Geometric Algebra for Computer Science

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

Produk Detail:

  • Author : Leo Dorst
  • Publisher : Elsevier
  • Pages : 664 pages
  • ISBN : 0080553109
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKGeometric Algebra for Computer Science

Geometric Algebra for Computer Science (Revised Edition)

Geometric Algebra for Computer Science (Revised Edition)
  • Author : Leo Dorst,Daniel Fontijne,Stephen Mann
  • Publisher : Morgan Kaufmann
  • Release : 24 February 2009
GET THIS BOOKGeometric Algebra for Computer Science (Revised Edition)

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

Geometric Algebra for Computer Science

Geometric Algebra for Computer Science
  • Author : Leo Dorst,Daniel Fontijne,Stephen Mann
  • Publisher : Elsevier
  • Release : 26 July 2010
GET THIS BOOKGeometric Algebra for Computer Science

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

Applications of Geometric Algebra in Computer Science and Engineering

Applications of Geometric Algebra in Computer Science and Engineering
  • Author : Leo Dorst,Chris Doran,Joan Lasenby
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKApplications of Geometric Algebra in Computer Science and Engineering

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

Geometric Algebra for Computer Graphics

Geometric Algebra for Computer Graphics
  • Author : John Vince
  • Publisher : Springer Science & Business Media
  • Release : 10 February 2008
GET THIS BOOKGeometric Algebra for Computer Graphics

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

Geometric Algebra Computing

Geometric Algebra Computing
  • Author : Eduardo Bayro-Corrochano,Gerik Scheuermann
  • Publisher : Springer Science & Business Media
  • Release : 19 May 2010
GET THIS BOOKGeometric Algebra Computing

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.

Geometric Algebra: An Algebraic System for Computer Games and Animation

Geometric Algebra: An Algebraic System for Computer Games and Animation
  • Author : John A. Vince
  • Publisher : Springer Science & Business Media
  • Release : 20 May 2009
GET THIS BOOKGeometric Algebra: An Algebraic System for Computer Games and Animation

Geometric algebra is still treated as an obscure branch of algebra and most books have been written by competent mathematicians in a very abstract style. This restricts the readership of such books especially by programmers working in computer graphics, who simply want guidance on algorithm design. Geometric algebra provides a unified algebraic system for solving a wide variety of geometric problems. John Vince reveals the beauty of this algebraic framework and communicates to the reader new and unusual mathematical concepts

Geometric Computing with Clifford Algebras

Geometric Computing with Clifford Algebras
  • Author : Gerald Sommer
  • Publisher : Springer Science & Business Media
  • Release : 29 June 2013
GET THIS BOOKGeometric Computing with Clifford Algebras

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

Geometric Algebra for Physicists

Geometric Algebra for Physicists
  • Author : Chris Doran,Anthony Lasenby
  • Publisher : Cambridge University Press
  • Release : 22 November 2007
GET THIS BOOKGeometric Algebra for Physicists

Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with early chapters providing a self-contained introduction to geometric algebra. Topics covered include new techniques for handling rotations in arbitrary dimensions, and the links between rotations, bivectors and the structure of the Lie groups. Following chapters extend the concept of a complex analytic function theory to arbitrary dimensions, with

Geometric Algebra Applications Vol. I

Geometric Algebra Applications Vol. I
  • Author : Eduardo Bayro-Corrochano
  • Publisher : Springer
  • Release : 20 June 2018
GET THIS BOOKGeometric Algebra Applications Vol. I

The goal of the Volume I Geometric Algebra for Computer Vision, Graphics and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner

Foundations of Geometric Algebra Computing

Foundations of Geometric Algebra Computing
  • Author : Dietmar Hildenbrand
  • Publisher : Springer Science & Business Media
  • Release : 31 December 2012
GET THIS BOOKFoundations of Geometric Algebra Computing

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

Guide to Geometric Algebra in Practice

Guide to Geometric Algebra in Practice
  • Author : Leo Dorst,Joan Lasenby
  • Publisher : Springer Science & Business Media
  • Release : 28 August 2011
GET THIS BOOKGuide to Geometric Algebra in Practice

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

Linear Algebra and Probability for Computer Science Applications

Linear Algebra and Probability for Computer Science Applications
  • Author : Ernest Davis
  • Publisher : CRC Press
  • Release : 02 May 2012
GET THIS BOOKLinear Algebra and Probability for Computer Science Applications

Based on the author's course at NYU, Linear Algebra and Probability for Computer Science Applications gives an introduction to two mathematical fields that are fundamental in many areas of computer science. The course and the text are addressed to students with a very weak mathematical background. Most of the chapters discuss relevant MATLAB functi

Linear Algebra for Computational Sciences and Engineering

Linear Algebra for Computational Sciences and Engineering
  • Author : Ferrante Neri
  • Publisher : Springer
  • Release : 15 July 2016
GET THIS BOOKLinear Algebra for Computational Sciences and Engineering

This book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor. Based on the idea that computational scientists and engineers need, in both research and professional life, an understanding of theoretical concepts of mathematics in order to be able to propose research advances and innovative solutions, every concept is thoroughly introduced and is accompanied by its informal interpretation. Furthermore, most of the theorems included are

Geometric Algebra with Applications in Engineering

Geometric Algebra with Applications in Engineering
  • Author : Christian Perwass
  • Publisher : Springer Science & Business Media
  • Release : 11 February 2009
GET THIS BOOKGeometric Algebra with Applications in Engineering

The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will result in intuitive and more robust algorithms. This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data. Formally, the book consists of two parts: theoretical foundations and

Introduction to Geometric Algebra Computing

Introduction to Geometric Algebra Computing
  • Author : Dietmar Hildenbrand
  • Publisher : CRC Press
  • Release : 29 December 2020
GET THIS BOOKIntroduction to Geometric Algebra Computing

From the Foreword: "Dietmar Hildenbrand's new book, Introduction to Geometric Algebra Computing, in my view, fills an important gap in Clifford's geometric algebra literature...I can only congratulate the author for the daring simplicity of his novel educational approach taken in this book, consequently combined with hands on computer based exploration. Without noticing, the active reader will thus educate himself in elementary geometric algebra algorithm development, geometrically intuitive, highly comprehensible, and fully optimized." --Eckhard Hitzer, International Christian University, Tokyo, Japan