Visualizing More Quaternions

Visualizing More Quaternions, Volume Two updates on proteomics-related material that will be useful for biochemists and biophysicists, including material related to electron microscopy (and specifically cryo-EVisualizing. Dr. Andrew J. Hanson's groundbreaking book updates and extends concepts that have evolved since the first book published in 2005, adding entirely new insights that Dr. Hanson's research has recently developed. This includes the applications of quaternion methods to proteomics and molecular crystallography problems, which are domains with significant current research and application activity.In addition to readers interested in quaternions for their own sake, scientists involved in computer graphics, animation, shape modeling, and scientific visualization, and 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. - Establishes basic principles for visual display of quaternions and their applications. - Explores quaternion based approaches to the matching of point cloud pairs, including approaches to data from orthographic and perspective projections. - Develops extensive applications of quaternion frames to protein orientation analysis. - Analyzes the application of quaternion methods to physics problems ranging from quantum computing to special relativity and gravitational instantons.