Geometry and Computing

Foundations of Geometric Algebra Computing

Authors: Hildenbrand, Dietmar

  • Defines geometric algebra computing as the geometrically intuitive development of algorithms with a focus on their efficient implementation
  • Author anticipates the forthcoming widespread adoption of parallel processor technology
  • New computing platforms can benefit from the inherent optimization and parallelization of the techniques described
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About this Textbook

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, computer 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 language 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 applications.

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

About the authors

Dr.-Ing. Dietmar Hildenbrand is a member of the Mathematics Department of the Technische Universität Darmstadt. He is one of the codevelopers of Gaalop (Geometic Algebra Algorithms Optimizer) a software package used to optimize geometric algebra files, and his research interests include geometric algebra, robotics, game engines, computer graphics, and high-performance parallel computing.

Reviews

From the book reviews:

“This textbook addresses students (undergraduate to postgraduate), scientists and engineers with an interest in intuitive and highly efficient computer programs based on W. K. Clifford’s geometric algebras. The book greatly benefits from the original work of the author, and is very readable. … After a general introduction to the benefits of geometric algebra, geometric algebra computing and its historical development, the book is divided into three main parts.” (Eckhard M. S. Hitzer, Mathematical Reviews, May, 2014)

Table of contents (14 chapters)

  • Introduction

    Hildenbrand, Dietmar

    Pages 1-14

  • Mathematical Introduction

    Hildenbrand, Dietmar

    Pages 17-25

  • Conformal Geometric Algebra

    Hildenbrand, Dietmar

    Pages 27-44

  • Maple and the Identification of Quaternions and Other Algebras

    Hildenbrand, Dietmar

    Pages 45-59

  • Fitting of Planes or Spheres to Sets of Points

    Hildenbrand, Dietmar

    Pages 61-68

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-642-31794-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.95
price for USA
  • ISBN 978-3-642-31793-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.95
price for USA
  • ISBN 978-3-642-44572-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Foundations of Geometric Algebra Computing
Authors
Series Title
Geometry and Computing
Series Volume
8
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-31794-1
DOI
10.1007/978-3-642-31794-1
Hardcover ISBN
978-3-642-31793-4
Softcover ISBN
978-3-642-44572-9
Series ISSN
1866-6795
Edition Number
1
Number of Pages
XXVIII, 196
Topics