This book is a complete introduction to vector analysis, especially within the context of computer graphics. The author shows why vectors are useful and how it is possible to develop analytical skills in manipulating vector algebra. Even though vector analysis is a relatively recent development in the history of mathematics, it has become a powerful and central tool in describing and solving a wide range of geometric problems. The book is divided into eleven chapters covering the mathematical foundations of vector algebra and its application to, among others, lines, planes, intersections, rotating vectors, and vector differentiation.

In this third edition of Foundation Mathematics for Computer Science, John Vince has reviewed and edited the second edition, and added chapters on systems of counting, area and volume. These subjects complement the existing chapters on visual mathematics, numbers, algebra, logic, combinatorics, probability, modular arithmetic, trigonometry, coordinate systems, determinants, vectors, complex numbers, matrices, geometric matrix transforms, differential and integral calculus. During this journey, the author touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barrycentric coordinates, transfinite sets and prime numbers. John Vince describes a range of mathematical topics that provide a solid foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with calculating area and volume using calculus. Readers will find that the author's visual approach should greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications. This third edition includes new, full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will help consolidate the understanding of abstract mathematical concepts. Whether you intend to pursue a career in programming, scientific visualisation, artificial intelligence, systems design, or real-time computing, you should find the author's literary style refreshingly lucid and engaging, and prepare you for more advanced texts.

John Vince explains a comprehensive range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, special effects, virtual reality, CAD and other areas of computer graphics in this completely revised and expanded sixth edition. The first five chapters cover a general introduction, number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on determinants, vectors, matrix algebra, complex numbers, geometric transforms, quaternion algebra, quaternions in space, interpolation, curves and patches, analytical geometry and barycentric coordinates. Following this, the reader is introduced to the relatively new subject of geometric algebra, followed by two chapters that introduce differential and integral calculus. Finally, there is a chapter on worked examples. Mathematics for Computer Graphics covers all of the key areas of the subject, including: * Number sets * Algebra * Trigonometry * Complex numbers * Coordinate systems * Determinants * Vectors * Quaternions * Matrix algebra * Geometric transforms * Interpolation * Curves and surfaces * Analytic geometry * Barycentric coordinates * Geometric algebra * Differential calculus * Integral calculus This sixth edition contains approximately 150 worked examples and over 330 colour illustrations, which are central to the author's descriptive writing style. Mathematics for Computer Graphics provides a sound understanding of the mathematics required for computer graphics software and setting the scene for further reading of more advanced books and technical research papers

Written by specialists in teaching computer animation, this text addresses key international topics of computer animation, such as: mathematics, modelling, rendering, and compositing. Each chapter discusses a particular topic and how it is applied, including state-of-the-art techniques that are used in computer animation. The handbook provides a complete and up-to-date picture of computer animation and will be a valuable reference source for programmers, technical directors and animators in computer animation, computer games and special effects and also undergraduate and postgraduate students. The editor, John Vince, has written and edited over 20 books on computer graphics, computer animation and virtual reality.

"Advances in computer technology and developments such as the Internet provide a constant momentum to design new techniques and algorithms to support computer graphics. Modelling, animation and rendering remain principal topics in the filed of computer graphics and continue to attract researchers around the world." This volume contains the papers presented at Computer Graphics International 2002, in July, at the University of Bradford, UK. These papers represent original research in computer graphics from around the world and cover areas such as: - Real-time computer animation - Image based rendering - Non photo-realistic rendering - Virtual reality - Avatars - Geometric and solid modelling - Computational geometry - Physically based modelling - Graphics hardware architecture - Data visualisation - Data compression The focus is on the commercial application and industrial use of computer graphics and digital media systems.

The very word "digital" has acquired a status that far exceeds its humble dictionary definition. Even the prefix digital, when associ ated with familiar sectors such as radio, television, photography and telecommunications, has reinvented these industries, and provided a unique opportunity to refresh them with new start-up companies, equipment, personnel, training and working practices - all of which are vital to modern national and international economies. The last century was a period in which new media stimulated new job opportunities, and in many cases created totally new sectors: video competed with film, CDs transformed LPs, and computer graphics threatened traditional graphic design sectors. Today, even the need for a physical medium is in question. The virtual digital domain allows the capture, processing, transmission, storage, retrieval and display of text, images, audio and animation without familiar materials such as paper, celluloid, magnetic tape and plastic. But moving from these media to the digital domain intro duces all sorts of problems, such as the conversion of analog archives, multimedia databases, content-based retrieval and the design of new content that exploits the benefits offered by digital systems. It is this issue of digital content creation that we address in this book. Authors from around the world were invited to comment on different aspects of digital content creation, and their contributions form the 23 chapters of this volume.

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.

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.

Although the computer's life has been relatively short, it has brought about an information revolution that is transforming our world on a scale that is still difficult to comprehend. This digital convergence is shaping society, technology and the media for the next millennium. Areas as diverse as home banking and shopping over the Internet; WWW access over mobile phone networks; and television systems such as Web TV which combine on-line services with television. But convergence is not just about technology. It is also about services and new ways of doing business and of interacting with society. Digital convergence heralds the 'Information Revolution'. Edited by John Vince and Rae Earnshaw this important new book on Digital Convergence: The Information Revolution is an edited volume of papers, bringing together state-of-the-art developments in the Internet and World Wide Web and should be compulsory reading for all those interested in and working in those areas.

As the Internet and the WWW impact on corporate and private activities, the human-computer interface is becoming a central issue for the designers of these systems. Such interfaces will decide the success or failure of future technologies, which will have to provide users with easy-to-use 'intelligent' problem solving tools.
'Intelligent Agents' are likely to play a significant role in the design of these interfaces, and this book explores how they are starting to influence media-based systems.
As you read Intelligent Agents for Mobile and Virtual Media, you will discover the considerable advances that have already been made on the long journey towards a day when computers will be truly described as an intelligent aid to our personal and business lives.

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.

"

Geometry is the cornerstone of computer graphics and computer animation, and provides the framework and tools for solving problems in two and three dimensions. This may be in the form of describing simple shapes such as a circle, ellipse, or parabola, or complex problems such as rotating 3D objects about an arbitrary axis.

Geometry for Computer Graphics draws together a wide variety of geometric information that will provide a sourcebook of facts, examples, and proofs for students, academics, researchers, and professional practitioners.

The book is divided into 4 sections: the first summarizes hundreds of formulae used to solve 2D and 3D geometric problems. The second section places these formulae in context in the form of worked examples. The third provides the origin and proofs of these formulae, and communicates mathematical strategies for solving geometric problems. The last section is a glossary of terms used in geometry.

This volume presents state-of-the-art research from a wide area of subjects brought about by the digital convergence of computing, television, telecommunications and the World-Wide Web. It represents a unique snapshot of trends across a wide range of subjects including virtual environments; virtual reality; telepresence; human-computer interface design; interactivity; avatars; and the Internet. Both researchers and practitioners will find it an invaluable source of reference.

Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems.

John Vince (author of numerous books including Geometry for Computer Graphics and Vector Analysis for Computer Graphics ) has tackled this complex subject in his usual inimitable style, and provided an accessible and very readable introduction.

As well as putting geometric algebra into its historical context, John tackles complex numbers and quaternions; the nature of wedge product and geometric product; reflections and rotations (showing how geometric algebra can offer a powerful way of describing orientations of objects and virtual cameras); and how to implement lines, planes, volumes and intersections. Introductory chapters also look at algebraic axioms, vector algebra and geometric conventions and the book closes with a chapter on how the algebra is applied to computer graphics."

The convergence of IT, telecommunications, and media is changing the way information is collected, stored and accessed. This revolution is having effects on the development and organisation of information and artefact repositories such as libraries and museums. This book presents key aspects in the rapidly moving field of digital convergence in the areas of technology and information sciences. Its chapters are written by international experts who are leaders in their fields.

Geometry is the cornerstone of computer graphics and computer animation, and provides the framework and tools for solving problems in two and three dimensions. This may be in the form of describing simple shapes such as a circle, ellipse, or parabola, or complex problems such as rotating 3D objects about an arbitrary axis.

Geometry for Computer Graphics draws together a wide variety of geometric information that will provide a sourcebook of facts, examples, and proofs for students, academics, researchers, and professional practitioners.

The book is divided into 4 sections: the first summarizes hundreds of formulae used to solve 2D and 3D geometric problems. The second section places these formulae in context in the form of worked examples. The third provides the origin and proofs of these formulae, and communicates mathematical strategies for solving geometric problems. The last section is a glossary of terms used in geometry.

During the last decade the word virtual became one of the most exposed words in the English language. Today we have virtual universities, virtual offices, virtual pets, virtual actors, virtual museums, virtual doctors - and all because of virtual reality. So what is virtual reality? Essentially, virtual reality is about the navigation and manipulation of 3D computer-generated environments. A VR user is able to navigate by walking, running or even flying through a virtual environment and explore viewpoints that would be impossible in the real world. But the real benefit of VR is the ability to touch, animate, pickup and reposition virtual objects and create totally new configurations. Key topics: The origins of VR How VR works How VR is being used The field of Virtual Reality is moving very quickly and increasing numbers of people need to know more about this exciting subject. Introduction to Virtual Reality explains what VR is about, without going into the underlying mathematical techniques, but at the same time providing a solid understanding and foundation of the techniques and applications involved.

One of the challenges facing professionals working in computer animation is keeping abreast of the latest developments and future trends - some of which are determined by industry where the state-of-the-art is continuously being re-defined by the latest computer-generated film special effects, while others arise from research projects whose results are quickly taken on board by programmers and animators working in industry. This handbook will be an invaluable toolkit for programmers, technical directors and professionals working in computer animation. A wide range of topics are covered including: * Computer games * Evolutionary algorithms * Shooting and live action * Digital effects * Cubic curves and surfaces * Subdivision surfaces * Rendering and shading Written by a team of experienced practitioners, each chapter provides a clear and precise overview of each area, reflecting the dynamic and fast-moving field of computer animation. This is a complete and up-to-date reference book on the state-of-the-art techniques used in computer animation.

"Advances in computer technology and developments such as the Internet provide a constant momentum to design new techniques and algorithms to support computer graphics. Modelling, animation and rendering remain principal topics in the filed of computer graphics and continue to attract researchers around the world." This volume contains the papers presented at Computer Graphics International 2002, in July, at the University of Bradford, UK. These papers represent original research in computer graphics from around the world and cover areas such as:- Real-time computer animation - Image based rendering - Non photo-realistic rendering - Virtual reality - Avatars - Geometric and solid modelling - Computational geometry - Physically based modelling - Graphics hardware architecture - Data visualisation - Data compression The focus is on the commercial application and industrial use of computer graphics and digital media systems.

The virtual digital domain allows the capture, processing, transmission, storage, retrieval and display of text, images, audio and animation, without familiar materials such as paper, celluloid, magnetic tape and plastic. But moving from these media to the digital domain introduces all sorts of problems, such as the conversion of analogue archives, multimedia databases, content-based retrieval and the design of new content that exploits the benefits offered by digital systems. It is this issue of digital content creation that is addressed in this book.Different aspects of digital content creation are discussed in this volume, contributed by authors from around the world. Although each chapter addresses an individual aspect of the digital domain, there are common threads that unite them into an exciting vision of the future.

Computer Animation is now worlds away from its early beginnings when programs merely mimicked the hand drawn cartoon process. Its now regularly used for creating wonderful special effects in major movies like Titanic, Toy Story, Antz and Bugs Life. John Vince tells you all about: The basic principles used in the powerful software products currently available on the market; The terms and processes involved; And in an easy-to-understand way, with no complicated math. So if you want to learn more about 3D computer animation without being swamped by complex mathematics, then read this book and have fun creating your own animated programs.

In this volume, John Vince provides a history of virtual reality (VR) and explains in easy-to-understand terms what computer graphics are and how they are integral to VR systems. He explains how important it is to understand the role human factors play in creating a good VR system, such as sound, sight, touch and balance. He also provides a detailed look at a working VR system and answers such questions as:
* What hardware and software is used?
* How does multi-user VR work?
* Can you network VR?
* What are the applications?
* What is the future for VR?

This book contains mainly a selection of papers that were presented at the International Workshop on High Performance Computing/or Computer Graphics and Visualisation, held in Swansea, United Kingdom on 3-4 July 1995. The workshop was sponsored by the HEFCWI Initiative on *Parallel Computing - Foundations and Applications*, and it has provided the international computer graphics community with a platform for: * assessing and reviewing the impact of the development of high performance computing on the progress of computer graphics and visualisation; * presenting the current use of high performance computing architecture and software tools in computer graphics and visualisation, and the development of parallel graphics algorithms; * identifying potential high performance computing applications in computer graphics and visualisation, and encouraging members of the graphics community to think about their problems from the perspective of parallelism. The book is divided into six sections. The first section, which acts as the introduction of the book, gives an overview of the current state of the art It contains a comprehensive survey, by Whitman, of parallel algorithms for computer graphics and visualisation; and a discussion, by Hansen, on the past, present and future high performance computing applications in computer graphics and visualisation. The second section is focused on the design and implementation of high performance architecture, software tools and algorithms for surface rendering.

If you have ever wondered what quaternions are - then look no further, John Vince will show you how simple and useful they are. This 2nd edition has been completely revised and includes extra detail on the invention of quaternions, a complete review of the text and equations, all figures are in colour, extra worked examples, an expanded index, and a bibliography arranged for each chapter. Quaternions for Computer Graphics includes chapters on number sets and algebra, imaginary and complex numbers, the complex plane, rotation transforms, and a comprehensive description of quaternions in the context of rotation. The book will appeal to students of computer graphics, computer science and mathematics, as well as programmers, researchers, academics and professional practitioners interested in learning about quaternions. John Vince explains in an easy-to-understand language, with the aid of useful figures, how quaternions emerged, gave birth to modern vector analysis, disappeared, and reemerged to be adopted by the flight simulation industry and computer graphics. This book will give you the confidence to use quaternions within your every-day mathematics, and explore more advanced texts.

If you have ever wondered what quaternions are - then look no further, John Vince will show you how simple and useful they are. This 2nd edition has been completely revised and includes extra detail on the invention of quaternions, a complete review of the text and equations, all figures are in colour, extra worked examples, an expanded index, and a bibliography arranged for each chapter. Quaternions for Computer Graphics includes chapters on number sets and algebra, imaginary and complex numbers, the complex plane, rotation transforms, and a comprehensive description of quaternions in the context of rotation. The book will appeal to students of computer graphics, computer science and mathematics, as well as programmers, researchers, academics and professional practitioners interested in learning about quaternions. John Vince explains in an easy-to-understand language, with the aid of useful figures, how quaternions emerged, gave birth to modern vector analysis, disappeared, and reemerged to be adopted by the flight simulation industry and computer graphics. This book will give you the confidence to use quaternions within your every-day mathematics, and explore more advanced texts.