Geometric Algebra with Applications in Engineering

  • Christian Perwass

Part of the Geometry and Computing book series (GC, volume 4)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Theory

    1. Pages 1-23
    2. Pages 51-117
    3. Pages 119-195
    4. Pages 197-251
  3. Applications

  4. Back Matter
    Pages 369-385

About this book

Introduction

The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will result in intuitive and more robust algorithms.

This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data. Formally, the book consists of two parts: theoretical foundations and applications. The first part includes chapters on random variables in geometric algebra, linear estimation methods that incorporate the uncertainty of algebraic elements, and the representation of geometry in Euclidean, projective, conformal and conic space. The second part is dedicated to applications of geometric algebra, which include uncertain geometry and transformations, a generalized camera model, and pose estimation.

Graduate students, scientists, researchers and practitioners will benefit from this book. The examples given in the text are mostly recent research results, so practitioners can see how to apply geometric algebra to real tasks, while researchers note starting points for future investigations. Students will profit from the detailed introduction to geometric algebra, while the text is supported by the author's visualization software, CLUCalc, freely available online, and a website that includes downloadable exercises, slides and tutorials.

Keywords

Algebra Applied mathematics CLUCalc Computer vision Geometric algebra Geometric computing Geometry Inversion camera model Pose estimation Pythagorean-hodographs Robotics Uncertain geometry Versor functions algorithms visualization

Authors and affiliations

  • Christian Perwass
    • 1
  1. 1.Dr. habil. Christian Bernd Ulrich Perwaβ Department of Computer ScienceChristian-Albrechts-Universität zu KielGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-89068-3
  • Copyright Information Springer Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-540-89067-6
  • Online ISBN 978-3-540-89068-3
  • Series Print ISSN 1866-6795
  • About this book