Sir William Rowan Hamilton was a genius, and will be remembered for his significant contributions to physics and mathematics. The Hamiltonian, which is used in quantum physics to describe the total energy of a system, would have been a major achievement for anyone, but Hamilton also invented quaternions, which paved the way for modern vector analysis.

Quaternions are one of the most documented inventions in the history of mathematics, and this book is about their invention, and how they are used to rotate vectors about an arbitrary axis. Apart from introducing the reader to the features of quaternions and their associated algebra, the book provides valuable historical facts that bring the subject alive.

Quaternions for Computer Graphics introduces the reader to quaternion algebra by describing concepts of sets, groups, fields and rings. It also includes chapters on imaginary quantities, complex numbers and the complex plane, which are essential to understanding quaternions. The book contains many illustrations and worked examples, which make it essential reading for students, academics, researchers and professional practitioners.

Provides valuable historical facts on the features of quaternions their associated algebra and how they can be used in computer graphics. Describes the concepts of sets, groups, fields and rings in order to enable the reader to design and code quaternion algorithms. Contains many illustrations and worked examples. Includes supplementary material: sn.pub/extras

Autorentext

Professor John Vince began working in computer graphics at Middlesex Polytechnic in 1968. His research activities centered on computer animation software and resulted in the PICASO and PRISM animation systems. Whilst at Middlesex, he designed the UK's first MSc course in Computer Graphics and developed a popular program of short courses in computer animation for television designers. In 1986 he joined Rediffusion Simulation as a Research Consultant and worked on the development of real-time computer systems for commercial flight simulators. In 1992 he was appointed Chief Scientist of Thomson Training Simulation Ltd. In 1995 he was appointed Professor of Digital Media at the National Centre for Computer Animation at Bournemouth University and in 1999 he was made Head of Academic Group for Computer Animation. He was awarded a DSc by Brunel University in recognition of his work in computer graphics. He has written and edited over 45 books on computer graphics, computer animation, computer science and virtual reality, including the following Springer titles: Calculus for Computer Graphics, 2nd edition (2019) Mathematics for Computer Graphics, 5th edition (2017) Imaginary Mathematics for Computer Science, (2018) Foundation Mathematics for Computer Science, 2nd edition (2015) Matrix Transforms for Computer Games and Animation (2012) Expanding the Frontiers of Visual Analytics and Visualization (2012) Quaternions for Computer Graphics (2011) Rotation Transforms for Computer Graphics (2011) Geometric Algebra: An Algebraic System for Computer Animation and Games (2009) Geometric Algebra for Computer Graphics (2008)

Inhalt

Introduction.-Number Sets and Algebra.-Complex Numbers.-The Complex Plane.-Quaternion Algebra.-3D Rotation Transforms.-Quaternions in Space.-Conclusion.