Mathematics for 3D Game Programming and Computer Graphics

EBook Description: This updated third edition illustrates the mathematical concepts that a game developer needs to develop 3D computer graphics and game engines at the professional level. It starts at a fairly basic level in areas such as vector geometry and linear algebra, and then progresses to more advanced topics in 3D programming such as illumination and visibility determination... .. Particular attention is given to derivations of key results, ensuring that the reader is not forced to endure gaps in the theory. The book assumes a working knowledge of trigonometry and calculus, but also includes sections that review the important tools used from these disciplines, such as trigonometric identities, differential equations, and Taylor series. The third edition expands upon topics that include projections, shadows, physics, cloth simulation, and numerical methods. All of the illustrations have been updated, and the shader code has been updated to the latest high-level shading language specifications

This updated third edition illustrates the mathematical concepts that a game developer needs to develop 3D computer graphics and game engines at the professional level. It starts at a fairly basic level in areas such as vector geometry and linear algebra, and then progresses to more advanced topics in 3D programming such as illumination and visibility determination. Particular attention is given to derivations of key results, ensuring that the reader is not forced to endure gaps in the theory. The book assumes a working knowledge of trigonometry and calculus, but also includes sections that review the important tools used from these disciplines, such as trigonometric identities, differential equations, and Taylor series.

Quaternions for Computer Graphics

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.

Computer Graphics World

Computer Graphics World

Computer Graphics World

Computer Graphics World (CGW) explores how leading-edge graphics techniques, including the 3D modeling, animation and visualization are used in such applications as CAD/CAM/CAE, architecture, scientific visualization, special effects, digital video, film and interactive entertainment.

Computer Graphics World 2008-2011

Computer Graphics World (CGW) explores how leading-edge graphics techniques, including the 3D modeling, animation and visualization are used in such applications as CAD/CAM/CAE, architecture, scientific visualization, special effects, digital video, film and interactive entertainment.

Computer Graphics World (January/February 2011)

CGW explores how leading-edge graphics techniques, including the 3D modeling, animation and visualization are used in such applications as CAD/CAM/CAE, architecture, scientific visualization, special effects, digital video, film, and interactive entertainment. Subscribe Today!

Computer Graphics World Magazine March 2011

CGW explores how leading-edge graphics techniques, including the 3D modeling, animation and visualization are used in such applications as CAD/CAM/CAE, architecture, scientific visualization, special effects, digital video, film, and interactive entertainment. Subscribe Today!

"Computer Graphics and Geometric Modelling: Implementation & Algorithms"

Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion. Computer Graphics and Geometric Modelling: Implementation and Algorithms, covers the computer graphics part of the field of geometric modelling and includes all the standard computer graphics topics. The first part deals with basic concepts and algorithms and the main steps involved in displaying photorealistic images on a computer. The second part covers curves and surfaces and a number of more advanced geometric modelling topics including intersection algorithms, distance algorithms, polygonizing curves and surfaces, trimmed surfaces, implicit curves and surfaces, offset curves and surfaces, curvature, geodesics, blending etc. The third part touches on some aspects of computational geometry and a few special topics such as interval analysis and finite element methods. The volume includes two companion programs.

"Fluid Simulation for Computer Graphics"

Animating fluids like water, smoke, and fire using physics-based simulation is increasingly important in visual effects, in particular in movies, like The Day After Tomorrow, and in computer games. This book provides a practical introduction to fluid simulation for graphics. The focus is on animating fully three-dimensional incompressible flow, from understanding the math and the algorithms to the actual implementation.

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