Advanced Computational Applications of Geometric Algebra
Author: David William Honorio Araujo Da Silva
Publisher: Springer Nature
Published:
Total Pages: 263
ISBN-13: 3031559851
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Advanced Computational Applications of Geometric Algebra
Author: David William Honorio Araujo Da Silva
Publisher: Springer
Published: 2024-05-27
Total Pages: 0
ISBN-13: 9783031559846
DOWNLOAD EBOOK →How Geometric Algebra can naturally serve for constructing solutions for pattern recognition, machine learning, data compression, games, robotics, quantum computing, data encoding, to cite a few. Moreover, there is ample evidence that further research on GA and related areas can significantly expand the number of real-world applications in a wide variety of areas. A mathematical system that is very easy to handle, highly robust and superior performance for engineering applications. Good thematic introduction for engineers and researchers new to the subject. Extensive illustrations and code examples. Thematically well structured with many hands on examples. Learning about GA and how to use it for daily tasks in engineering research and development.
Applications of Geometric Algebra in Computer Science and Engineering
Author: Leo Dorst
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 479
ISBN-13: 146120089X
DOWNLOAD EBOOK →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.
Advanced Computational Applications of Geometric Algebra
Author: David W. Silva
Publisher: Springer
Published: 2023-12-27
Total Pages: 0
ISBN-13: 9783031340307
DOWNLOAD EBOOK →This book constitutes the post-conference proceedings of the First International Conference on Advanced Computational Applications of Geometric Algebra, ICACGA 2022, held in Denver, CO, USA, during October 2-5, 2022. The 18 full papers presented in this book together with 12 abstracts of invited talks were carefully reviewed and selected from 24 submissions. The papers are grouped in the following topical sections: geometric applications; computer science applications; technological applications; and applications to physics and mathematics.
Geometric Algebra Computing
Author: Eduardo Bayro Corrochano
Publisher: Springer
Published: 2014-09-25
Total Pages: 526
ISBN-13: 9781447157687
DOWNLOAD EBOOK →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 with Applications in Science and Engineering
Author: Eduardo Bayro Corrochano
Publisher: Springer Science & Business Media
Published: 2011-06-28
Total Pages: 607
ISBN-13: 1461201594
DOWNLOAD EBOOK →The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers.
Lectures on Clifford (Geometric) Algebras and Applications
Author: Rafal Ablamowicz
Publisher: Springer Science & Business Media
Published: 2011-06-28
Total Pages: 221
ISBN-13: 0817681906
DOWNLOAD EBOOK →The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird's-eye view of the discipline is presented by six of the world's leading experts in the field; it features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The book is ideal for graduate students in mathematics, physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications.
Geometric Algebra for Computer Science
Author: Leo Dorst
Publisher: Elsevier
Published: 2010-07-26
Total Pages: 664
ISBN-13: 0080553109
DOWNLOAD EBOOK →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
The Power of Geometric Algebra Computing
Author: Dietmar Hildenbrand
Publisher: CRC Press
Published: 2021-09-30
Total Pages: 189
ISBN-13: 1000461238
DOWNLOAD EBOOK →Geometric Algebra is a very powerful mathematical system for an easy and intuitive treatment of geometry, but the community working with it is still very small. The main goal of this book is to close this gap from a computing perspective in presenting the power of Geometric Algebra Computing for engineering applications and quantum computing. The Power of Geometric Algebra Computing is based on GAALOPWeb, a new user-friendly, web-based tool for the generation of optimized code for different programming languages as well as for the visualization of Geometric Algebra algorithms for a wide range of engineering applications. Key Features: Introduces a new web-based optimizer for Geometric Algebra algorithms Supports many programming languages as well as hardware Covers the advantages of high-dimensional algebras Includes geometrically intuitive support of quantum computing This book includes applications from the fields of computer graphics, robotics and quantum computing and will help students, engineers and researchers interested in really computing with Geometric Algebra.
Geometric Algebra Computing
Author: Eduardo Bayro-Corrochano
Publisher: Springer Science & Business Media
Published: 2010-05-19
Total Pages: 527
ISBN-13: 1849961085
DOWNLOAD EBOOK →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.
