Applications of Geometric Algebra in Computer Science and Engineering

Editors: Dorst, Leo, Doran, Chris, Lasenby, Joan (Eds.)

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About this book

Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.

Reviews

"This book contains papers presented at the conference "Applied Geometric Algebra in Computer Science and Engineering" (AGACSE 2001)…. The goal was to demonstrate how the framework of geometric algebra (Clifford algebra) could unify and illuminate diverse fields of science and engineering.

The articles reveal [a] range [of] fields: from quantum physics to robotics, from crystallographic groups to image understanding, from relativistic mechanics to signal processing. Despite this diversity, the combination of these subjects was not felt to be artificial.

This book should be…useful to mathematicians…physicists, [and] to mechanical and computer engineers."

—Iasi Polytechnic Magazine

"The conference ‘Applied Geometric Algebras in Computer Science and Engineering’ (AGACSE 2001) was held… July 9–13, 2001. The present book contains the papers of this scientific meeting and reflects the constantly growing interest in searching the applications of geometric algebra (or Clifford algebra) in various fields of science.

Geometric algebra includes a lot of techniques from several mathematical theories (linear algebra, vector calculus, projective geometry, complex analysis) and offers new directions in some unexpected domains like quantum physics, robotics, crystallographic groups, image understanding, relativistic mechanics, signal processing.

The volume begins with a preface written by the Editors and a useful list with contributors…. There are four sections: Algebra and Geometry…, Applications to Physics…, Computer Vision and Robotics…, Signal Processing and Other Applications….

In conclusion, a very useful book both for beginners and specialists!"

—Memoriile Sectiilor Stiintifice


Table of contents (41 chapters)

  • Point Groups and Space Groups in Geometric Algebra

    Hestenes, David

    Pages 3-34

  • The Inner Products of Geometric Algebra

    Dorst, Leo

    Pages 35-46

  • Unification of Grassmann’s Progressive and Regressive Products using the Principle of Duality

    Blake, Stephen

    Pages 47-57

  • From Unoriented Subspaces to Blade Operators

    Bouma, Timaeus A.

    Pages 59-67

  • Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra

    Li, Hongbo

    Pages 69-78

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-1-4612-0089-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $229.00
price for USA
  • ISBN 978-0-8176-4267-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $199.00
price for USA
  • ISBN 978-1-4612-6606-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Applications of Geometric Algebra in Computer Science and Engineering
Editors
  • Leo Dorst
  • Chris Doran
  • Joan Lasenby
Copyright
2002
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0089-5
DOI
10.1007/978-1-4612-0089-5
Hardcover ISBN
978-0-8176-4267-9
Softcover ISBN
978-1-4612-6606-8
Edition Number
1
Number of Pages
XXV, 478
Topics