geometric algebra an algebraic system for computer games and animation

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Geometric Algebra An Algebraic System For Computer Games And Animation

Author : John A. Vince
ISBN : 1848823797
Genre : Computers
File Size : 25. 44 MB
Format : PDF
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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.

Mathematics For Computer Graphics

Author : John Vince
ISBN : 9781447173366
Genre : Computers
File Size : 71. 88 MB
Format : PDF, Kindle
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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.

Evolve A Bridge Between Probability Set Oriented Numerics And Evolutionary Computation Iv

Author : Michael Emmerich
ISBN : 9783319011288
Genre : Computers
File Size : 78. 35 MB
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Numerical and computational methods are nowadays used in a wide range of contexts in complex systems research, biology, physics, and engineering. Over the last decades different methodological schools have emerged with emphasis on different aspects of computation, such as nature-inspired algorithms, set oriented numerics, probabilistic systems and Monte Carlo methods. Due to the use of different terminologies and emphasis on different aspects of algorithmic performance there is a strong need for a more integrated view and opportunities for cross-fertilization across particular disciplines. These proceedings feature 20 original publications from distinguished authors in the cross-section of computational sciences, such as machine learning algorithms and probabilistic models, complex networks and fitness landscape analysis, set oriented numerics and cell mapping, evolutionary multiobjective optimization, diversity-oriented search, and the foundations of genetic programming algorithms. By presenting cutting edge results with a strong focus on foundations and integration aspects this work presents a stepping stone towards efficient, reliable, and well-analyzed methods for complex systems management and analysis.

Rotation Transforms For Computer Graphics

Author : John Vince
ISBN : 0857291548
Genre : Computers
File Size : 82. 66 MB
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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.

Handbook Of Digital Image Synthesis

Author : Vincent Pegoraro
ISBN : 9781315395210
Genre : Computers
File Size : 62. 58 MB
Format : PDF, ePub, Mobi
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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.

The British National Bibliography

Author : Arthur James Wells
ISBN : STANFORD:36105211722686
Genre : English literature
File Size : 79. 5 MB
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Books In Print 2009 2010

Author :
ISBN : 0835250210
Genre : Publishers' catalogs
File Size : 40. 57 MB
Format : PDF
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Foundation Mathematics For Computer Science

Author : John Vince
ISBN : 9783319214375
Genre : Computers
File Size : 69. 1 MB
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John Vince describes a range of mathematical topics to provide a foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus. Readers will find that the author's visual approach will greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications. Each chapter includes full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will consolidate comprehension of abstract mathematical concepts. Foundation Mathematics for Computer Science covers number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus, and reveals the names of the mathematicians behind such inventions. During this journey, John Vince touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barycentric coordinates, transfinite sets and prime numbers. Whether you intend to pursue a career in programming, scientific visualisation, systems design, or real-time computing, you should find the author’s literary style refreshingly lucid and engaging, and prepare you for more advanced texts.

The Software Encyclopedia

Author :
ISBN : STANFORD:36105026453774
Genre : Computer industry
File Size : 57. 99 MB
Format : PDF, Docs
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Mathematik Und Technologie

Author : Christiane Rousseau
ISBN : 9783642300929
Genre : Mathematics
File Size : 51. 55 MB
Format : PDF, Mobi
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Zusammen mit der Abstraktion ist die Mathematik das entscheidende Werkzeug für technologische Innovationen. Das Buch bietet eine Einführung in zahlreiche Anwendungen der Mathematik auf dem Gebiet der Technologie. Meist werden moderne Anwendungen dargestellt, die heute zum Alltag gehören. Die mathematischen Grundlagen für technologische Anwendungen sind dabei relativ elementar, was die Leistungsstärke der mathematischen Modellbildung und der mathematischen Hilfsmittel beweist. Mit zahlreichen originellen Übungen am Ende eines jeden Kapitels.

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