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Quaternions for Computer Graphics, by John Vince
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Sir William Rowan Hamilton was a genius, and will be remembered for his significant contributions to physics and mathematics. The Hamiltonian, which is used in quantum physics to describe the total energy of a system, would have been a major achievement for anyone, but Hamilton also invented quaternions, which paved the way for modern vector analysis.
Quaternions are one of the most documented inventions in the history of mathematics, and this book is about their invention, and how they are used to rotate vectors about an arbitrary axis. Apart from introducing the reader to the features of quaternions and their associated algebra, the book provides valuable historical facts that bring the subject alive.
Quaternions for Computer Graphics introduces the reader to quaternion algebra by describing concepts of sets, groups, fields and rings. It also includes chapters on imaginary quantities, complex numbers and the complex plane, which are essential to understanding quaternions. The book contains many illustrations and worked examples, which make it essential reading for students, academics, researchers and professional practitioners.
- Sales Rank: #1970526 in Books
- Published on: 2011-06-24
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .44" w x 6.14" l, .88 pounds
- Binding: Hardcover
- 140 pages
Review
From the reviews:
“The goal of this book is to demonstrate the use of quaternions for rotating objects in three-dimensional space, a frequent requirement in computer graphics. The target audience is computer graphics developers … . Brief historical notes appear throughout. … Summing Up: … . Upper-division undergraduates through professionals/practitioners.” (C. A. Gorini, Choice, Vol. 49 (8), April, 2012)
“This is a neat little book on real and complex numbers as well as quaternions. … book is devoted to the algebra of numbers and the rest covers quaternions. The section on quaternion is spiced up with their application to 3-D rotation. Pedagogically the book is well written, it is easy to follow, even a good high school student would be able to understand … . If you are a bookworm or a book collector and like mathematical plums, this is the book for you.” (Leslie P. Piegl, Zentralblatt MATH, Vol. 1233, 2012)
From the Back Cover
Sir William Rowan Hamilton was a genius, and will be remembered for his significant contributions to physics and mathematics. The Hamiltonian, which is used in quantum physics to describe the total energy of a system, would have been a major achievement for anyone, but Hamilton also invented quaternions, which paved the way for modern vector analysis.
Quaternions are one of the most documented inventions in the history of mathematics, and this book is about their invention, and how they are used to rotate vectors about an arbitrary axis. Apart from introducing the reader to the features of quaternions and their associated algebra, the book provides valuable historical facts that bring the subject alive.
Quaternions for Computer Graphics introduces the reader to quaternion algebra by describing concepts of sets, groups, fields and rings. It also includes chapters on imaginary quantities, complex numbers and the complex plane, which are essential to understanding quaternions. The book contains many illustrations and worked examples, which make it essential reading for students, academics, researchers and professional practitioners.
Most helpful customer reviews
8 of 8 people found the following review helpful.
Excellent introduction to quaternions
By Sean Silva
If you know nothing about quaternions, and want to get a feel for how they work and what they can be used for, this book is perfect for you.
This book is also perfect e.g. if you are a programmer writing code that has to rotate things in 3D space. I'm not currently doing any coding that requires it, but I am confident that I could code up quaternion rotations without much trouble should the need arise. In fact, that is the purpose of this book more or less, to teach you to be able to do just that.
Those that are looking for a mathematically rigorous development of quaternions should look elsewhere. However, even for the more mathematically inclined (like I consider myself to be), since there are no difficult proofs to follow, the book can be read blazingly fast (just a few hours). If you are mathematically knowledgeable but have no real knowledge of quaternions (they aren't covered in any regular courses at my university, for example), this little book (it is quite slim!) can get you familiar, and fast. Some of the stuff covered in the book for the sake of completeness is extremely elementary, so if you are already familiar with these things (e.g. what a field is), I would say go ahead and skim those parts.
I give this book 5 stars for being the perfect book to get any mathematically adept person up to speed on the somewhat obscure mathematical entities called "quaternions"; if you are additionally a programmer, the book will also prepare you to write code to rotate arbitrary vectors using quaternions. The book also contains a marvelous discussion of complex numbers and their rotational properties, which naturally sets the stage for quaternions and their own rotational properties.
Note that in order to read this book you should at least be familiar with basic vector operations (mainly dot product and cross product; Calculus 3 is more than enough), as well as very basic linear algebra (i.e., know what a matrix is, how it operates on a vector, and how to multiply matrices).
0 of 0 people found the following review helpful.
Easy read to quickly understand quaternions
By Sven
This is a great book on quaternions. Its a superb introduction and an easy read that takes you from the very basics of complex numbers to rotation matrices. Its a pretty short read if you already have some experience with complex numbers and rotation matrices, but I think it should be very accessible if you have little experience with either. It is well written, the language keeps a good flow and it is a pleasure to read. As a bonus, the author puts quaternions into a historical context with just the right amount of added information. Its neither too much or too little history. I would like to see a couple more illustrations throughout the book, but the most important examples are well illustrated.
0 of 0 people found the following review helpful.
Expensive for its size but worth it
By Matthew H. Phillips
Very clean, clear introduction. His use of the modern ordered-pair (s, v) notation makes understanding the derivations very easy. Anybody coming into this book with a reasonable grasp of vector algebra will leave with a clear understanding of quaternions in a short time.
The only quibbles are that it's pretty expensive and the author does not complete the p' = qpq* proof, only illustrating with examples that the resulting quaternion p' is in fact the sought-after rotation. But the reader can prove this as an exercise using the material on pg. 79.
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