Rating: 
Summary: An easy to follow primer lacking references
Review: The book delivers exactly what it promises, an in-depth study of rotations using quaternions. However, if you are looking for a complete description of how to use quaternions, it is missing a lot. Specifically it doesn't explain anything about interpolating rotations, which is absolutely required in the field of animation. After reading this book, I would recommend finding a copy of Ken Shoemake's article "Animating Rotation with Quaternion Curves", which explains slerp and squad, there are many references available on the Internet. The Flipcode.com site has some code by Tim Sweeney (lead programmer for Unreal) under "Vector Math and Quaternions", which explains how to use quaternion logarithms to handles higher-order (Hermite, Bezier, TCB) interpolations. It could be argued that this is out of the scope of the book, but I suspect many people interested in buying this book will need this information. This is the main way quaternions are used in game programming, for example. Still, this book gives you a good starting point and its explanation of Euler angles and conversion to/from is about the best I have ever read. The derivation of quaternions as an extension of complex numbers is quite easy to follow and has a very easy-going style, which still giving a firm mathematical basis.
Rating:
Summary: Good beginning, not enough for most applications
Review: The book delivers exactly what it promises, an in-depth study of rotations using quaternions. However, if you are looking for a complete description of how to use quaternions, it is missing a lot. Specifically it doesn't explain anything about interpolating rotations, which is absolutely required in the field of animation. After reading this book, I would recommend finding a copy of Ken Shoemake's article "Animating Rotation with Quaternion Curves", which explains slerp and squad, there are many references available on the Internet. The Flipcode.com site has some code by Tim Sweeney (lead programmer for Unreal) under "Vector Math and Quaternions", which explains how to use quaternion logarithms to handles higher-order (Hermite, Bezier, TCB) interpolations. It could be argued that this is out of the scope of the book, but I suspect many people interested in buying this book will need this information. This is the main way quaternions are used in game programming, for example. Still, this book gives you a good starting point and its explanation of Euler angles and conversion to/from is about the best I have ever read. The derivation of quaternions as an extension of complex numbers is quite easy to follow and has a very easy-going style, which still giving a firm mathematical basis.
Rating:
Summary: An easy to follow primer lacking references
Review: The main asset of this delightful book is its methodical and unencumbered presentation of the most basic mathematics, vector and matrix operations from the first page. Specifically, it illustrates basic algebraic field theory and generalizes complex numbers into quaternions in an uncomplicated way. The fluid presentation encourages the reader to continue through the necessarily lengthy introduction of the classical rotation operators (as detailed use of quaternions doesn't start until about 100 pages, in Chapter 5). I appreciated the fact its introductory nature is honestly clarified by the subtitle: it is a self-declared primer. It is also one of the few textbooks I have seen making extensive use of a marginal gloss (explanatory notes in the margin), which seems much more efficient than footnotes or appendices. Many facts are repeated - noticeable but not too annoying, and handled well in the gloss. This level of presentation will certainly benefit most readers new to the subject. Anyone writing a technically oriented textbook should consider reviewing this title for its format alone. The book defines a quaternion as a 3-D vector plus a scalar. Defining the quaternion with these more conventional mathematical notions makes the very concept more approachable. But it is not clear whether this (and other) notation is truly unique to this book or otherwise widely acknowledged in literature. For example, most of the notation adopted for classic rotation operators seemed unnecessarily different (and therefore slightly confusing) compared to those few other engineering and science textbooks I've been able to reference on the subject. And a few terms, such as "kyperplane", appear unique to this book alone. Considering that this is an introductory textbook, the recommended "further reading" list was by far the most disappointing aspect of this title. Out of sixteen (16) meager references provided, 1/4 are Prof. Kuipers' own patent declarations; the rest are mostly hard-to-get Air Force reports, out of print books, and a few specialty journal articles. The lack of specific references is especially bothersome when facts or theorems are cited without support or proof, such as "Euler's Theorem" (p. 83). Engineers and engineering students should also be aware that some of the "applications to orbits and aerospace" (from the subtitle) appear to be more for academic or illustrative purposes than for immediate, practical application. For example, the publisher's on-line table of contents identifies "Chapter 11 - Quaternion Calculus for Kinematics and Dynamics." However, this chapter doesn't really cover the conventional transformations of relative velocity or accelerations with respect to rotating frames of reference, which is essential to the study of dynamics and kinematics of air and space vehicles. In the preface, the author acknowledges that "It was difficult knowing where to stop, since the subject deserves much more attention and greater depth." As a result, the book may have slightly more appeal to those interested in 3-D programming and visualization. God bless the author, who at age 80 apparently supplied the textbook copy in camera ready form. Unfortunately, my 3rd printing still contains many obvious typographical errors, which is the publisher's responsibility (who holds the copyright). A lack of editorial review normally implies that less obvious errors are lurking in those all-important equations, but thankfully Prof. Kuipers is kind enough to provide an errata sheet if the reader requests it via email. However, the reader should be aware that his printed book is still be published uncorrected, and no official errata appears at the publisher's website at this time. In summary, I would recommend this primer for the engineering student or programmer with a novice to intermediate level of familiarity with rotational sequences. The book's style of presentation is commendable, and the extensive gloss makes the subject matter more understandable to the beginner. Discussions of some engineering applications, as well as specific topics such as orbital mechanics, gravitational theory, etc., are presented with far less detail, clarity, and rigor. While disappointing, this is forgivable as the author seemingly intends to illustrate, rather than develop rigorously complete relationships, for these applications. However, the lack of modern, easily obtained references and some seemingly unique notation may give this title less longevity as a research or reference text.
Rating: 
Summary: Aerospace Engineer is Highly Complimentary.....
Review: This book is a masterpiece. It has a beautiful blending of both the theory and the practical. An abstract subject has been transformed by an expert with many new and heretofore unused explications. I highly recommend that this book be studied from cover to cover by students of Mathematical Physics and many fields of Engineering. The halls of academia should incorporate this great work into their courses. I also recommend that MathCAD and Mathematica embrace the material into their tools with the permission of the author. I would be happy to offer some suggestions for such a venture.
Rating:
Summary: A Superb Treatment of Rotation Operations
Review: This book is a true joy to read, study, and reference. It is thorough, yet the approach used throughout is crafted to show the motivation for the techniques it describes. It is clear to see that the author spent a great deal of time in making it very readable, especially considering the nature of the material. For example, repeating key expressions and figures in the margin is far beyond what one expects these days. And the quality of the writing and figures is superb.
Rating:
Summary: Very, very good reference for 3D modelers.
Review: This book is great. The author goes into great depth on Matrices and Quaternions. Topics such as Aerospace sequences and Tracking sequences are covered in clear detail. This book is a must have for anyone taking a Computer Graphics course. If you have ever studied Shoemake's arcball then you will appreaciate the Tracking sequence. It is just too bad other authors don't accumulate this much information and present it in a clear usuable format. I give this book a very high recommendation. You will not find better information than this on quaternion and/or rotation sequences.
Rating:
Summary: Excellent content; supremely well-written!
Review: This book is one of the most understandable and down-to-earth mathematics texts I've ever read. For instance, after presenting a new concept, he'll summarize it again in the sideline of the book every time he refers to it for the next twenty pages or so. At first, I was finding myself getting annoyed, and thinking, "What, does he think I'm stupid?" Then I considered the alternative, the terse style of so many mathematical texts that has me regularly flipping between eight different pages trying to put everything together. I stopped complaining and started appreciating Kuipers' approach. Kuipers does assume a certain amount of familiarity with mathematics, but not any knowledge in particular, as he reviews basic matrix multiplication and the like at the beginning of the book. For a topic that can seem daunting (our artist always makes fun of me using seemingly gratuitous big phrases like "spherically interpolated quaternion splines") this book makes it very understandable. If you need to work with computational rotation, for a flight sim, robotics visualization, or (most importantly) for a computer game, I can't recommend this book highly enough!
Rating:
Summary: A Delightful Read!
Review: This book was a delightful read! If you ever have been curious or puzzled or even
terrified by Euler angles then read this text. Many questions will be answered and much
knowledge revealed. For a gentle introduction to quaternions this is also a good place
to start. The book starts out with a review of complex numbers (in order to emphazise
the similarity to quaternions later on), then reviews rotations and matrix methods
(sorry but vectors don't do rotations) and then gets into the nitty-gritty of
rotations in 2-space and on into 3-space. Three problems involving rotations are
discussed in detail. All of this at first with matrix methods and then a nice easy
introduction to quaternions is given and these three problems are then handled with
quaternions. There is a strong comparison made between compex number arithmetic and
quaternion arithmetic, such as norms, conjugates and computation of multiplicative
inverses.
Ever wonder how far it is between say Dallas and London? And what direction
to take to go from to the other? Well, airplanes do it every day but if I were asked
that question on an exam I would have flunked it. Not anymore! The explanation of
the answer to such questions is presented in a simple/y delightful manner in this
text. There is also stuff here on spherical trigonometry and a description of an
orientation and distance sensing system, using the near field pattern of magnetic dipole
antennas. Finally there is discussion of ordinary differential equations and an
overview of what is needed for displaying moving objects with computer graphics.
Well, that is quite a lot, but the pace is easy going and the text takes this into
account by reproducing say the equation or the figure under discussion in the margins
as it goes along. A very well executed text, no constant back-paging to figure out
what we were talking about! The text has the flavor being written from lecture notes, not the usual cryptic
ones, but well expanded and well thought out ones. This leads to some repetition but
that's O.K. by me. It makes easy reading for a varied audience. Who is this text aimed at? Well I did find it enlightening even with a background
in physics and a rudimentary introduction to Euler angles in an advanced classical
mechanics course, but I never had the occasion to use them in my career, so this was
a good refresher for me. What do you need to know to get something out of this text?
A good grip on the meaning of sines and cosines and the various addition and
multipication formulas or at least know where to look them up. A little knowledge of
vectors, the dot and cross product will also be handy even though it is explained in
the text. For one chapter a smattering of differential calculus is useful and for
another a whole lot of knowledge about differential equations, more than I have is
needed. But if you don't have this background you can safely skip these parts and not loose any of the further stuff in the text. You should know how to solve sets of
simultaneous equations, inhomogeneous and homogeneous. Matrix operations are all discussed in detail and you can learn them here. You will
probably get one of the best introductions to the concept of eigenvectors that you
can find anywhere, something that will stick with you for the rest of your career.
Well who is it aimed at? Anyone interested in spherical metrology, astronomy, robotics,
orbital mechanics, graphical stuff, classical mechanics and so on. A smart high school
student could learn a lot here and anyone with a few years of college math/science
under his belt will find it profitable as will some, like me, with an advanced degree
but no detailed experience in this field. What did I miss in this text? You know how you visualize two component complex numbers
as points in the plane and you might think that a 3 component entity might do the same
thing with points in 3 dimensional space. Not so if you want it to be an algebra says
Frobenius, as mentioned in the book. But there is a short (half page) demonstration that
a 3 component hyper-complex number with real coefficients leads immediately to a
logical contradiction (e.g. Simmons, Calculus Gems.) This demo would reinforce the
need for 4 component quaternions. Why do quaternions describe a rotation in terms of the half angle? Well maybe because
you need a quaternion and its conjugate both to describe the rotation. But to me there
is an even better source for this oddity, namely the description of a rotation as two
successive relections. Then the origin of half angles shines right out of the geometry
(e.g. Snygg, Cilfford Algebra, a 2-3 page description in Chapter 1. Also find here a
solution to the spinning top problem using quaternion calculus.) Quaternions do simplify the derivation of many formulas but do they speed up the
numerical computations? There is no real discussion of this topic. It might take a
couple of chapters and you need to quit somewhere I guess. Criticsisms?. No, merely matters of taste. The final chapter treats the more general motion of a body: rotations, translations,
scaling, perspective and sensivity factors. Here we run into the puzzle that all this
can be easily handled with matrix methods but apparently not with quaternions. The
question then arises why bother with quaternions at all, at least for numerical
work. I found the text here a little weak. A criticism that I do have is the definition by the author of the reversal of the
vector part of the quaternion as its complex conjugate. One property of this conjugate
is that the conjugate of the product of two quaternions is the product of the conjugates
in reverse order. But this is not true of the usual complex conjugate, the compex
conjugate of the product of two matrices, say, is the product of the complex conjugates
of each matrix but in the same order. Does this lead to problems in this text? No,
complex numbers and matrices or quaternions are never mixed here. But the idea can lead
a novice astray in future work. At any rate this is a great text with no typos in the many formulas that I could detect.
As I said a Great Read.
Rating:
Summary: Excellent for a variety of readers
Review: This is a superb book, even for those who are not working with quaternions. Rotations (and applications such as tracking and navigation) constitute one of the trickier parts of vector analysis, and Prof. Kuipers provides the best treatment I have ever seen, integrating complex numbers, rotation matrices, and quaternions. The geometric point of view is prominent, but algebraic properties are also emphasized in a balanced way. The mathematics is clearly and carefully presented, but never "dumbed down", so the book manages to be comprehensible to beginners, while still being suitable for those with deeper mathematical backgrounds. The graphic design, using clear, simple black & white graphics complementing the text, is a masterpiece--vastly superior to all the fancy halftone and colored illustrations that overburden many modern textbooks. I put this book well into the 99th percentile on any measure of what makes a good mathematics text.
Rating:
Summary: A well written text
Review: This is a very well written book in that it is very easy to understand, all of the concepts are explained clearly, the chapters section-off the topics nicely, and it very readable despite the technical nature of the subject. I found every page of this book to be very interesting. The author includes some historical notes on the origins of quaternions and why they are so important. There's nothing quite like learning an interesting class of mathematics in which you are told right off the bat why you should be interested. This book is great for those who dabble in computer graphics. I do game programming as a hobby and I find that all my resources use quaternions from time to time. I picked up this book not knowing anything about them and found myself with all the information and motivation that I needed all in one place. I highly recommend this book to all who are interesting in quaternion mathematics.
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