Visualizing Quaternions SERIES IN INTERACTIVE 3D TECHNOLOGY

The night the first Mars Exploration Rover landed, the engineering team at the Jet Propulsion Laboratory in Pasadena excitedly announced: "We have excellent quaternions for the rover!" This meant that through the application of a technique developed 160 years before they were able to determine the precise orientation of the spacecraft on Mars after traveling millions of miles through space. Quaternions are widely used in computer graphics, simulations, Hollywood special effects, computer games, and space travel, but they are conceptually very hard to grasp. The computer graphics community has a general familiarity with quaternions and their uses, but there are still many unresolved issues and controversies with them. And the subject mystifies many new engineers, such as game developers who lack a background in mathematics. While there are books that approach quaternions from a mathematician's perspective, this is the first that will give a professional developer an intuitive understanding of quaternions through visual representations. Visualizing Quaternions introduces new developers to this powerful technique and will provide the definitive explanation to those who have been struggling to use them.
1558600210LangtextGame development is still in its infancy, but games are poised for a major evolution: Ready to move from mostly plot-driven stories to more character based ones. The problem is that the principles of sophisticated character design and interaction are not widely understood in the game development community. And gender and cultural issues within the game genre are growing in importance. Katherine Isbister has spent 10 years examining what makes interactions with computer characters useful and engaging to different audiences. The key is to understand what's memorable, exciting, useful, and engaging to the participant about real-life social interactions, and applying that to character design. Game designers who create great characters often make use of these principles without realizing it. This book gives game design professionals and other designers a framework for how social roles and perceptual manipulations function, so that they are more aware of what they are doing when they design characters, and why it works.

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 important-a 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.

Andrew J. Hanson Ph.D. is an Emeritus Professor of Computer Science at Indiana University. He earned a bachelor's degree in Chemistry and Physics from Harvard University in 1966 and a PhD in Theoretical Physics from MIT under Kerson Huang in 1971. His interests range from general relativity to computer graphics, artificial intelligence, and bioinformatics; he is particularly concerned with applications of quaternions and with exploitation of higher-dimensional graphics for the visualization of complex scientific contexts such as Calabi-Yau spaces. He is the co-discoverer of the Eguchi-Hanson "gravitational instanton Einstein metric (1978), author of Visualizing Quaternions (Elsevier, 2006), and designer of the iPhone Apps "4Dice and "4DRoom (2012) for interacting with four-dimensional virtual reality.