## Essential Mathematics for Games and Interactive Applications: A Programmer's Guide, Second EditionEssential Mathematics for Games and Interactive Applications, 2nd edition presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix multiplication and expands on this foundation to cover such topics as color and lighting, interpolation, animation and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout. The new edition Windows code will now use Visual Studio.NET. There will also be DirectX support provided, along with OpenGL - due to its cross-platform nature. Programmers will find more concrete examples included in this edition, as well as additional information on tuning, optimization and robustness. The book has a companion CD-ROM with exercises and a test bank for the academic secondary market, and for main market: code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction. |

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affine combination affine transformation algorithm angle APIs apply approximation axis basic basis vectors Bézier curves bits chapter clipping collision color column common compute concatenating create cross product curve define depth buffer Direct3D direction discussed distance dot product equation Euler example exponent Figure float format fragment shader frame framebuffer frustum function geometry GLSL Gouraud shading graphics hardware implement integer interpolation intersection inverse IvVector3 known length light source line segment linear transformation mantissa mapping matrix method mipmap mipmap level multiplication normal object OpenGL operations orientation per-vertex perform pipeline pixel plane position projection quaternion random number rasterization rendering represent representation result rotation sample scalar scale screen simulation Source Code Demo specular sphere standard surface tangent texel texture coordinates texture image triangle values vec4 vector space velocity vertex shader vertices view frustum view window we’ll z-axis zero