Essential Mathematics for Games and Interactive Applications: A Programmer's Guide

Description

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 Notationž
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 ¡°vectors¡±
Operations On Colors
Color Range Limitation
Alpha Values
Color Storage Formats
Colors In Opengl
Points And Vertices
Per-vertex Attributes
Surface Representation
Vertices And Surface Ambiguity
Triangles
Triangle Attributes
Vertex Indices
Opengl Vertex Indices
Coloring A Surface
Using Constant Colors
Per-object Colors
Per-triangle Colors
Per-vertex Colors
Limitations Of Basic Shading Methods
Texture Mapping
Introduction
Shading Via Image Lookup
Texture Images
Texture Coordinates
Mapping Texture Coordinates
Generating Texture Coordinates
Texture Coordinate Discontinuities
Mapping Outside The Unit Square
Reviewing The Steps Of Texturing
Limitations Of Texturing
Procedural Colors And Shaders
Chapter Summary
Lighting
Introduction
Basics Of Light Approximation
Measuring Light
Light As A Ray
Lighting Approximation (opengl)
Types Of Light Sources
Directional Lights
Point Lights
Spotlights
Other Types Of Light Sources
Surface Materials And Light Interaction
Opengl Materials
Categories Of Light
Emission
Ambient
Diffuse
Specular
Combined Lighting Equation
Lighting And Shading
Flat-shaded Lighting
Per-vertex Lighting
Per-pixel Lighting (phong Shading)
Merging Textures And Lighting
Specular Lighting And Textures
Lighting And Programmable Shaders
Chapter Summary
Rasterization
Introduction
Displays And Framebuffers
Framebuffer Memory Organization
Interlacing
Multiple Buffers
Conceptual Rasterization Pipeline
Determining The Pixels Contained By A Triangle
Determining Which Pixels Are Visible
Depth Sorting
Depth Buffering
Depth-buffering In Opengl
Computing Source Pixel Colors
Flat Colors
Gouraud Colors
Rasterizing Textures
Texture Coordinate Review
Interpolating Texture Coordinates
Mapping A Coordinate To A Texel
Mipmapping
Blending
Blending And Z-buffering
Alternative Blending Modes
Blending And Opengl
Antialiasing
Antialiasing In Practice
Antialiasing In Opengl
Chapter Summary
Part III - Animation
Curves
Introduction
General Definitions
Linear Interpolation
Definition
Piecewise Linear Interpolation
Lagrange Polynomials
Hermite Curves
Definition
Automatic Generation Of Hermite Curves
Natural, Cyclic, And Acyclic End Conditions
Catmull-rom Splines
B¨¦zier Curves
Definition
Piecewise B¨¦zier Curves
B-splines
Rational Curves
Rendering Curves
Forward Differencing
Midpoint Subdivision
Using Opengl
Controlling Speed Along A Curve
Moving At Constant Speed
Computing Arc Length
Ease-in And Ease-out
Camera Control
Chapter Summary
Orientation Representation
Introduction
Rotation Matrices
Fixed And Euler Angles
Definition
Format Conversion
Concatenation
Vector Rotation
Other Issues
Axis-angle Representation
Definition
Format Conversion
Concatenation
Vector Rotation
Section Summary
Quaternions
Definition
Rotation Quaternions
Format Conversion
Addition And Scalar Multiplication
Negation
Magnitude And Normalization
Dot Product
Concatenation
Identity And Inverse
Vector Rotation
Quaternions And Transformations
Interpolation
Linear Interpolation
Spherical Linear Interpolation
Performance Improvements
Chapter Summary
Part IV - Simulation
Intersection Testing
Introduction
Closest Point And Distance Tests
Closest Point On Line To Point
Line-point Distance
Closest Point On Line Segment To Point
Line Segment-point Distance
Closest Points Between Two Lines
Line-line Distance
Closest Points Between Two Line Segments
Line Segment¨Cline Segment Distance
General Linear Components
Object Intersection
Spheres
Axis-aligned Bounding Boxes
Swept Spheres
Object-oriented Boxes
Triangles
A Simple Collision System
Choosing A Base Primitive
Bounding Hierarchies
Dynamic Objects
Performance Improvements
Related Systems
Section Summary
Chapter Summary
Rigid Body Dynamics
Introduction
Linear Dynamics
Moving With Constant Acceleration
Forces
Linear Momentum
Moving With Variable Acceleration
Initial Value Problems
Definition
Euler¡¯s Method
Midpoint Method
Higher-order Methods
Verlet Integration
Implicit Methods
Rotational Dynamics
Definitions
Orientation And Angular Velocity
Torque
Angular Momentum And Inertial Tensor
Integrating Rotational Quantities
Collision Response
Locating The Point Of Collision
Linear Collision Response
Rotational Collision Response
Other Response Techniques
Efficiency
Chapter Summary
Appendix A - Trigonometry Review
Basic Definitions
Ratios On The Right Triangle
Extending To General Angles
Properties Of Triangles
Trigonometric Identities
Pythagorean Identities
Complementary Angle
Even-odd
Compound Angle
Double Angle
Half Angle
Inverses
Appendix B - Calculus Review
Limits And Continuity
Limits
Continuity
Derivatives
Definition
Basic Derivatives
Derivatives Of Transcendental Functions
Taylor¡¯s Series
Integrals
Definition
Evaluating Integrals
Trapezoidal Rule
Gaussian Quadrature
Space Curves
Index
Trademarks
About The Cd-rom
Contents Of The Cd-rom
Glossary Of Notation
Scalars
Vectors, Points, And Lines
Matrices And Transformations
Functions And Calculus
Orientation
Simulation

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