Visualizing More Quarternions

Introduced 175 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in computer modelling, as they offer a powerful way to represent efficient interpolation of rotations. Visualizing More Quaternions is essentially a second volume of Dr. Andrew J. Hanson’s groundbreaking book, Visualizing Quaternions. This second volume updates and extends concepts that have evolved since the first book published in 2005 and adds entirely new insights that Dr. Hanson’s research has developed recently. This includes in particular the applications of quaternion methods to proteomics and molecular crystallography problems, which are domains with significant current research and application activity. The breadth of the topics to which Dr. Hanson has been applying quaternions has expanded significantly over the last decade, and Visualizing More Quaternions reflects the broader audience, in more diverse fields of science, involved with those scientific domains. In addition to readers interested in quaternions for their own sake, along with scientists involved in computer graphics, animation, shape modeling, and scientific visualization, readers from several other disciplines will benefit from this new volume. Foremost among these, and the target of the first several chapters, are scientists involved in molecular chemistry, where techniques based on quaternion eigensystems have become a standard tool for evaluating the quality of shape matching. Dr. Hanson’s contribution to this domain is the formulation of protein amino acid signatures using per-residue quaternion-based frame triads, along with new methods for evaluating matching problems involving such frames. In addition to proteomics-related material useful for biochemists and biophysicists, Visualizing More Quaternions includes material that is related to electron microscopy (and specifically cryo-EM). The book also covers a spectrum of robotics problems that includes both orientation matching and alignment, and six-degree-of-freedom contexts based on dual quaternions, which were not covered at all in the author’s first book. Finally, there is a challenging set of chapters involving improved quaternion formulations of a wide range of mathematical physics problems that will appeal to readers involved in several domains of current research, including material related to gravitational instantons and Clifford algebras. Visualizing More Quaternions appeals to a broad population of scientific specialties, while treating a wide spectrum of difficulties, from fairly straightforward applications to very sophisticated applications. The book contains extensive computer graphics images of all sorts, including interactive device-independent web-based visualization applications that correspond to key static figures in the print version of the book, which are suitable for displaying the 4D properties of quaternions interactively. Richly illustrated for researchers and practitioners in the fields of mathematics, computer science, engineering, computer graphics, scientific visualization, molecular chemistry, biochemistry, biophysics, robotics, and mathematical physics Provides key applications that appeal to a broad population of scientific specialties, while treating a wide spectrum of difficulties, from fairly straightforward applications to very sophisticated applications Includes a companion website with an assortment of quaternion utilities and sample code, and data sets for the book's illustrations, including interactive device-independent web-based visualization applications that