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Applications of Geometric Algebra in Computer Science and Engineering

  • Leo Dorst
  • Chris Doran
  • Joan Lasenby

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Algebra and Geometry

    1. Front Matter
      Pages 1-1
    2. Timaeus A. Bouma
      Pages 59-67
    3. W. E. Baylis, S. Hadi
      Pages 79-90
    4. Neil Gordon
      Pages 91-98
    5. Uwe Prells, Michael I. Friswell, Seamus D. Garvey
      Pages 109-118
    6. Frank Sommen
      Pages 119-128
    7. Jeffrey A. Chard, Vadim Shapiro
      Pages 129-131
    8. Richard Baker, Chris J. L. Doran
      Pages 133-143
    9. John P. Fletcher
      Pages 157-167
    10. Alyn Rockwood, Shoeb Binderwala
      Pages 179-185
    11. Cemal Koc, Songul Esin
      Pages 193-194
  3. Applications to Physics

    1. Front Matter
      Pages 195-195
    2. David Hestenes, Ernest D. Fasse
      Pages 197-212
    3. Rachel Parker, Chris J. L. Doran
      Pages 213-226
    4. Timothy F. Havel, Chris J. L. Doran
      Pages 227-247
    5. T. Schulte-Herbrüggen, K. Hüper, U. Helmke, S. J. Glaser
      Pages 271-283
    6. V. Labunets, E. Rundblad, J. Astola
      Pages 285-295
    7. Quirino M. Sugon, Daniel McNamara
      Pages 297-306
    8. Patrick R. Girard
      Pages 307-315
  4. Computer Vision and Robotics

    1. Front Matter
      Pages 317-317
    2. Jan J. Koenderink
      Pages 319-332
    3. Eduardo Bayro-Corrochano, Sandino Flores
      Pages 333-339
    4. Christian B. U. Perwass, Gerald Sommer
      Pages 341-350
    5. Seamus D. Garvey, Michael I. Friswell, Uwe Prells
      Pages 351-359
    6. Eduardo Bayro-Corrochano, Pertti Lounesto, Leo Reyes Lozano
      Pages 361-372
    7. Bodo Rosenhahn, Oliver Granert, Gerald Sommer
      Pages 373-383
    8. W. Neddermeyer, M. Schnell, W. Winkler, A. Lilienthal
      Pages 385-394
    9. Hiniduma Udugama Gamage Sahan Sajeewa, Joan Lasenby
      Pages 395-406
    10. Michael A. Baswell, Rafał Abłamowicz, Joe N. Anderson
      Pages 407-421
  5. Signal Processing and Other Applications

    1. Front Matter
      Pages 423-423
    2. V. Labunets, E. Rundblad, J. Astola
      Pages 425-435
    3. Michael Felsberg, Gerald Sommer
      Pages 437-448
    4. Erwin Hocevar
      Pages 459-467
    5. Vladimir G. Labunets, Ekaterina Rundblad, J. Astola
      Pages 469-478

About this book

Introduction

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.

Keywords

Algebra algorithm calculus differential equation electromagnetism geometry information theory kinematics linear algebra mechanics model operator partial differential equation robotics transformation

Editors and affiliations

  • Leo Dorst
    • 1
  • Chris Doran
    • 2
  • Joan Lasenby
    • 3
  1. 1.Informatics InstituteUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Cavendish LaboratoryCambridge UniversityCambridgeUK
  3. 3.Department of Engineering-Signal ProcessingCambridge UniversityCambridgeUK

Bibliographic information