Guide to Geometric Algebra in Practice

  • Leo Dorst
  • Joan Lasenby

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Rigid Body Motion

    1. Front Matter
      Pages 1-1
    2. Anthony Lasenby, Robert Lasenby, Chris Doran
      Pages 3-24
    3. Andreas Aristidou, Joan Lasenby
      Pages 47-62
  3. Interpolation and Tracking

    1. Front Matter
      Pages 79-79
    2. Liam Candy, Joan Lasenby
      Pages 105-125
    3. Robert Valkenburg, Nawar Alwesh
      Pages 127-148
  4. Image Processing

    1. Front Matter
      Pages 149-149
    2. Eduardo Bayro-Corrochano, Eduardo Ulises Moya-Sánchez
      Pages 151-173
    3. Jose Mennesson, Christophe Saint-Jean, Laurent Mascarilla
      Pages 175-191
  5. Theorem Proving and Combinatorics

    1. Front Matter
      Pages 193-193
    2. Hongbo Li, Yuanhao Cao
      Pages 195-215
    3. Philippe Serré, Nabil Anwer, JianXin Yang
      Pages 217-232
    4. René Schott, G. Stacey Staples
      Pages 233-249
  6. Applications of Line Geometry

    1. Front Matter
      Pages 251-251
    2. Lilian Aveneau, Sylvain Charneau, Laurent Fuchs, Frederic Mora
      Pages 273-294

About this book

Introduction

Geometric algebra (GA), also known as Clifford algebra, is a powerful unifying framework for geometric computations that extends the classical techniques of linear algebra and vector calculus in a structural manner. Its benefits include cleaner computer-program solutions for known geometric computation tasks, and the ability to address increasingly more involved applications.

This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software tools. Contributions are included from an international community of experts spanning a broad range of disciplines.

Topics and features:

  • Provides hands-on review exercises throughout the book, together with helpful chapter summaries
  • Presents a concise introductory tutorial to conformal geometric algebra (CGA)
  • Examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing
  • Reviews the employment of GA in theorem proving and combinatorics
  • Discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA
  • Proposes applications of coordinate-free methods of GA for differential geometry

This comprehensive guide/reference is essential reading for researchers and professionals from a broad range of disciplines, including computer graphics and game design, robotics, computer vision, and signal processing. In addition, its instructional content and approach makes it suitable for course use and students who need to learn the value of GA techniques.

Dr. Leo Dorst is Universitair Docent (tenured assistant professor) in the Faculty of Sciences, University of Amsterdam, The Netherlands. Dr. Joan Lasenby is University Senior Lecturer in the Engineering Department of Cambridge University, U.K.

Keywords

Clifford Algebra Conformal Model Geometric Algebra Linear Algebra Quaternions Vector Mathematics

Editors and affiliations

  • Leo Dorst
    • 1
  • Joan Lasenby
    • 2
  1. 1.Informatics InstituteUniversity of AmsterdamAmsterdamNetherlands
  2. 2.Department of EngineeringUniversity of CambridgeCambridgeUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-811-9
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Computer Science
  • Print ISBN 978-0-85729-810-2
  • Online ISBN 978-0-85729-811-9
  • About this book