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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
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
From the Foreword: "Dietmar Hildenbrand's new book, Introduction to
Geometric Algebra Computing, in my view, fills an important gap in
Clifford's geometric algebra literature...I can only congratulate
the author for the daring simplicity of his novel educational
approach taken in this book, consequently combined with hands on
computer based exploration. Without noticing, the active reader
will thus educate himself in elementary geometric algebra algorithm
development, geometrically intuitive, highly comprehensible, and
fully optimized." --Eckhard Hitzer, International Christian
University, Tokyo, Japan 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 with an
introduction to Geometric Algebra from an engineering/computing
perspective. This book is intended to give a rapid introduction to
computing with Geometric Algebra and its power for geometric
modeling. From the geometric objects point of view, it focuses on
the most basic ones, namely points, lines and circles. This algebra
is called Compass Ruler Algebra, since it is comparable to working
with a compass and ruler. The book explores how to compute with
these geometric objects, and their geometric operations and
transformations, in a very intuitive way. The book follows a
top-down approach, and while it focuses on 2D, it is also easily
expandable to 3D computations. Algebra in engineering applications
such as computer graphics, computer vision and robotics are also
covered.
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Advanced Computational Applications of Geometric Algebra - First International Conference, ICACGA 2022, Colorado Springs, CO, USA, October 2-5, 2022, Proceedings (1st ed. 2023)
David W. Silva, Eckhard Hitzer, Dietmar Hildenbrand
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R1,790
Discovery Miles 17 900
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Ships in 10 - 15 working days
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This book constitutes the post-conference proceedings of the First
International Conference on Advanced Computational Applications of
Geometric Algebra, ICACGA 2022, held in Colorado Springs, 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.
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.
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.
From the Foreword: "Dietmar Hildenbrand's new book, Introduction to
Geometric Algebra Computing, in my view, fills an important gap in
Clifford's geometric algebra literature...I can only congratulate
the author for the daring simplicity of his novel educational
approach taken in this book, consequently combined with hands on
computer based exploration. Without noticing, the active reader
will thus educate himself in elementary geometric algebra algorithm
development, geometrically intuitive, highly comprehensible, and
fully optimized." --Eckhard Hitzer, International Christian
University, Tokyo, Japan 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 with an
introduction to Geometric Algebra from an engineering/computing
perspective. This book is intended to give a rapid introduction to
computing with Geometric Algebra and its power for geometric
modeling. From the geometric objects point of view, it focuses on
the most basic ones, namely points, lines and circles. This algebra
is called Compass Ruler Algebra, since it is comparable to working
with a compass and ruler. The book explores how to compute with
these geometric objects, and their geometric operations and
transformations, in a very intuitive way. The book follows a
top-down approach, and while it focuses on 2D, it is also easily
expandable to 3D computations. Algebra in engineering applications
such as computer graphics, computer vision and robotics are also
covered.
|
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