Rotation Transforms For Computer Graphics
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Rotation Transforms For Computer Graphics
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Author : John Vince
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-04
Rotation Transforms 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 2011-01-04 with Computers categories.
Rotation transforms are used everywhere in computer graphics from rotating pictures in editing software, to providing an arbitrary view of a 3D virtual environment. Although the former is a trivial operation, the latter can be a challenging task. 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. It includes many worked examples and over 100 illustrations that make it essential reading for students, academics, researchers and professional practitioners. The book includes introductory chapters on complex numbers, matrices, quaternions and geometric algebra, and further chapters on how these techniques are employed in 2D and 3D computer graphics. In particular, matrix and bivector transforms are developed and evaluated to rotate points in a fixed frame of reference, and vice versa.
Quaternions For Computer Graphics
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Author : John Vince
language : en
Publisher: Springer Nature
Release Date : 2021-09-02
Quaternions For Computer Graphics written by John Vince and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-02 with Computers 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.
Matrix Transforms For Computer Games And Animation
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Author : John Vince
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-26
Matrix Transforms For Computer Games And Animation 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 2012-06-26 with Computers categories.
Matrix transforms are ubiquitous within the world of computer graphics, where they have become an invaluable tool in a programmer’s toolkit for solving everything from 2D image scaling to 3D rotation about an arbitrary axis. Virtually every software system and hardware graphics processor uses matrices to undertake operations such as scaling, translation, reflection and rotation. Nevertheless, for some newcomers to the world of computer games and animation, matrix notation can appear obscure and challenging. Matrices and determinants were originally used to solve groups of simultaneous linear equations, and were subsequently embraced by the computer graphics community to describe the geometric operations for manipulating two- and three-dimensional structures. Consequently, to place matrix notation within an historical context, the author provides readers with some useful background to their development, alongside determinants. Although it is assumed that the reader is familiar with everyday algebra and the solution of simultaneous linear equations, Matrix Transforms for Computer Games and Animation does not expect any prior knowledge of matrix notation. It includes chapters on matrix notation, determinants, matrices, 2D transforms, 3D transforms and quaternions, and includes many worked examples to illustrate their practical use.
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 Science & Business Media
Release Date : 2013-12-11
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 2013-12-11 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 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.
Calculus For Computer Graphics
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Author : John Vince
language : en
Publisher: Springer
Release Date : 2019-03-12
Calculus 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 2019-03-12 with Computers categories.
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.
Vector Analysis For Computer Graphics
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Author : John Vince
language : en
Publisher: Springer Nature
Release Date : 2021-06-01
Vector Analysis For Computer Graphics written by John Vince and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-01 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.
Two Dimensional Computer Graphics
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Author : Fouad Sabry
language : en
Publisher: One Billion Knowledgeable
Release Date : 2024-05-05
Two Dimensional Computer Graphics written by Fouad Sabry and has been published by One Billion Knowledgeable this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-05 with Computers categories.
What is Two Dimensional Computer Graphics 2D computer graphics is the computer-based generation of digital images-mostly from two-dimensional models and by techniques specific to them. It may refer to the branch of computer science that comprises such techniques or to the models themselves. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: 2D computer graphics Chapter 2: Orthogonal matrix Chapter 3: Ellipsoid Chapter 4: Rotation (mathematics) Chapter 5: Transformation matrix Chapter 6: Rotation matrix Chapter 7: Rotation formalisms in three dimensions Chapter 8: Axis-angle representation Chapter 9: Kinematics Chapter 10: Three-dimensional rotation operator (II) Answering the public top questions about two dimensional computer graphics. (III) Real world examples for the usage of two dimensional computer graphics in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Two Dimensional Computer Graphics.
Transformations And Projections In Computer Graphics
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Author : David Salomon
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-21
Transformations And Projections In Computer Graphics written by David Salomon 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 2007-01-21 with Computers categories.
This book introduces perspective, and discusses the mathematics of perspective in a detailed, yet accessible style. It also reviews nonlinear projections, including the fisheye, panorama, and map projections frequently used to enhance digital images. Topics and features include a complete and self-contained presentation of concepts, principles, and methods; a 12-page colour section, and numerous figures. This essential resource for computer professionals both within and outside the field of Computer Graphics is also suitable for graduates and advanced undergraduates in Computer Graphics and Computer-Aided Design. Key ideas are introduced, examined and illustrated by figures and examples, and reinforced through solved exercises.
Mathematical Basics Of Motion And Deformation In Computer Graphics
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Author : Ken Anjyo
language : en
Publisher: Springer Nature
Release Date : 2014-10-22
Mathematical Basics Of Motion And Deformation In Computer Graphics written by Ken Anjyo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-22 with Mathematics categories.
This synthesis lecture presents an intuitive introduction to the mathematics of motion and deformation in computer graphics. Starting with familiar concepts in graphics, such as Euler angles, quaternions, and affine transformations, we illustrate that a mathematical theory behind these concepts enables us to develop the techniques for efficient/effective creation of computer animation. This book, therefore, serves as a good guidepost to mathematics (differential geometry and Lie theory) for students of geometric modeling and animation in computer graphics. Experienced developers and researchers will also benefit from this book, since it gives a comprehensive overview of mathematical approaches that are particularly useful in character modeling, deformation, and animation. Table of Contents: Preface / Symbols and Notations / Introduction / Rigid Transformation / Affine Transformation / Exponential and Logarithm of Matrices / 2D Affine Transformation between Two Triangles / Global 2D Shape Interpolation / Parametrizing 3D Positive Affine Transformations / Further Readings / Bibliography / Authors' Biographies