Algebras

• Fitting of Planes or Spheres to Sets of Points

Part II – Interactive and Visual Geometric Algebra Computing

• A Tutorial on Geometric Algebra Using CLUCalc

• Inverse Kinematics of a Simple Robot

• Robot Grasping an Object

Part III – Runtime Performance of Geometric Algebra Computing

• Efficient Computer Animation Application in CGA

• Using Gaalop for High-Performance Geometric Algebra Computing

• Collision Detection Using the Gaalop Precompiler

• Gaalop Precompiler for GPUs

• Molecular Dynamics Using Gaalop GPC for OpenCL

• Geometric Algebra Computers

References

Source: Email by D. Hildenbrand, 2012/07/07 2:06, d.hildenbrand_at_cocoon.tu-darmstadt.de