Bøger af John Vince

Students studying different branches of computer graphics need to be familiar with geometry, matrices, vectors, rotation transforms, quaternions, curves and surfaces. And as computer graphics software becomes increasingly sophisticated, calculus is also being used to resolve its associated problems.In this 3rd edition, the author extends the scope of the original book to include vector differential operators and differential equations and draws upon his experience in teaching mathematics to undergraduates to make calculus appear no more challenging than any other branch of mathematics. He introduces the subject by examining how functions depend upon their independent variables, and then derives the appropriate mathematical underpinning and definitions. This gives rise to a function¿s derivative and its antiderivative, or integral. Using the idea of limits, the reader is introduced to derivatives and integrals of many common functions. Other chapters address higher-order derivatives, partial derivatives, Jacobians, vector-based functions, single, double and triple integrals, with numerous worked examples and almost two hundred colour illustrations. This book complements the author¿s other books on mathematics for computer graphics and assumes that the reader is familiar with everyday algebra, trigonometry, vectors and determinants. After studying this book, the reader should understand calculus and its application within the world of computer graphics, games and animation.

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.

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.

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.

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 my last book, Geometry for Computer Graphics, I employed a mixture of algebra and vector analysis to prove many of the equations used in computer graphics. At the time, I did not make any distinction between the two methodologies, but slowly it dawned upon me that I had had to discover, for the first time, how to use vector analysis and associated strategies for solving geometric problems. I suppose that mathematicians are taught this as part of their formal mathematical training, but then, I am not a mathematician! After some deliberation, I decided to write a book that would introduce the beginner to the world of vectors and their application to the geometric problems encountered in computer graphics. I accepted the fact that there would be some duplication of formulas between this and my last book; however, this time I would concentrate on explaining how problems are solved. The book contains eleven chapters: The first chapter distinguishes between scalar and vector quantities, which is reasonably straightforward. The second chapter introduces vector repres- tation, starting with Cartesian coordinates and concluding with the role of direction cosines in changes in axial systems. The third chapter explores how the line equation has a natural vector interpretation and how vector analysis is used to resolve a variety of line-related, geometric problems. Chapter 4 repeats Chapter 3 in the context of the plane.

The updated and expanded 4th edition of this book explores mathematical techniques and problem-solving strategies for computer games, animation, virtual reality, CAD and other areas of computer graphics. Includes 120 worked examples and some 270 illustrations.

This book is a complete introduction to vector analysis, especially within the context of computer graphics. 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.

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.

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.

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.

This book introduces the features of quaternions and explains their associated algebra, offers historical details about their invention by Sir William Rowan Hamilton and shows how they are used in computer graphics to rotate vectors about an arbitrary axis.

Rotation transforms are used everywhere in computer graphics from rotating pictures in editing software, to providing an arbitrary view of a 3D virtual environment. 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.