How to Read this Guide to Geometric Algebra in Practice
Leo Dorst and Joan Lasenby
Part I: Rigid Body Motion
Rigid Body Dynamics and Conformal Geometric Algebra
Anthony Lasenby, Robert Lasenby and Chris Doran
Estimating Motors from a Variety of Geometric Data in 3D Conformal Geometric Algebra
Robert Valkenburg and Leo Dorst
Inverse Kinematics Solutions Using Conformal Geometric Algebra
Andreas Aristidou and Joan Lasenby
Reconstructing Rotations and Rigid Body Motions from Exact Point Correspondences through Reflections
Daniel Fontijne and Leo Dorst
Part II: Interpolation and Tracking
Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra using Polar Decomposition
Leo Dorst and Robert Valkenburg
Attitude and Position Tracking / Kinematics
L.P Candy and J Lasenby
Calibration of Target Positions using Conformal Geometric Algebra
Robert Valkenburg and Nawar Alwesh
Part III: Image Processing
Quaternion Atomic Function for Image Processing
Eduardo Bayro-Corrochano and Ulises Moya-Sánchez
Color Object Recognition Based on a Clifford Fourier Transform
Jose Mennesson, Christophe Saint-Jean and Laurent Mascarilla
Part IV: Theorem Proving and Combinatorics
On Geometric Theorem Proving with Null Geometric Algebra
Hongbo Li and Yuanhao Cao
On the Use of Conformal Geometric Algebra in Geometric Constraint Solving
Philippe Serré, Nabil Anwer and JianXin Yang
On the Complexity of Cycle Enumeration for Simple Graphs
René Schott and G. Stacey Staples
Part V: Applications of Line Geometry
Line Geometry in Terms of the Null Geometric Algebra over R3,3, and Application to the Inverse Singularity Analysis of Generalized Stewart Platforms
Hongbo Li and Lixian Zhang
A Framework for n-dimensional Visibility Computations
L. Aveneau, S. Charneau, L Fuchs and F. Mora
Part VI: Alternatives to Conformal Geometric Algebra
On the Homogeneous Model of Euclidean Geometry
Charles Gunn
A Homogeneous Model for 3-Dimensional Computer Graphics Based on the Clifford Algebra for R3
Ron Goldman
Rigid-Body Transforms using Symbolic Infinitesimals
Glen Mullineux and Leon Simpson
Rigid Body Dynamics in a Constant Curvature Space and the ’1D-up’ Approach to Conformal Geometric Algebra
Anthony Lasenby
Part VII: Towards Coordinate-Free Differential Geometry
The Shape of Differential Geometry in Geometric Calculus
David Hestenes
On the Modern Notion of a Moving Frame
Elizabeth L. Mansfield and Jun Zhao
Tutorial: Structure Preserving Representation of Euclidean Motions through Conformal Geometric Algebra
Leo Dorst
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, TheNetherlands. Dr. Joan Lasenby is University Senior Lecturer in the Engineering Department of Cambridge University, U.K.
