Language: en
Pages: 530
Pages: 530
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
Language: en
Pages: 157
Pages: 157
In addition to these theoretical issues, we also address some computational questions. We develop straightforward formulas for converting back and forth between quaternion and matrix representations for rotations, reflections, and perspective projections, and we discuss the relative advantages and disadvantages of the quaternion and matrix representations for these transformations. Moreover,
Language: en
Pages: 846
Pages: 846
This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game
Language: en
Pages: 885
Pages: 885
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer
Language: en
Pages: 160
Pages: 160
Based on updates to signal and image processing technology made inthe last two decades, this text examines the most recent researchresults pertaining to Quaternion Fourier Transforms. QFT is acentral component of processing color images and complex valuedsignals. The book’s attention to mathematical concepts,imaging applications, and Matlab compatibility render it anirreplaceable