Vector Analysis For Computer Graphics
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Vector Analysis For Computer Graphics
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Author : John Vince
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-18
Vector Analysis For Computer Graphics written by John Vince and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-18 with Computers categories.
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
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Author : John Vince
language : en
Publisher:
Release Date : 2021
Vector Analysis For Computer Graphics written by John Vince and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This second edition has been completely restructured, resulting in a compelling description of vector analysis from its first appearance as a byproduct of Hamilton's quaternions to the use of vectors in solving geometric problems. The result provides readers from different backgrounds with a complete introduction to vector analysis. The author shows why vectors are so useful and how it is possible to develop analytical skills in manipulating vector algebra. Using over 150 full-colour illustrations, the author demonstrates in worked examples how this relatively young branch of mathematics has become a powerful and central tool in describing and solving a wide range of geometric problems. These may be in the form of lines, surfaces and volumes, which may touch, collide, intersect, or create shadows upon complex surfaces. The book is divided into eleven chapters covering the history of vector analysis, linear equations, vector algebra, vector products, differentiating vector-valued functions, vector differential operators, tangent and normal vectors, straight lines, planes, intersections and rotating vectors. The new chapters are about the history, differentiating vector-valued functions, differential operators and tangent and normal vectors. The original chapters have been reworked and illustrated.
Mathematics For Computer Graphics
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Author : John A. Vince
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-26
Mathematics For Computer Graphics written by John A. Vince and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-26 with Computers categories.
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. Covering all the mathematical techniques required to resolve geometric problems and design computer programs for computer graphic applications, each chapter explores a specific mathematical topic prior to moving forward into the more advanced areas of matrix transforms, 3D curves and surface patches. Problem-solving techniques using vector analysis and geometric algebra are also discussed. All the key areas are covered including: Numbers, Algebra, Trigonometry, Coordinate geometry, Transforms, Vectors, Curves and surfaces, Barycentric coordinates, Analytic geometry. Plus – and unusually in a student textbook – a chapter on geometric algebra is included.
Geometric Algebra For Computer Graphics
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Author : John Vince
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-21
Geometric Algebra For Computer Graphics written by John Vince and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-21 with Computers categories.
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.
Quaternions For Computer Graphics
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Author : John Vince
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-11
Quaternions For Computer Graphics written by John Vince and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-11 with Computers categories.
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.
Geometric Algebra An Algebraic System For Computer Games And Animation
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Author : John A. Vince
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-20
Geometric Algebra An Algebraic System For Computer Games And Animation written by John A. Vince and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-20 with Computers categories.
Geometric algebra is still treated as an obscure branch of algebra and most books have been written by competent mathematicians in a very abstract style. This restricts the readership of such books especially by programmers working in computer graphics, who simply want guidance on algorithm design. Geometric algebra provides a unified algebraic system for solving a wide variety of geometric problems. John Vince reveals the beauty of this algebraic framework and communicates to the reader new and unusual mathematical concepts using colour illustrations, tabulations, and easy-to-follow algebraic proofs. The book includes many worked examples to show how the algebra works in practice and is essential reading for anyone involved in designing 3D geometric algorithms.
Quaternions For Computer Graphics
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Author : John Vince
language : en
Publisher:
Release Date : 2021
Quaternions For Computer Graphics written by John Vince and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
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.
Mathematics For Computer Graphics
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Author : John Vince
language : en
Publisher: Springer
Release Date : 2017-08-28
Mathematics For Computer Graphics written by John Vince and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-28 with Computers categories.
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.
Computer Visualization
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Author : Richard S. Gallagher
language : en
Publisher: CRC Press
Release Date : 2023-06-09
Computer Visualization written by Richard S. Gallagher and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-09 with Computers categories.
Rapid advances in 3-D scientific visualization have made a major impact on the display of behavior. The use of 3-D has become a key component of both academic research and commercial product development in the field of engineering design. Computer Visualization presents a unified collection of computer graphics techniques for the scientific visualization of behavior. The book combines a basic overview of the fundamentals of computer graphics with a practitioner-oriented review of the latest 3-D graphics display and visualization techniques. Each chapter is written by well-known experts in the field. The first section reviews how computer graphics visualization techniques have evolved to work with digital numerical analysis methods. The fundamentals of computer graphics that apply to the visualization of analysis data are also introduced. The second section presents a detailed discussion of the algorithms and techniques used to visualize behavior in 3-D, as static, interactive, or animated imagery. It discusses the mathematics of engineering data for visualization, as well as providing the current methods used for the display of scalar, vector, and tensor fields. It also examines the more general issues of visualizing a continuum volume field and animating the dimensions of time and motion in a state of behavior. The final section focuses on production visualization capabilities, including the practical computational aspects of visualization such as user interfaces, database architecture, and interaction with a model. The book concludes with an outline of successful practical applications of visualization, and future trends in scientific visualization.
Mathematics For Computer Graphics
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Author : John Vince
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-19
Mathematics For Computer Graphics written by John Vince and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-19 with Computers categories.
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.