Foundations of Geometric Algebra Computing
By: by Dietmar Hildenbrand
Contributors: SpringerLink (Online service)
Series: Geometry and Computing -- 8
Publisher: Springer Berlin Heidelberg; Imprint: Springer
Published: 2013
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 196
ISBN-13: 9783642317941
Subjects: Computer Imaging, Vision, Pattern Recognition and Graphics; Appl.Mathematics/Computational Methods of Engineering; Computer vision; Engineering mathematics; Computer science; Geometry
Description: <p>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.</p><p><p>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.</p><p>The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.
Table of contents: title: Chap. 1 Introduction; title: Chap. 2 Mathematical Introduction; title: Chap. 3 The Conformal Geometric Algebra; title: Chap. 4 Maple and the Identification of Quaternions and Other Algebras; title: Chap. 5 Fitting of Planes or Spheres into Point Sets; title: Chap. 6 Geometric Algebra Tutorial Using CLUCalc; title: Chap. 7 Inverse Kinematics of a Simple Robot; title: Chap. 8 Robot Grasping an Object; title: Chap. 9 Efficient Computer Animation Application in CGA; title: Chap. 10 Using Gaalop for Performant Geometric Algebra Computing; title: Chap. 11 Collision Detection Using the Gaalop Precompiler; title: Chap. 12 Gaalop Precompiler for GPGPUs; title: Chap. 13 Molecular Dynamics Using Gaalop GPC for OpenCL; title: Chap. 14 Geometric Algebra Computers.