Applications of Geometric Algebra in Computer Science and Engineering
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Beschreibung
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.
State-of-the-art survey chapters by leading researchers covering
geometric algebra---a powerful mathematical tool for solving problems
in computer science, engineering, physics, and mathematics. Focus is
on interdisciplinary applications and techniques. Self-contained
assuming only a knowledge of linear algebra and calculus.
Professionals and researchers interested in geometric algebra and its
applications will find this book an excellent up-to-date reference and
resource. Also appealing to graduate students who need to become
familar with the most recent research, results, and methods.
Autor*in
Leo Dorst
Themen in »Applications of Geometric Algebra in Computer Science and Engineering«
Algebra algorithm calculus differential equation electromagnetism geometry information theory kinematics linear algebra mechanics model operator partial differential equation robotics transformation
Stimmen zu »Applications of Geometric Algebra in Computer Science and Engineering«
"This book contains papers presented at the conference "Applied Geometric Algebra in Computer Science and Engineering" (AGACSE 2001)…. The goal was to demonstrate how the framework of geometric algebra (Clifford algebra) could unify and illuminate diverse fields of science and engineering.
The articles reveal [a] range [of] fields: from quantum physics to robotics, from crystallographic groups to image understanding, from relativistic mechanics to signal processing. Despite this diversity, the combination of these subjects was not felt to be artificial.
This book should be…useful to mathematicians…physicists, [and] to mechanical and computer engineers."
—Iasi Polytechnic Magazine
"The conference ‘Applied Geometric Algebras in Computer Science and Engineering’ (AGACSE 2001) was held… July 9–13, 2001. The present book contains the papers of this scientific meeting and reflects the constantly growing interest in searching the applications of geometric algebra (or Clifford algebra) in various fields of science.
Geometric algebra includes a lot of techniques from several mathematical theories (linear algebra, vector calculus, projective geometry, complex analysis) and offers new directions in some unexpected domains like quantum physics, robotics, crystallographic groups, image understanding, relativistic mechanics, signal processing.
The volume begins with a preface written by the Editors and a useful list with contributors…. There are four sections: Algebra and Geometry…, Applications to Physics…, Computer Vision and Robotics…, Signal Processing and Other Applications….
In conclusion, a very useful book both for beginners and specialists!"
—Memoriile Sectiilor Stiintifice
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