Guide to Geometric Algebra in Practice

1. Front Matter

   Pages I-XVII

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2. Rigid Body Motion

   1. Front Matter

      Pages 1-1

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   2. Rigid Body Dynamics and Conformal Geometric Algebra

      • Anthony Lasenby, Robert Lasenby, Chris Doran

      Pages 3-24

   3. Estimating Motors from a Variety of Geometric Data in 3D Conformal Geometric Algebra

      • Robert Valkenburg, Leo Dorst

      Pages 25-45

   4. Inverse Kinematics Solutions Using Conformal Geometric Algebra

      • Andreas Aristidou, Joan Lasenby

      Pages 47-62

   5. Reconstructing Rotations and Rigid Body Motions from Exact Point Correspondences Through Reflections

      • Daniel Fontijne, Leo Dorst

      Pages 63-78

3. Interpolation and Tracking

   1. Front Matter

      Pages 79-79

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   2. Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra Using Polar Decomposition

      • Leo Dorst, Robert Valkenburg

      Pages 81-104

   3. Attitude and Position Tracking

      • Liam Candy, Joan Lasenby

      Pages 105-125

   4. Calibration of Target Positions Using Conformal Geometric Algebra

      • Robert Valkenburg, Nawar Alwesh

      Pages 127-148

4. Image Processing

   1. Front Matter

      Pages 149-149

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   2. Quaternion Atomic Function for Image Processing

      • Eduardo Bayro-Corrochano, Eduardo Ulises Moya-Sánchez

      Pages 151-173

   3. Color Object Recognition Based on a Clifford Fourier Transform

      • Jose Mennesson, Christophe Saint-Jean, Laurent Mascarilla

      Pages 175-191

5. Theorem Proving and Combinatorics

   1. Front Matter

      Pages 193-193

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   2. On Geometric Theorem Proving with Null Geometric Algebra

      • Hongbo Li, Yuanhao Cao

      Pages 195-215

   3. On the Use of Conformal Geometric Algebra in Geometric Constraint Solving

      • Philippe Serré, Nabil Anwer, JianXin Yang

      Pages 217-232

   4. On the Complexity of Cycle Enumeration for Simple Graphs

      • René Schott, G. Stacey Staples

      Pages 233-249

6. Applications of Line Geometry

   1. Front Matter

      Pages 251-251

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   2. 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, Lixian Zhang

      Pages 253-272

   3. A Framework for n-Dimensional Visibility Computations

      • Lilian Aveneau, Sylvain Charneau, Laurent Fuchs, Frederic Mora

      Pages 273-294

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 and hardware tools. 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) in the appendices; 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.

• Clifford Algebra
• Conformal Model
• Geometric Algebra
• Linear Algebra
• Quaternions
• Vector Mathematics

• Informatics Institute, University of Amsterdam, Amsterdam, Netherlands

  Leo Dorst

• Department of Engineering, University of Cambridge, Cambridge, United Kingdom

  Joan Lasenby

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