The third edition presents updated insights and comprehensive analysis, enhancing the reader's understanding of the subject matter. It features new chapters, revised content, and additional resources that reflect the latest research and developments. The author’s expertise shines through as they explore complex themes and provide practical applications, making it an essential resource for both students and professionals. This edition aims to deepen knowledge and encourage critical thinking in the field.
Students studying different branches of computer graphics have 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 2nd edition, the author extends the scope of the original book to include applications of calculus in the areas of arc-length parameterisation of curves, geometric continuity, tangent and normal vectors, and curvature. The author 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 over a hundred and seventy 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
The book explores the historical and mathematical significance of the imaginary unit i = -1, which has puzzled mathematicians for centuries. Initially labeled "imaginary" by René Descartes, this term has contributed to misconceptions about complex numbers. The text highlights how i has become integral to various fields, including mathematics, physics, electrical engineering, and quantum field theory, illustrating its essential role in solving complex problems across disciplines.
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 updated and expanded fourth edition. The first four chapters revise number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on vectors, transforms, interpolation, 3D curves and patches, analytic geometry and barycentric coordinates. Following this, the reader is introduced to the relatively new topic of geometric algebra, and the last two chapters provide an introduction to differential and integral calculus, with an emphasis on geometry. Mathematics for Computer Graphics covers all of the key areas of the subject, including: Number sets Algebra Trigonometry Coordinate systems Transforms Quaternions Interpolation Curves and surfaces Analytic geometry Barycentric coordinates Geometric algebra Differential calculus Integral calculus This fourth edition contains over 120 worked examples and over 270 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.
Focusing on matrix transforms essential for computer graphics, this book provides a comprehensive introduction to key concepts such as notation, determinants, and various matrix types. It explores both 2D and 3D transformations, along with quaternions, and includes numerous worked examples to demonstrate practical applications. This resource is ideal for those looking to deepen their understanding of mathematical foundations in graphics.
"Quaternions for Computer Graphics" by John Vince provides a clear introduction to quaternions, covering their invention, applications in rotation, and relevance in computer graphics. The revised 2nd edition features color figures, extra examples, and a detailed index. It's ideal for students and professionals in computer science, mathematics, and programming.
Focusing on the essential role of geometry in computer graphics and animation, this book explores the techniques for addressing both simple and complex spatial problems. It covers fundamental shapes like circles and ellipses, as well as advanced concepts such as the manipulation of 3D objects around arbitrary axes, providing a comprehensive understanding of geometric principles applied in digital environments.
Geometric algebra is explored in a unique and engaging manner, making complex concepts accessible to readers. The author offers a clear introduction enriched with numerous examples and illustrations, enhancing understanding and retention. This approachable style invites both newcomers and those familiar with the topic to delve into the intricacies of Clifford Algebra.
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.
