Advertisement

Foundations of Geometric Algebra Computing

  • Dietmar Hildenbrand

Part of the Geometry and Computing book series (GC, volume 8)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Dietmar Hildenbrand
    Pages 1-14
  3. Mathematical Foundations

    1. Front Matter
      Pages 15-15
    2. Dietmar Hildenbrand
      Pages 17-25
    3. Dietmar Hildenbrand
      Pages 27-44
    4. Dietmar Hildenbrand
      Pages 61-68
  4. Interactive and Visual Geometric Algebra Computing

    1. Front Matter
      Pages 69-69
    2. Dietmar Hildenbrand
      Pages 71-100
    3. Dietmar Hildenbrand
      Pages 101-106
    4. Dietmar Hildenbrand
      Pages 107-117
  5. Runtime Performance of Geometric Algebra Computing

    1. Front Matter
      Pages 119-119
    2. Dietmar Hildenbrand
      Pages 121-139
    3. Dietmar Hildenbrand
      Pages 155-160
    4. Dietmar Hildenbrand
      Pages 161-164
    5. Dietmar Hildenbrand
      Pages 165-177
    6. Dietmar Hildenbrand
      Pages 179-188
  6. Back Matter
    Pages 189-196

About this book

Introduction

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.

Keywords

CLUCalc GPGPU animation conformal geometric algebra (CGA) gaalop geometric algebra maple molecular dynamics planes point sets quaternions robotics spheres

Authors and affiliations

  • Dietmar Hildenbrand
    • 1
  1. 1.University of Technology DarmstadtDarmstadtGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-31794-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-31793-4
  • Online ISBN 978-3-642-31794-1
  • Series Print ISSN 1866-6795
  • Series Online ISSN 1866-6809
  • Buy this book on publisher's site