Hildenbrand D. Foundations to Geometric Algebra Computing

Springer, 2013. — 198 p. — (Geometry and Computing 08). — e-ISBN 978-3-642-31794-1.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.Mathematical Introduction
Conformal Geometric Algebra
Maple and the Identification of Quaternions and Other Algebras
Fitting of Planes or Spheres to Sets of Points
A Tutorial on Geometric Algebra Using CLUCalc
Inverse Kinematics of a Simple Robot
Robot Grasping an Object
Efficient Computer Animation Application in CGA
Using Gaalop for High-Performance Geometric Algebra Computing
Collision Detection Using the Gaalop Precompiler
The Gaalop Precompiler for GPUs
Molecular Dynamics Using Gaalop GPC for OpenCL
Geometric Algebra Computers