This book is an introduction to matrix transforms, which are ubiquitous in the world of computer graphics. Covers notation, determinants, matrices, 2D transforms, 3D transforms and quaternions, and offers many worked examples to illustrate their practical use.

Matrix transforms are ubiquitous within the world of computer graphics, where they have become an invaluable tool in a programmer's toolkit for solving everything from 2D image scaling to 3D rotation about an arbitrary axis. Virtually every software system and hardware graphics processor uses matrices to undertake operations such as scaling, translation, reflection and rotation. Nevertheless, for some newcomers to the world of computer games and animation, matrix notation can appear obscure and challenging.

Matrices and determinants were originally used to solve groups of simultaneous linear equations, and were subsequently embraced by the computer graphics community to describe the geometric operations for manipulating two- and three-dimensional structures. Consequently, to place matrix notation within an historical context, the author provides readers with some useful background to their development, alongside determinants.

Although it is assumed that the reader is familiar with everyday algebra and the solution of simultaneous linear equations, Matrix Transforms for Computer Games and Animation does not expect any prior knowledge of matrix notation. It includes chapters on matrix notation, determinants, matrices, 2D transforms, 3D transforms and quaternions, and includes many worked examples to illustrate their practical use.

Assumes no prior knowledge of matrix notation Chapters contain practical worked examples Easy to read descriptions on how to apply matrix notation within the world of computer games and animation Includes supplementary material: sn.pub/extras 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

Preface.- Introduction.- Introduction to Matrix Notation.- Determinants.- Matrices.- Matrix Transforms.- Transforms.- Quaternions.- Conclusion.- Composite Point Rotation Sequences.- Index.