John Vince – författare

Rotation transforms are used everywhere in computer graphics from rotating pictures in editing software, to providing an arbitrary view of a 3D virtual environment. Although the former is a trivial operation, the latter can be a challenging task. 

Rotation Transforms for Computer Graphics covers a wide range of mathematical techniques used for rotating points and frames of reference in the plane and 3D space. It includes many worked examples and over 100 illustrations that make it essential reading for students, academics, researchers and professional practitioners. 

The book includes introductory chapters on complex numbers, matrices, quaternions and geometric algebra, and further chapters on how these techniques are employed in 2D and 3D computer graphics. In particular, matrix and bivector transforms are developed and evaluated to rotate points in a fixed frame of reference, and vice versa.

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.

The field of computer graphics combines display hardware, software, and interactive techniques in order to display and interact with data generated by applications. Visualization is concerned with exploring data and information graphically in such a way as to gain information from the data and determine significance. Visual analytics is the science of analytical reasoning facilitated by interactive visual interfaces.

Expanding the Frontiers of Visual Analytics and Visualization provides a review of the state of the art in computer graphics, visualization, and visual analytics by researchers and developers who are closely involved in pioneering the latest advances in the field. It is a unique presentation of multi-disciplinary aspects in visualization and visual analytics, architecture and displays, augmented reality, the use of color, user interfaces and cognitive aspects, and technology transfer. It provides readers with insights into the latest developments in areas such as new displays and new display processors, new collaboration technologies, the role of visual, multimedia, and multimodal user interfaces, visual analysis at extreme scale, and adaptive visualization.

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.