# Geometric Algebra For Computer Science

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### Geometric Algebra for Computer Science

Author | : Leo Dorst,Daniel Fontijne,Stephen Mann |

Publsiher | : Elsevier |

Total Pages | : 664 |

Release | : 2010-07-26 |

Genre | : Computers |

ISBN | : 9780080553108 |

**Download Geometric Algebra for Computer Science Book in PDF, Epub and Kindle**

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. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full colour book includes a website with GAViewer, a program to experiment with GA

### Geometric Algebra for Computer Science Revised Edition

Author | : Leo Dorst,Daniel Fontijne,Stephen Mann |

Publsiher | : Morgan Kaufmann |

Total Pages | : 664 |

Release | : 2009-02-24 |

Genre | : Computers |

ISBN | : 9780080958798 |

**Download Geometric Algebra for Computer Science Revised Edition Book in PDF, Epub and Kindle**

Geometric Algebra for Computer Science (Revised Edition) presents a compelling alternative to the limitations of linear algebra. Geometric algebra (GA) is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. This book explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics. It systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA. It covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space. Numerous drills and programming exercises are helpful for both students and practitioners. A companion web site includes links to GAViewer, a program that will allow you to interact with many of the 3D figures in the book; and Gaigen 2, the platform for the instructive programming exercises that conclude each chapter. The book will be of interest to professionals working in fields requiring complex geometric computation such as robotics, computer graphics, and computer games. It is also be ideal for students in graduate or advanced undergraduate programs in computer science. Explains GA as a natural extension of linear algebra and conveys its significance for 3D programming of geometry in graphics, vision, and robotics. Systematically explores the concepts and techniques that are key to representing elementary objects and geometric operators using GA. Covers in detail the conformal model, a convenient way to implement 3D geometry using a 5D representation space. Presents effective approaches to making GA an integral part of your programming. Includes numerous drills and programming exercises helpful for both students and practitioners. Companion web site includes links to GAViewer, a program that will allow you to interact with many of the 3D figures in the book, and Gaigen 2, the platform for the instructive programming exercises that conclude each chapter.

### Applications of Geometric Algebra in Computer Science and Engineering

Author | : Leo Dorst,Chris Doran,Joan Lasenby |

Publsiher | : Springer Science & Business Media |

Total Pages | : 478 |

Release | : 2012-12-06 |

Genre | : Mathematics |

ISBN | : 9781461200895 |

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Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.

### Geometric Algebra Computing

Author | : Eduardo Bayro-Corrochano,Gerik Scheuermann |

Publsiher | : Springer Science & Business Media |

Total Pages | : 526 |

Release | : 2010-05-19 |

Genre | : Computers |

ISBN | : 9781849961080 |

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This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Its accessible style is enhanced by examples, figures and experimental analysis.

### Applications of Geometric Algebra in Computer Science and Engineering

Author | : Leo Dorst,Chris J. L. Doran,Joan Lasenby |

Publsiher | : Birkhauser |

Total Pages | : 478 |

Release | : 2002 |

Genre | : Computer science |

ISBN | : 3764342676 |

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### Geometric Algebra for Computer Graphics

Author | : John Vince |

Publsiher | : Springer Science & Business Media |

Total Pages | : 268 |

Release | : 2008-04-21 |

Genre | : Computers |

ISBN | : 9781846289965 |

**Download Geometric Algebra for Computer Graphics Book in PDF, Epub and Kindle**

Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems. The author tackles this complex subject with inimitable style, and provides an accessible and very readable introduction. The book is filled with lots of clear examples and is very well illustrated. Introductory chapters look at algebraic axioms, vector algebra and geometric conventions and the book closes with a chapter on how the algebra is applied to computer graphics.

### Foundations of Geometric Algebra Computing

Author | : Dietmar Hildenbrand |

Publsiher | : Springer Science & Business Media |

Total Pages | : 196 |

Release | : 2012-12-31 |

Genre | : Computers |

ISBN | : 9783642317941 |

**Download Foundations of Geometric Algebra Computing Book in PDF, Epub and Kindle**

The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics. This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications. The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.

### Geometric Computing with Clifford Algebras

Author | : Gerald Sommer |

Publsiher | : Springer Science & Business Media |

Total Pages | : 551 |

Release | : 2013-06-29 |

Genre | : Computers |

ISBN | : 9783662046210 |

**Download Geometric Computing with Clifford Algebras Book in PDF, Epub and Kindle**

This monograph-like anthology introduces the concepts and framework of Clifford algebra. It provides a rich source of examples of how to work with this formalism. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work shows that Clifford algebra provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics.