Visualizing Quaternions (The Morgan Kaufmann Series in Interactive 3D Technology)
by Andrew J. Hanson
List Price:
Our Price: $53.69
You Save: $25.26 (32%)
Availability: Usually ships in 1-2 business days
Category: Book
See more book details and other editions
Compare Prices for Visualizing Quaternions (The Morgan Kaufmann Series in Interactive 3D Technology)
Book Summary Information
Author: Andrew J. HansonEdition: Hardcover
Audio: German (Original Language); English (Unknown); English (Published)
Published: 2005-12-29
ISBN: 0120884003
Number of pages: 600
Publisher: Morgan Kaufmann
Book Reviews of Visualizing Quaternions (The Morgan Kaufmann Series in Interactive 3D Technology)
Book Review: Worth a look
Summary: 4 Stars
This is a very interesting book in the Morgan Kaufmann series, and will appeal to those with a mathematical bent. Visualizing quaternions is broken into three parts. Part 1 treats the elements of quaternions, and parts 2 and 3 treats advanced mathematical topics that place considerably more demands on the reader's mathematical knowledge (and also on the author).
Part 1 is an introduction for those readers new to the topic. As far as introductions go, it is not too bad. It does in fact contain one important subject - quaternion interpolation - that is not always covered in other texts. Hanson covers interpolation in part 1 and again in part 2. If your interest is computer animation, this may be sufficient reason to acquire the book...analogous to purchasing an album just to get one song. However, if you are completely new to quaternions and want to develop a firm intuition grounded in first principles, then a book that is at least an order of magnitude better is "Quaternions and Rotation Sequences" by J. B. Kuipers.
Parts 2 and 3 are the most interesting parts of the book. Hanson presents a series of small chapters that discuss quaternions from different advanced mathematical viewpoints (differential geometry, group theory, Clifford algebras, octonions). The chapters are small, and so they by necessity contain references to the literature where the considerable background material required for understanding the topics is developed. If you have a good background in differential geometry and some abstract algebra, then the chapters are quite nice. In this sense, parts 2 and 3 of the book are more appropriate for mathematicians.
The technique of including routine, "turn the crank" type of calculations in the text, and deferring the sometimes considerable details and theory to references allows Hanson to cover more topics than usual. However, it is exactly those details that distinguish between what is useful and well conceived mathematical theory from mathematical gibberish. Deferring details to the literature can also encourage an over-reaching of the author beyond his understanding of the material. Hanson has walked a fine line here, but still I must mention two issues that I found annoying:
1) A Riemannian manifold is not specified only by giving the charts ("local patches") as Hanson seems to think on page 352. One must also add constraints on the topology -- typically Hausdorff with a countable basis of open sets. These are not just moot considerations; the topology allows a construction of a partition of unity which in turns guarantees the existence of the Riemannian metric. In particular, the mild condition of paracompactness will ensure the existence of the partition of unity.
2) It is a gross over-simplification, and mathematically non-trivial, to claim the basis vectors of Euclidean space have precise analogs in Fourier transform theory, as Hanson does on page 340. Heuristic analogs...yes... but precise analogs?...only if one has developed the necessary mathematical machinery using the theory of distributions. The inner product relation ei.ej = kronecker delta ij given by Hanson on page 340 would have to be generalized to a delta function. It was one of the major accomplishments of 20th century mathematics that Schwartz was able to put the delta function on a firm mathematical basis with his theory of distributions (for which he received the Fields medal) Before Schwartz, delta functions were at best a useful computational tool in the hands of physicists like Dirac who were guided by their physical intuition, and at worst, an example of the mathematical gibberish alluded to earlier.
In short, this is a good book for those with the mathematical prerequisites. Those with a more traditional background in computer science might be advised to first peruse a copy at their local bookstore to verify it matches their interests.
Summary of Visualizing Quaternions (The Morgan Kaufmann Series in Interactive 3D Technology)
Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available.The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are importanta beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions.
* Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing.
* Covers both non-mathematical and mathematical approaches to quaternions.
* Companion website with an assortment of quaternion utilities and sample code, data sets for the book's illustrations, and Mathematica notebooks with essential algebraic utilities.
Games & Strategy Guides Books
Book Subjects
- Arts & Photography
- Audiobooks on Cassette
- Audiobooks on CD
- Biographies & Memoirs
- Business & Investing
- Children's Books
- Comics & Graphic Novels
- Computers & Internet
- Cooking, Food & Wine
- e-Books
- Engineering
- Entertainment
- Gay & Lesbian
- Health, Mind & Body
- History
- Home & Garden
- Horror
- Law
- Literature & Fiction
- Medicine
- Mystery & Thrillers
- Nonfiction
- Outdoors & Nature
- Parenting & Families
- Professional & Technical
- Reference
- Religion & Spirituality
- Romance
- Science
- Science Fiction & Fantasy
- Sports
- Teens
- Travel
Most talked about in Math, Physics, Stats, Computer Graphics and Cartography
Else/ Where: Mapping ? New Cartographies of Networks and TerritoriesUniv Minnesota Design Institute; Published: 2006-03-30; Paperback; Book
Best price: $31.31
Price in other shops:
Making Maps: A Visual Guide to Map Design for GISby John Krygier, Denis Wood
The Guilford Press; Published: 2005-08-17; Paperback; Book
Best price: $35.00
Price in other shops:
Essential MATLAB for Engineers and Scientists, Third Editionby Brian Hahn, Dan Valentine
Newnes; Published: 2007-03-22; Paperback; Book
Best price: $28.64
Price in other shops:
Getting Started with MATLAB 7: A Quick Introduction for Scientists and Engineers (The Oxford Series in Electrical and Computer Engineering)by Rudra Pratap
Oxford University Press, USA; Published: 2005-08-04; Paperback; Book
Best price: $27.49
Price in other shops:
Visualizing Quaternions (The Morgan Kaufmann Series in Interactive 3D Technology)by Andrew J. Hanson
Morgan Kaufmann; Published: 2006-01-12; Hardcover; Book
Best price: $57.99
Price in other shops:
Statistics for People Who (Think They) Hate Statistics with SPSS Student Version 13.0 2nd Editionby Neil J. Salkind
Sage Publications, Inc; Published: 2005-03-08; Paperback; Book
Best price: $50.00
Price in other shops:
Physics Demystified : A Self-Teaching Guide (Demystified)by Stan Gibilisco
McGraw-Hill Professional; Published: 2002-08-01; Paperback; Book
Best price: $4.29
Price in other shops:
Mathematics and Physics for Programmers (Game Development Series)by Danny Kodicek
Charles River Media; Published: 2005-05; Paperback; Book
Best price: $30.00
Price in other shops:
Computer Graphics for Java Programmersby Leen Ammeraal, Kang Zhang
Wiley; Published: 2007-03-09; Paperback; Book
Best price: $44.99
Price in other shops:
Geometry, Relativity and the Fourth Dimensionby Rudolf Rucker
Dover Publications; Published: 1977-06-01; Paperback; Book
Best price: $4.18
Price in other shops:
Similar Books and other products
Game Physics Engine Development (The Morgan Kaufmann Series in Interactive 3D Technology)by Ian Millington
Morgan Kaufmann; Published: 2007-03-07; Hardcover; Book
Best price: $31.09
Price in other shops:
GPU Gems 3by Hubert Nguyen
Addison-Wesley Professional; Published: 2007-08-12; Hardcover; Book
Best price: $48.05
Price in other shops:
Geometric Algebra for Physicistsby Chris Doran, Anthony Lasenby
Cambridge University Press; Published: 2007-12-10; Paperback; Book
Best price: $67.09
Price in other shops:
Lie Groups, Lie Algebras, and Some of Their Applicationsby Robert Gilmore
Dover Publications; Published: 2006-01-04; Paperback; Book
Best price: $19.77
Price in other shops:
Essential Mathematics for Games and Interactive Applications: A Programmer's Guide (The Morgan Kaufmann Series in Interactive 3d Technology) (The Morgan Kaufmann Series in Interactive 3d Technology)by James M. Van Verth, Lars M. Bishop
Morgan Kaufmann; Published: 2004-03-25; Hardcover; Book
Best price: $50.00
Price in other shops:
Real-Time Collision Detection (The Morgan Kaufmann Series in Interactive 3-D Technology)by Christer Ericson
Morgan Kaufmann; Published: 2004-12-22; Hardcover; Book
Best price: $59.95
Price in other shops:
On Quaternions and Octonionsby John Horton Conway, Derek Smith
AK Peters; Published: 2003-01-01; Hardcover; Book
Best price: $25.60
Price in other shops:
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (The Morgan Kaufmann Series in Computer Graphics)by Leo Dorst, Daniel Fontijne, Stephen Mann
Morgan Kaufmann; Published: 2007-04-19; Hardcover; Book
Best price: $55.94
Price in other shops:
Rotations, Quaternions, and Double Groupsby Simon L. Altmann
Dover Publications; Published: 2005-11-03; Paperback; Book
Best price: $14.46
Price in other shops:
Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Realityby J. B. Kuipers
Princeton University Press; Published: 2002-08-19; Paperback; Book
Best price: $36.20
Price in other shops: