GA Online Resources


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GA Resources

Before getting into the links, I found a very good online list compiled by Pablo Bleyer Kocik containing many sources of information about Geometric Algebra. I highly recommend visiting his list.

 

Introductory Papers

  • “Geometric Algebra”, Eric Chisolm, 2012 (online)
  • “A Survey of Geometric Algebra and Geometric Calculus”, Alan Macdonald, 2016 (online)
  • “Geometric Algebra for Electrical and Electronic Engineers”, by James M. Chappell et. al., IEEE 2014 (online)
  • “Applications of Clifford’s Geometric Algebra”, Eckhard Hitzer, Tohru Nitta and Yasuaki Kuroe, 2013 (online)

Introductory Books

  • The simplest book to start from is “Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics” by Kenichi Kanatani. (online)
  • “Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry” by Leo Dorst, Daniel Fontijne, and Stephen Mann (online), and (book website)
  • “Visualizing Quaternions” by Andrew J. Hanson (online)
  • “Geometric Algebra with Applications in Engineering” by Christian Perwass (online)

Important Web Pages \ Blogs

  • Geometric Calculus Research and Development (web page). Dr. David Hestenes page, chief architect of geometric algebra as a unified language for mathematics and physics.
  • The GA-Net Updates (web page) containing information about events, publications, and more regarding GA and its applications
  • Waterloo Computer Graphics Lab (online)
  • University of Cambridge Geometric Algebra (web page), created by Dr. Chris Doran and Professor Anthony Lasenby
  • Ian C. G. Bell’s “Math for Game Programmers” (web page), one of the oldest online pages (since 1998) containing good information about the mathematics and applications of GA
  • Dr. Dietmar Hildenbrand (web page) the creator of Gaalop (Geometric Algebra Algorithms Optimizer).
  • Three pages from Steven Lahar, an independent researcher with some radical ideas about harmonic resonance and spatial standing waves as the computational principle behind perception and cognition:
  • Applied Geometric Algebra in Computer Science and Engineering 2015 (online)
  • Eduardo Jose Bayro-Corrochano Page (online)
  • The Chair of Cognitive Systems, Prof. Dr. G. Sommer, Institute of Computer Science, Faculty of Engineering, Christian-Albrechts-University of Kiel (online)
  • Geometric Algebra Facebook Page (online)
  • GA Computing (web page) and (blog) by Ahmad Eid
  • The “EuclideanSpace – Mathematics and Computing” (web site). This site looks at mathematics and how it can be computed. It contains several (sections) on Geometric Algebra.
  • The Pre-University Geometric Algebra Linkedin Group (online). This group is a space for the sharing and collaborative development of resources for teaching GA at the high-school level. More advanced materials are welcome, especially if prepared with the additional intent of helping high-school students develop the abilities needed to understand and do such work themselves within a few years.

Journals and Conferences

  • Advances in Applied Clifford Algebras (AACA) Journal.
  • GA Net Updates Conferences (Web Page).
  • The Empowering Novel Geometric Algebra for Graphics & Engineering (ENGAGE 2017) Workshop.
  • Computer Graphics, Computer Vision and Computational Mathematics (GraVisMa) and (GraVisMa2010)
  • Applied Geometric Algebra in Computer Science and Engineering (AGACSE 2015), (AGACSE 2012), (AGACSE 2008), and (ACACSE’99)
  • International Conference on Applied Geometric Algebra in Computer Science and Engineering (ICAGACSE)
  • Workshop on Geometric Algebra (online)
  • Alterman Conference on Geometric Algebra (online)
  • Geometric Algebra and Geographical Information Science: Development and Applications (CAGIS)

Online Videos


Software

Details on GA-related software can be found in the Geometric Algebra Software page.


Wikipedia Pages


Applications in Computer Graphics

  • Geomerics Company: (online)
  • Computer Graphics from a Geometric Algebra Perspective (online)
  • Computer Graphics Using Conformal Geometric Algebra (online)
  • “Rethinking Quaternions – Theory and Computation” by Ron Goldman (online)
  • “Geometric Algebra for Computer Graphics” by John Vince (online) who also authored several (other) related books
  • Waterloo Computer Graphics Lab (online)
  • Applications of Conformal Geometric Algebra in Computer Vision and Graphics (online)
  • Geometric Algebra and its Application to Computer Graphics (online)
  • Geometric Algebra Computing in Engineering and Computer Science (online)
  • Guide to Geometric Algebra in Practice (online)

Applications in Signal and Image Processing

  • “Quaternion and Clifford Fourier Transforms and Wavelets” (online)
  • Tutorial on Fourier Transformations and Wavelet Transformations in Clifford Geometric Algebra (online)
  • Geometric Algebra Computing in Engineering and Computer Science (online)
  • Guide to Geometric Algebra in Practice (online)
  • Geometric Computing with Clifford Algebras: Theoretical Foundations and Applications in Computer Vision and Robotics (online)
  • Clifford Algebras and Dimensionality Reduction for Signal Separation and Classification (online)
  • Spatial color image processing using Clifford algebras: application to color active contour (online)
  • Registration of Multichannel Images using Geometric Algebra (online)
  • ConformalALU: A Conformal Geometric Algebra Coprocessor for Medical Image Processing (online)
  • Geometric algebra colour image representations and derived total orderings for morphological operators – Part I: Colour quaternions (online)
  • Advancement in Color Image Processing using Geometric Algebra (online)
  • AWCGAIT2015, 27 Mar. 2015: Overview of Quaternion and Clifford Fourier Transforms, E. Hitzer (online video)
  • Clifford Algebras as Unified Language for Image Processing and Pattern Recognition (online)
  • The Chair of Cognitive Systems, Prof. Dr. G. Sommer, Christian-Albrechts-University of Kiel (web page)

Applications in Mechanics

  • “New Foundations for Classical Mechanics, 2nd Ed.” by David Hestenes (online)
  • “Clifford Algebras – Geometric Modeling and Chain Geometries with Application in Kinematics” by Daniel Klawitter (online)
  • Guide to Geometric Algebra in Practice (online).
  • “Geometric (Clifford) Algebra Calculation of the Trajectory of a Gas Molecule Desorbed from the Earth’s Surface” by James A. Smith (online).

Applications in Differential Geometry \ Calculus

  • “An Introduction to Geometric Algebra and Calculus” by Alan Bromborsky (online)
  • “A Geometric Approach to Differential Forms, 2nd Ed” by David Bachman (online)
  • “A New Approach to Differential Geometry using Clifford’s Geometric Algebra” by John Snygg (online)
  • “Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics” by D. Hestenes and Garret Sobczyk (online)
  • “Noncommutative Functional Calculus” by Fabrizio Colombo et. al. (online)
  • Guide to Geometric Algebra in Practice (online)

Applications in Neural Networks and Machine Learning

  • Geometric Algebra Computing in Engineering and Computer Science (online)
  • Geometric Algebra with Applications in Science and Engineering (online)
  • Geometric Computing with Clifford Algebras: Theoretical Foundations and Applications in Computer Vision and Robotics (online)
  • A Note on Geometric Algebra and Neural Networks (online)
  • A new Selforganizing Neural Network using Geometric Algebra (online)
  • The Chair of Cognitive Systems, Prof. Dr. G. Sommer, Christian-Albrechts-University of Kiel (web page)

Applications in Robotics and Computer Vision

  • “Geometric Algebra with Applications in Engineering” by Christian Perwass. (online)
  • Geometric Algebra with Applications in Science and Engineering (online)
  • “Geometric Fundamentals of Robotics 2nd Edition” by J.M. Selig (online)
  • “Clifford Algebras – Geometric Modeling and Chain Geometries with Application in Kinematics” by Daniel Klawitter (online)
  • Geometric Algebra Computing in Engineering and Computer Science (online)
  • “Geometric Computing: for Wavelet Transforms, Robot Vision, Learning, Control and Action” by Eduardo Bayro-Corrochano (online)
  • Geometric Computing with Clifford Algebras: Theoretical Foundations and Applications in Computer Vision and Robotics (online)
  • Guide to Geometric Algebra in Practice (online)
  • Eduardo Jose Bayro-Corrochano (web page)
  • The Chair of Cognitive Systems, Prof. Dr. G. Sommer, Christian-Albrechts-University of Kiel (web page)

Applications in Electromagnetic Theory

  • Mathematical Descriptions of the Electromagnetic Field (online)
  • “Understanding Geometric Algebra for Electromagnetic Theory“ by John W. Arthur (online)
  • “Electrodynamics: A Modern Geometric Approach Corrected Edition” by William Baylis (online)
  • Electromagnetism using Geometric Algebra versus Components (online)

 

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