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Technical Essential Mathematics for Games and Interactive Applications: A Programmer's Guide
Posted on 2010-03-15
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Essential Mathematics for Games and Interactive Applications: A Programmer's Guide (The Morgan Kaufmann Series in Interactive 3d Technology) (The Morgan Kaufmann Series in Interactive 3d Technology) By James M. Van Verth, Lars M. Bishop, Publisher: Morgan Kaufmann
Number Of Pages: 676 Publication Date: 2004-03-25 Sales Rank: 36602 ISBN / ASIN: 155860863X EAN: 9781558608634 Binding: Hardcover Manufacturer: Morgan Kaufmann Studio: Morgan Kaufmann Average Rating: 4.5 "Even though I've worked with these systems for years, I found new ways of looking at several topics that make them easier to remember and use. For someone new to 3D programming, it is extremely usefulit gives them a solid background in pretty much every area they need to understand." Peter Lipson, Toys for Bob, Inc. Based on the authors popular tutorials at the Game Developers Conference, Essential Mathematics for Games and Interactive Applications presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix read.freeduan.com manipulation and expands on this foundation to cover such topics as texture filtering, interpolation, animation, and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout. *Covers concepts in sufficient detail for a programmer to understand the foundations of 3D without feeling overwhelmed by proofs and theory *Companion CD-ROM with 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 *Provides guidance for students trying to understand how games are actually developed, including optimization techniques Contents: Preface The Adventure Begins Those Who Helped Us Along The Road Introduction The (continued) Rise Of 3d Games How To Read This Book Part I, Core Mathematics Part II, Rendering Part III, Animation Part IV, Simulation Appendices Interactive Demo Applications Support Libraries Math Libraries Engine And Rendering Libraries References And Further Reading Part I - Core Mathematics Vectors And Points Introduction Vectors Vectors As Geometry Real Vector Spaces Linear Combinations And Basis Vectors Basic Vector Class Implementation Vector Length Dot Product Gram-schmidt Orthogonalization Cross Product Triple Products Points Points As Geometry Affine Spaces Affine Combinations Point Implementation Polar And Spherical Coordinates Lines Definition Parameterized Lines Generalized Line Equation Collinear Points Planes Parameterized Planes Generalized Plane Equation Coplanar Points Polygons And Triangles Chapter Summary Linear Transformations And Matrices Introduction Linear Transformations Definitions Null Space And Range Linear Transformations And Basis Vectors Matrices Introduction To Matrices Simple Operations Vector Representation Block Matrices Matrix Product Transforming Vectors Combining Linear Transformations Identity Matrix Performing Vector Operations With Matrices Implementation Systems Of Linear Equations Definition Solving Linear Systems Gaussian Elimination Matrix Inverse Definition Simple Inverses The Determinant Definition Computing The Determinant Determinants And Elementary Row Operations Adjoint Matrix And Inverse Chapter Summary Affine Transformations Introduction Affine Transformations Definition Representation Standard Affine Transformations Translation Rotation Scaling Reflection Shear Applying An Affine Transformation Around An Arbitrary Point Transforming Plane Normals Using Affine Transformations Manipulation Of Game Objects Matrix Decomposition Avoiding Matrix Decomposition Object Hierarchies And Scene Graphs Object Hierarchies Scene Graphs Chapter Summary Real-world Computer Number Representation Introduction Representing Integral Types On A Computer Finiteness Of Representation Range Representing Real Numbers Approximations Precision And Error Fixed Point Introduction Basic Representation Range And Precision Addition And Subtraction Multiplication Division Real-world Fixed Point Intermediate Value Overflow And Underflow Limits Of Fixed Point Fixed Point Summary Floating-point Numbers Review: Scientific Notation A Restricted Scientific Notation Binary scientific Notation& 382; Ieee 754 Floating-point Standard Basic Representation Range And Precision Arithmetic Operations Special Values Very Small Values Catastrophic Cancelation Double Precision Real-world Floating Point Internal Fpu Precision Performance Ieee Specification Compliance Code Chapter Summary Part II - Rendering Viewing And Projection Introduction The View Frame And View Transformation Defining A Virtual Camera Controlling The Camera Constructing The View Transformation Projective Transformation Definition The View Frustum Normalized Device Coordinates Homogeneous Coordinates Perspective Projection Oblique Perspective Orthographic Parallel Projection Oblique Parallel Projection Culling And Clipping Why Cull Or Clip? Culling General Plane Clipping Homogeneous Clipping Screen Transformation Picking Management Of Viewing Transformations Chapter Summary Geometry, Shading, And Texturing Introduction Color Representation The Rgb Color Model Colors As
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