Rae Earnshaw

John Vince

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.

Digital Content Creation

This is a concise and informal introductory book on the mathematical concepts that underpin computer graphics. The author, John Vince, makes the concepts easy to understand, enabling non-experts to come to terms with computer animation work. The book complements the author's other works and is written in the same accessible and easy-to-read style. It is also a useful reference book for programmers working in the field of computer graphics, virtual reality, computer animation, as well as students on digital media courses, and even mathematics courses.

Mathematics for Computer Graphics

John Vince explains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD and other areas of computer graphics in this completely revised and expanded fifth edition. The first five chapters cover a general introduction, number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on vectors, matrix algebra, transforms, interpolation, curves and patches, analytic geometry and barycentric coordinates. Following this, the reader is introduced to the relatively new topic 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 · Coordinate systems · Determinants · Vectors · Quaternions · Matrix algebra · Geometric transforms · Interpolation · Curves and surfaces · Analytic geometry · Barycentric coordinates · Geometric algebra · Differential calculus · Integral calculus This fifth edition contains over 120 worked examples and over 320 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, giving a fascinating insight into the design of computer graphics software and setting the scene for further reading of more advanced books and technical research papers.

A complete overview of the geometry associated with computer graphics that provides everything a reader needs to understand the topic. Includes a summary hundreds of formulae used to solve 2D and 3D geometric problems; worked examples; proofs; mathematical strategies for solving geometric problems; a glossary of terms used in geometry.

Formulae, Examples and Proofs

Geometry for Computer Graphics

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.

Vector Analysis for Computer Graphics

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

John Vince describes a range of mathematical topics to provide a foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus. Readers will find that the author's visual approach will greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications. Each chapter includes 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 consolidate comprehension of abstract mathematical concepts. Foundation Mathematics for Computer Science covers number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus, and reveals the names of the mathematicians behind such inventions. During this journey, John Vince touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barycentric coordinates, transfinite sets and prime numbers. Whether you intend to pursue a career in programming, scientific visualisation, 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.

A Visual Approach

Foundation Mathematics for Computer Science

"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.

Advances in Modelling, Animation and Rendering

Virtual Reality Systems

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.

Digital Media: The Future

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.

Digital Convergence: The Information Revolution

Judith R. Brown

Mikail Jern

Shows how visualizations can be created, from simple 2D to the latest virtual reality. CD gives examples ranging from basic charting and graphing to more advanced video, animation and volume visualization techniques.

Using Computer Graphics to Explore Data and Present Information

Visualization

Andries Van Dam

Richard Guedj

Rae Earnshawand John A. Vince --_. . _----- 1 Introduction The USPresident's Information Technology Advisory Committee (PITAC)recently advised the US Senate of the strategic importance of investing in IT for the 21st century, particularlyin the areas of software,human-computer interaction, scalable information infrastructure, high-end computing and socioeconomic issues [1]. Research frontiers ofhuman-computer interaction include the desire that interac tion be more centered around human needs and capabilities, and that the human environment be considered in virtual environments and in other contextual infor mation-processing activities. The overall goal is to make users more effective in their information or communication tasks by reducing learning times, speeding performance, lowering error rates, facilitating retention and increasing subjective satisfaction. Improved designs can dramatically increase effectiveness for users, who range from novices to experts and who have diverse cultures with varying educational backgrounds. Their lives could be made more satisfying, their work safer, their learning easier and their health better.

Frontiers of Human-Centered Computing, Online Communities and Virtual Environments

For those who want to learn more about computer animation without being swamped with complex mathematics, this is the book to read! Beginning with the relationship between animation, the human visual system, and computers, Essential Computer Animation fast takes readers through a broad exploration of the subject. Readers will learn all about computer animation techniques; computer animation hardware; animation software, such as Softimage, Maya, 3D-Studio, MAX, and Lightwave; post-production techniques; and animation applications.

How to Understand the Techniques and Potential of Computer Animation

Essential Computer Animation fast

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.

Digital Convergence - Libraries of the Future

The imaginary unit i = √-1 has been used by mathematicians for nearly five-hundred years, during which time its physical meaning has been a constant challenge. Unfortunately, René Descartes referred to it as “imaginary”, and the use of the term “complex number” compounded the unnecessary mystery associated with this amazing object. Today, i = √-1 has found its way into virtually every branch of mathematics, and is widely employed in physics and science, from solving problems in electrical engineering to quantum field theory. John Vince describes the evolution of the imaginary unit from the roots of quadratic and cubic equations, Hamilton’s quaternions, Cayley’s octonions, to Grassmann’s geometric algebra. In spite of the aura of mystery that surrounds the subject, John Vince makes the subject accessible and very readable. The first two chapters cover the imaginary unit and its integration with real numbers. Chapter 3 describes how complex numbers work with matrices, and shows how to compute complex eigenvalues and eigenvectors. Chapters 4 and 5 cover Hamilton’s invention of quaternions, and Cayley’s development of octonions, respectively. Chapter 6 provides a brief introduction to geometric algebra, which possesses many of the imaginary qualities of quaternions, but works in space of any dimension. The second half of the book is devoted to applications of complex numbers, quaternions and geometric algebra. John Vince explains how complex numbers simplify trigonometric identities, wave combinations and phase differences in circuit analysis, and how geometric algebra resolves geometric problems, and quaternions rotate 3D vectors. There are two short chapters on the Riemann hypothesis and the Mandelbrot set, both of which use complex numbers. The last chapter references the role of complex numbers in quantum mechanics, and ends with Schrödinger’s famous wave equation. Filled with lots of clear examples and useful illustrations, this compact book provides an excellent introduction to imaginary mathematics for computer science.

Imaginary Mathematics for Computer Science

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. The author tackles this complex subject with inimitable style, and provides an accessible and very readable introduction. The book is filled with lots of clear examples and is very well illustrated. Introductory chapters 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.

John Vince

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