MATRIX TRANSFORMS FOR COMPUTER GAMES AND ANIMATION

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Matrix Transforms For Computer Games And Animation

Author : John Vince
ISBN : 9781447143215
Genre : Computers
File Size : 89.51 MB
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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.
Category: Computers

Mathematics For Computer Graphics

Author : John Vince
ISBN : 9781447173366
Genre : Computers
File Size : 79.84 MB
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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.
Category: Computers

Calculus For Computer Graphics

Author : John Vince
ISBN : 9781447154662
Genre : Computers
File Size : 75.10 MB
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Students studying computer animation and computer games 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. 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 illustrations. Calculus for Computer Graphics 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 games and animation.
Category: Computers

Handbook Of Digital Image Synthesis

Author : Vincent Pegoraro
ISBN : 9781315395210
Genre : Computers
File Size : 53.68 MB
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The Handbook of Digital Image Synthesis constitutes a comprehensive reference guide in the rapidly-developing field of computer graphics, whose applications span not only the movie and gaming industries, but also digital marketing, industrial and architectural design, virtual-environment simulators, and medical imaging. This resource provides an extensive, yet concise, treatment of the elementary principles and advanced concepts underpinning digital image synthesis, while covering a broad range of scientific topics such as pure and applied mathematics, geometric surfaces and data structures, the physics of light interaction and propagation, analytical and numerical simulation schemes, and optical perception and imaging. With its foundations laid from the ground up, the content includes a compilation of the theoretical formulas relevant for practical implementation in an actual rendering system, along with their step-by-step derivation, which provides field practitioners with a thorough understanding of their underlying assumptions and limitations, as well as with the methodologies necessary to adapt the results to new problems. Throughout, the presentation of the material is substantiated by numerous figures and computer-generated images illustrating the core ideas, several tables synthesizing results and industry standards, and platform-independent pseudo-code highlighting the core algorithms, in addition to a large collection of bibliographic references to the literature and an index of the standard scientific terms defined therein, thereby allowing the reader to rapidly harness fundamental notions and experimental trends.
Category: Computers

Rotation Transforms For Computer Graphics

Author : John Vince
ISBN : 0857291548
Genre : Computers
File Size : 63.14 MB
Format : PDF
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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.
Category: Computers

Mathematics For 3d Game Programming And Computer Graphics Third Edition

Author : Eric Lengyel
ISBN : 9781435458871
Genre : Computer games
File Size : 79.54 MB
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This updated third edition addresses the mathematical skills that a programmer needs to develop a 3D game engine and computer graphics for professional-level games. MATHEMATICS FOR 3D GAME PROGRAMMING & COMPUTER GRAPHICS, THIRD EDITION is suitable for adv
Category: Computer games

The Matrix Trilogy

Author : Stacy Gillis
ISBN : 1904764320
Genre : Performing Arts
File Size : 61.75 MB
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This is a collection of essays on the films as well as the websites, games and The Animatrix video and DVD. Among the topics discussed are the new cyberpunk, Baudrillarian simulacra and simulation, gender, race and costume, cyberculture and the body, virtual realities and special effects.
Category: Performing Arts

Understanding Motion Capture For Computer Animation And Video Games

Author : Alberto Menache
ISBN : 0124906303
Genre : Computers
File Size : 24.78 MB
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Motion capture is a technique for recording a performance and then translating it into mathematical terms. Animating motion is critical for the development of applications such as animation, virtual environments and video games. Character animation is the process by which natural movements are modelled and digitized so that digital character movements appear as natural as possible. There are three approaches to character animation: keyframe animation, motion capture, and simulation.
Category: Computers

Transactions On Edutainment Iii

Author : Maiga Chang
ISBN : 9783642112447
Genre : Computers
File Size : 52.86 MB
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This journal subline serves as a forum for stimulating and disseminating innovative research ideas, theories, emerging technologies, empirical investigations, state-of-the-art methods, and tools in all different genres of edutainment, such as game-based learning and serious games, interactive storytelling, virtual learning environments, VR-based education, and related fields. It covers aspects from educational and game theories, human-computer interaction, computer graphics, artificial intelligence, and systems design. The third volume in this series contains a selection of 12 outstanding contributions from Edutainment 2009, the 4th International Conference on E-Learning and Games, held in Canada in August 2009. The main focus of these papers is on the use of games to stimulate learners. In addition, 10 regular papers are included, presenting a wide range of edutainment tools and applications.
Category: Computers

3d Math Primer For Graphics And Game Development 2nd Edition

Author : Fletcher Dunn
ISBN : 9781568817231
Genre : Computers
File Size : 33.86 MB
Format : PDF, Kindle
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This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.
Category: Computers