Vector Analysis For Computer Graphics

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Vector Analysis for Computer Graphics

John Vince
Vector Analysis for Computer Graphics Book PDF

Author : John Vince
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 44,7 Mb
Release : 2007-05-15
Category : Computers
ISBN : 9781846288043

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Vector Analysis for Computer Graphics by John Vince Pdf

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

John Vince
Vector Analysis for Computer Graphics Book PDF

Author : John Vince
Publisher : Unknown
Page : 0 pages
File Size : 41,5 Mb
Release : 2021
Category : Electronic
ISBN : 1447175069

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Vector Analysis for Computer Graphics by John Vince Pdf

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.

Vector Analysis for Computer Graphics

John Vince
Vector Analysis for Computer Graphics Book PDF

Author : John Vince
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 50,9 Mb
Release : 2007-06-18
Category : Computers
ISBN : 9781846288036

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Vector Analysis for Computer Graphics by John Vince Pdf

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.

Mathematics for Computer Graphics

John A. Vince
Mathematics for Computer Graphics Book PDF

Author : John A. Vince
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 46,5 Mb
Release : 2010-01-26
Category : Computers
ISBN : 9781849960236

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Mathematics for Computer Graphics by John A. Vince Pdf

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

John Vince
Geometric Algebra for Computer Graphics Book PDF

Author : John Vince
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 55,6 Mb
Release : 2008-04-21
Category : Computers
ISBN : 9781846289965

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Geometric Algebra for Computer Graphics by John Vince Pdf

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.

Mathematics for Computer Graphics

John Vince
Mathematics for Computer Graphics Book PDF

Author : John Vince
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 55,6 Mb
Release : 2005-12-19
Category : Computers
ISBN : 9781846282836

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Mathematics for Computer Graphics by John Vince Pdf

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.

Quaternions for Computer Graphics

John Vince
Quaternions for Computer Graphics Book PDF

Author : John Vince
Publisher : Springer Science & Business Media
Page : 147 pages
File Size : 45,8 Mb
Release : 2011-06-11
Category : Computers
ISBN : 9780857297600

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Quaternions for Computer Graphics by John Vince Pdf

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.

Calculus for Computer Graphics

John Vince
Calculus for Computer Graphics Book PDF

Author : John Vince
Publisher : Springer
Page : 303 pages
File Size : 40,5 Mb
Release : 2019-03-12
Category : Computers
ISBN : 9783030113766

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Calculus for Computer Graphics by John Vince Pdf

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.

Quaternions for Computer Graphics

John Vince
Quaternions for Computer Graphics Book PDF

Author : John Vince
Publisher : Unknown
Page : 0 pages
File Size : 47,6 Mb
Release : 2021
Category : Electronic
ISBN : 1447175107

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Quaternions for Computer Graphics by John Vince Pdf

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

John Vince
Mathematics for Computer Graphics Book PDF

Author : John Vince
Publisher : Springer
Page : 505 pages
File Size : 41,8 Mb
Release : 2017-08-28
Category : Computers
ISBN : 9781447173366

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Mathematics for Computer Graphics by John Vince Pdf

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.

Quaternions for Computer Graphics

John Vince
Quaternions for Computer Graphics Book PDF

Author : John Vince
Publisher : Springer Nature
Page : 188 pages
File Size : 41,9 Mb
Release : 2021-09-02
Category : Computers
ISBN : 9781447175094

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Quaternions for Computer Graphics by John Vince Pdf

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.

Geometric Algebra: An Algebraic System for Computer Games and Animation

John A. Vince
Geometric Algebra An Algebraic System for Computer Games and Animation Book PDF

Author : John A. Vince
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 51,6 Mb
Release : 2009-05-20
Category : Computers
ISBN : 9781848823792

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Geometric Algebra: An Algebraic System for Computer Games and Animation by John A. Vince Pdf

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.

Computer Visualization

Richard S. Gallagher,0 Solomon Press,,
Computer Visualization Book PDF

Author : Richard S. Gallagher,0 Solomon Press,,
Publisher : CRC Press
Page : 328 pages
File Size : 54,5 Mb
Release : 2023-06-09
Category : Computers
ISBN : 9781000939811

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Computer Visualization by Richard S. Gallagher,0 Solomon Press,, Pdf

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

John Vince
Mathematics for Computer Graphics Book PDF

Author : John Vince
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 44,7 Mb
Release : 2013-12-11
Category : Computers
ISBN : 9781447162902

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Mathematics for Computer Graphics by John Vince Pdf

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.

3D Computer Graphics

Samuel R. Buss
3D Computer Graphics Book PDF

Author : Samuel R. Buss
Publisher : Cambridge University Press
Page : 397 pages
File Size : 55,6 Mb
Release : 2003-05-19
Category : Computers
ISBN : 9781139440387

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3D Computer Graphics by Samuel R. Buss Pdf

This textbook, first published in 2003, emphasises the fundamentals and the mathematics underlying computer graphics. The minimal prerequisites, a basic knowledge of calculus and vectors plus some programming experience in C or C++, make the book suitable for self study or for use as an advanced undergraduate or introductory graduate text. The author gives a thorough treatment of transformations and viewing, lighting and shading models, interpolation and averaging, Bézier curves and B-splines, ray tracing and radiosity, and intersection testing with rays. Additional topics, covered in less depth, include texture mapping and colour theory. The book covers some aspects of animation, including quaternions, orientation, and inverse kinematics, and includes source code for a Ray Tracing software package. The book is intended for use along with any OpenGL programming book, but the crucial features of OpenGL are briefly covered to help readers get up to speed. Accompanying software is available freely from the book's web site.