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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, The Netherlands. Dr. Joan Lasenby is University Senior Lecturer in the Engineering Department of Cambridge University, U.K.

Geometry, Algebraic --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Geometry --- Computer Science --- Geometry, Algebraic. --- Algebras, Linear. --- Linear algebra --- Algebraic geometry --- Computer science. --- Computer science --- Artificial intelligence. --- Computer graphics. --- Image processing. --- Computer-aided engineering. --- Computer Science. --- Math Applications in Computer Science. --- Symbolic and Algebraic Manipulation. --- Computer Graphics. --- Artificial Intelligence (incl. Robotics). --- Image Processing and Computer Vision. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Mathematics. --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Algebra --- Computer vision. --- Computer aided design. --- Artificial Intelligence. --- Data processing. --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Engineering graphics --- Informatics --- Science --- Digital techniques --- Computer science—Mathematics. --- Optical data processing. --- CAE --- Engineering --- Optical computing --- Visual data processing --- Integrated optics --- Photonics --- Computers --- Data processing --- Optical equipment

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Until recently, all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limit

Geometry, Algebraic. --- Computer science --- Object-oriented methods (Computer science) --- Mathematics. --- Object development methods (Computer science) --- Object orientation (Computer science) --- Object-oriented development (Computer science) --- Object technology (Computer science) --- System design --- Computer mathematics --- Electronic data processing --- Mathematics --- Algebraic geometry --- Geometry

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Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming.Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down.--

Computer science --- Geometry, Algebraic. --- Object-oriented methods (Computer science). --- Mathematics. --- Object-oriented methods (Computer science) --- Object development methods (Computer science) --- Object orientation (Computer science) --- Object-oriented development (Computer science) --- Object technology (Computer science) --- System design --- Computer mathematics --- Electronic data processing --- Mathematics --- Algebraic geometry --- Geometry

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Computer science --- Engineering mathematics. --- Geometry, Algebraic. --- Mathematics.