Geometric Algebra: An Algebraic System for Computer Games and Animation

Geometric Algebra: An Algebraic System for Computer Games and Animation

Author: John A. Vince

Publisher: Springer

ISBN: 1848823789

Category: Computers

Page: 195

View: 702

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.

Geometric Algebra: An Algebraic System for Computer Games and Animation

Geometric Algebra: An Algebraic System for Computer Games and Animation

Author: John A. Vince

Publisher: Springer Science & Business Media

ISBN: 9781848823792

Category: Computers

Page: 195

View: 357

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

Mathematics for Computer Graphics

Author: John A. Vince

Publisher: Springer Science & Business Media

ISBN: 9781849960236

Category: Computers

Page: 293

View: 197

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.

Mathematics for Computer Graphics

Mathematics for Computer Graphics

Author: John Vince

Publisher: Springer

ISBN: 1447175190

Category: Computers

Page: 564

View: 501

John Vince explains a comprehensive range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, special effects, virtual reality, CAD and other areas of computer graphics in this completely revised and expanded sixth edition. The first five chapters cover a general introduction, number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on determinants, vectors, matrix algebra, complex numbers, geometric transforms, quaternion algebra, quaternions in space, interpolation, curves and patches, analytical geometry and barycentric coordinates. Following this, the reader is introduced to the relatively new subject 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 • Complex numbers • Coordinate systems • Determinants • Vectors • Quaternions • Matrix algebra • Geometric transforms • Interpolation • Curves and surfaces • Analytic geometry • Barycentric coordinates • Geometric algebra • Differential calculus • Integral calculus This sixth edition contains approximately 150 worked examples and over 330 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 software and setting the scene for further reading of more advanced books and technical research papers

Quaternions for Computer Graphics

Quaternions for Computer Graphics

Author: John Vince

Publisher: Springer

ISBN: 1447175085

Category: Computers

Page: 181

View: 802

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

Mathematics for Computer Graphics

Author: John Vince

Publisher: Springer Science & Business Media

ISBN: 9781447162902

Category: Computers

Page: 391

View: 185

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.

EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV

EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV

Author: Michael Emmerich

Publisher: Springer Science & Business Media

ISBN: 9783319011288

Category: Technology & Engineering

Page: 323

View: 556

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.

Advanced Applications of Computational Mathematics

Advanced Applications of Computational Mathematics

Author: Akshay Kumar

Publisher: CRC Press

ISBN: 9781000793208

Category: Mathematics

Page: 272

View: 997

This book “Advanced Applications of Computational Mathematics” covers multidisciplinary studies containing advanced research in the field of computational and applied mathematics. The book includes research methodology, techniques, applications, and algorithms. The book will be very useful to advanced students, researchers and practitioners who are involved in the areas of computational and applied mathematics and engineering.

Rotation Transforms for Computer Graphics

Rotation Transforms for Computer Graphics

Author: John Vince

Publisher: Springer Science & Business Media

ISBN: 9780857291547

Category: Computers

Page: 232

View: 268

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.

Exterior Calculus: Theory and Cases

Exterior Calculus: Theory and Cases

Author: Carlos Polanco

Publisher: Bentham Science Publishers

ISBN: 9789814998796

Category: Mathematics

Page: 141

View: 919

Exterior calculus is a branch of mathematics which involves differential geometry. In Exterior calculus the concept of differentiations is generalized to antisymmetric exterior derivatives and the notions of ordinary integration to differentiable manifolds of arbitrary dimensions. It therefore generalizes the fundamental theorem of calculus to Stokes' theorem. This textbook covers the fundamental requirements of exterior calculus in curricula for college students in mathematics and engineering programs. Chapters start from Heaviside-Gibbs algebra, and progress to different concepts in Grassman algebra. The final section of the book covers applications of exterior calculus with solutions. Readers will find a concise and clear study of vector calculus and differential geometry, along with several examples and exercises. The solutions to the exercises are also included at the end of the book. This is an ideal book for students with a basic background in mathematics who wish to learn about exterior calculus as part of their college curriculum and equip themselves with the knowledge to apply relevant theoretical concepts in practical situations.

Vector Analysis for Computer Graphics

Vector Analysis for Computer Graphics

Author: John Vince

Publisher: Springer

ISBN: 1447175042

Category: Computers

Page: 246

View: 943

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.

Handbook of Digital Image Synthesis

Handbook of Digital Image Synthesis

Author: Vincent Pegoraro

Publisher: CRC Press

ISBN: 9781315395210

Category: Computers

Page: 838

View: 890

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.