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Geometry and Computing #8: Foundations of Geometric Algebra Computing

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Geometry and Computing #8: Foundations of Geometric Algebra Computing Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This book lays the foundation for the widespread use of geometric algebra as a new, up-and-coming field of geometrically intuitive and performant computing technology with a wide range of potential engineering applications in academia and industry.

About the Author

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Table of Contents

Chap. 1 Introduction.- Chap. 2 Mathematical Introduction.- Chap. 3 The Conformal Geometric Algebra.- Chap. 4 Maple and the Identification of Quaternions and Other Algebras.- Chap. 5 Fitting of Planes or Spheres into Point Sets.- Chap. 6 Geometric Algebra Tutorial Using CLUCalc.- Chap. 7 Inverse Kinematics of a Simple Robot.- Chap. 8 Robot Grasping an Object.- Chap. 9 Efficient Computer Animation Application in CGA.- Chap. 10 Using Gaalop for Performant Geometric Algebra Computing.- Chap. 11 Collision Detection Using the Gaalop Precompiler.- Chap. 12 Gaalop Precompiler for GPGPUs.- Chap. 13 Molecular Dynamics Using Gaalop GPC for OpenCL.- Chap. 14 Geometric Algebra Computers.

Product Details

ISBN:
9783642317934
Author:
Hildenbrand, Dietmar
Publisher:
Springer
Subject:
Computer Vision
Subject:
CLUCalc
Subject:
GPGPU
Subject:
Animation
Subject:
conformal geometric algebra (CGA)
Subject:
gaalop
Subject:
geometric algebra
Subject:
Maple
Subject:
Molecular dynamics
Subject:
Planes
Subject:
point sets
Subject:
Quaternions
Subject:
Robotics
Subject:
Spheres
Subject:
Computer Imaging, Vision, Pattern Recognition and Graphics
Subject:
Geometry
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
Mathematics-Applied
Copyright:
Edition Description:
2012
Series:
Geometry and Computing
Series Volume:
8
Publication Date:
20120902
Binding:
HARDCOVER
Language:
English
Pages:
223
Dimensions:
235 x 155 mm

Related Subjects

Computers and Internet » Computers Reference » General
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Computer
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry

Geometry and Computing #8: Foundations of Geometric Algebra Computing New Hardcover
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Product details 223 pages Springer - English 9783642317934 Reviews:
"Synopsis" by , This book lays the foundation for the widespread use of geometric algebra as a new, up-and-coming field of geometrically intuitive and performant computing technology with a wide range of potential engineering applications in academia and industry.
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