Guide to geometric algebra in practice

著者

書誌事項

Guide to geometric algebra in practice

Leo Dorst, Joan Lasenby, editors

Springer, c2011

  • :hbk.

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注記

Includes bibliographical references and index.

内容説明・目次

内容説明

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.

目次

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-Sanchez 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 Serre, Nabil Anwer and JianXin Yang On the Complexity of Cycle Enumeration for Simple Graphs Rene 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

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