Guide to Geometric Algebra in Practice (eBook)

Leo Dorst, Joan Lasenby (Herausgeber)

eBook Download: PDF

2011 | 2011
XVII, 458 Seiten
Springer London (Verlag)
978-0-85729-811-9 (ISBN)

Infos

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.

Inhalt

How to Read this Guide to Geometric Algebra in PracticeLeo Dorst and Joan LasenbyPart I: Rigid Body MotionRigid Body Dynamics and Conformal Geometric AlgebraAnthony Lasenby, Robert Lasenby and Chris DoranEstimating Motors from a Variety of Geometric Data in 3D Conformal Geometric AlgebraRobert Valkenburg and Leo DorstInverse Kinematics Solutions Using Conformal Geometric AlgebraAndreas Aristidou and Joan LasenbyReconstructing Rotations and Rigid Body Motions from Exact Point Correspondences through ReflectionsDaniel Fontijne and Leo DorstPart II: Interpolation and TrackingSquare Root and Logarithm of Rotors in 3D Conformal Geometric Algebra using Polar DecompositionLeo Dorst and Robert ValkenburgAttitude and Position Tracking / KinematicsL.P Candy and J LasenbyCalibration of Target Positions using Conformal Geometric AlgebraRobert Valkenburg and Nawar AlweshPart III: Image ProcessingQuaternion Atomic Function for Image ProcessingEduardo Bayro-Corrochano and Ulises Moya-SánchezColor Object Recognition Based on a Clifford Fourier TransformJose Mennesson, Christophe Saint-Jean and Laurent MascarillaPart IV: Theorem Proving and CombinatoricsOn Geometric Theorem Proving with Null Geometric AlgebraHongbo Li and Yuanhao CaoOn the Use of Conformal Geometric Algebra in Geometric Constraint SolvingPhilippe Serré, Nabil Anwer and JianXin YangOn the Complexity of Cycle Enumeration for Simple GraphsRené Schott and G. Stacey StaplesPart V: Applications of Line GeometryLine Geometry in Terms of the Null Geometric Algebra over R3,3, and Application to the Inverse Singularity Analysis of Generalized Stewart PlatformsHongbo Li and Lixian ZhangA Framework for n-dimensional Visibility ComputationsL. Aveneau, S. Charneau, L Fuchs and F. MoraPart VI: Alternatives to Conformal Geometric AlgebraOn the Homogeneous Model of Euclidean GeometryCharles GunnA Homogeneous Model for 3-Dimensional Computer Graphics Based on the Clifford Algebra for R3 Ron GoldmanRigid-Body Transforms using Symbolic InfinitesimalsGlen Mullineux and Leon SimpsonRigid Body Dynamics in a Constant Curvature Space and the ‘1D-up’ Approach to Conformal Geometric AlgebraAnthony LasenbyPart VII: Towards Coordinate-Free Differential GeometryThe Shape of Differential Geometry in Geometric CalculusDavid HestenesOn the Modern Notion of a Moving FrameElizabeth L. Mansfield and Jun ZhaoTutorial: Structure Preserving Representation of Euclidean Motions through Conformal Geometric AlgebraLeo Dorst

Produkt-Details

• Erscheint lt. Verlag: 28.8.2011
• Zusatzinfo: XVII, 458 p.
• Verlagsort: London
• Sprache: englisch
• Themenwelt: Informatik ► Grafik / Design ► Digitale Bildverarbeitung
• Themenwelt: Mathematik / Informatik ► Informatik ► Software Entwicklung
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Informatik ► Weitere Themen ► CAD-Programme
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: Clifford Algebra • Conformal Model • Geometric Algebra • linear algebra • quaternions • Vector Mathematics
• ISBN-10: 0-85729-811-9 / 0857298119
• ISBN-13: 978-0-85729-811-9 / 9780857298119