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.
"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.
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.
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.
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.
Virtual reality (VR) allows users to enter computer generated 3D scenes that can be navigated and manipulated. Essential Virtual Reality fast shows readers what is and isn't VR. The author provides an overview of the history of virtual reality and explains, in easy-to-understand terms, the concepts of computer graphics and how they are integral to VR systems. The importance of integrating human factors, such as vision, sound, touch and balance, is emphasized. Exploring actual VR systems, readers will learn about all the important aspects of virtual environments, including the hardware, software, and sound systems, as well as the latest VR techniques on the Internet.
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 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.
This book provides a quick, concise introduction to the most important mathematics used in computer graphics. Vince makes the concepts easy to understand, so that non-mathematicians can grasp the math that lies behind computer animation.
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.
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.