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Tricks of the 3D
Game Programming
Gurus
Advanced 3D Graphics and Rasterization
André LaMothe
201 West 103rd Street, Indianapolis, Indiana 46290
00 0672318350 fm 05•02•2003 2:31 PM Page ii
Tricks of the 3D Game Programming Gurus: Associate Publisher
Advanced 3D Graphics and Rasterization Michael Stephens
Copyright © 2003 by Sams Publishing Acquisitions Editor
All rights reserved. No part of this book shall be reproduced, stored in Kim Spilker
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Contents at a Glance
Foreword.....................................................................................xix
Introduction...................................................................................1
Part I Introduction to 3D Game Programming
1 Getting Started with 3D Game Programming........................................9
2 A Crash Course in Windows and DirectX...........................................69
3 3D Game Programming with a Virtual Computer..............................115
Part II 3D Math and Transformation
4 It’s a Math, Math, Math World—Trigonometry, Vectors, Matrices, and
Quaternions................................................................................241
5 Building a Math Engine.................................................................363
6 Introduction to 3D Graphics..........................................................493
7 Rendering Wireframe Worlds in 3D.................................................621
Part III Basic 3D Rendering
8 Basic Lighting and Solid Modeling..................................................743
9 Interpolative Shading Techniques and Affine Texture Mapping............869
10 Clipping in 3D++........................................................................1005
11 Depth Buffering and Visibility ......................................................1087
Part IV Advanced 3D Rendering
12 Advanced Texturing Techniques....................................................1147
13 Spatial Partitioning and Visible Algorithms.....................................1307
14 Lighting, Shadows, and Secrets of the id.........................................1439
Part V Advanced Animation and Physics Modeling and Optimization
15 Character Animation, Motion, and Collision Detection.....................1493
16 Optimization Technologies...........................................................1549
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Part VI CD-ROM Appendixes
A About The CD-ROM
B Installing DirectX and Using Visual C/C++
C Trigonometry and Vector Reference
D C++ Primer
E Game Programming Resources
F ASCII Tables
Index.........................................................................................000
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Table of Contents
Introduction 1
Part I Introduction to 3D Game Programming
1 Getting Started with 3D Game Programming 9
A Brief Introduction.........................................................................9
The Elements of a 2D/3D Game........................................................11
Section 1: Initialization...........................................................12
Section 2: Enter Game Loop.....................................................12
Section 3: Retrieve Player Input................................................12
Section 4: Perform AI and Game Logic.......................................12
Section 5: Render Next Frame...................................................13
Section 6: Synchronize Display.................................................13
Section 7: Loop......................................................................13
Section 8: Shutdown...............................................................13
General Game Programming Guidelines............................................17
Using Tools...................................................................................22
3D Level Editors.....................................................................26
Setting Up to Get Down—Using The Compiler............................28
A Sample 3D Game: Raiders 3D.......................................................32
The Event Loop......................................................................61
The Core 3D Game Logic.........................................................61
3D Projections.......................................................................63
The Star Field........................................................................66
The Laser Cannons and Collision Detection................................66
The Explosions......................................................................67
Playing Raiders3D..................................................................67
Summary......................................................................................67
2 A Crash Course in Windows and DirectX 69
The Win32 Programming Model.......................................................69
The Bare Minimum for a Windows Program.......................................71
It All Begins with WinMain().....................................................71
A Basic Windows Application...........................................................77
The Windows Class................................................................78
Registering the Windows Class.................................................84
Creating the Window..............................................................85
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vi Tricks of the 3D Game Programming Gurus: Advanced 3D Graphics and Rasterization
The Event Handler.................................................................87
The Main Event Loop..............................................................94
Making a Real-Time Event Loop................................................99
DirectX and COM Crash Course.....................................................101
The HEL and HAL.................................................................103
The DirectX Foundation Classes in Depth.................................104
Flash Introduction to COM............................................................106
What Exactly Is a COM Object?..............................................107
Creating and Using DirectX COM Interfaces.............................110
Querying for Interfaces..........................................................111
Summary....................................................................................114
3 3D Game Programming with a Virtual Computer 115
Introduction to the Virtual Computer Interface.................................115
Building the Virtual Computer Interface...........................................118
The Frame Buffer and Video System.........................................118
Working with Color..............................................................123
Animating the Display...........................................................125
The Complete Virtual Graphics System.....................................128
I/O, Sound, and Music...........................................................129
The T3DLIBGame Console.............................................................130
T3DLIBSystem Overview........................................................131
The Basic Game Console........................................................131
The T3DLIB1Library......................................................................139
The DirectX Graphics Engine Architecture................................139
Basic Definitions ..................................................................140
Working Macros...................................................................142
Data Types and Structures......................................................143
Function Prototypes..............................................................147
Global Domination...............................................................153
The DirectDraw Interface.......................................................155
2D Polygon Functions...........................................................160
Math and Error Functions......................................................169
Bitmap Functions.................................................................171
8-Bit Palette Functions...........................................................177
Utility Functions..................................................................181
The BOB (Blitter Object) Engine..............................................183
The T3DLIB2DirectX Input System..................................................193
The T3DLIB3Sound and Music Library.............................................201
The Header..........................................................................201
The Types............................................................................202
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Contents vii
Global Domination...............................................................203
The DirectSound API Wrapper................................................204
The DirectMusic API Rapper...........................................................210
Building the Final T3D Game Console.............................................214
Mapping the Real Graphics to the Unreal Graphics of the
Virtual Interface.................................................................214
The Final T3DLIBGame Console..............................................218
Sample T3LIBApplications.............................................................231
Windowed Applications.........................................................231
Full-Screen Applications.........................................................232
Sound and Music..................................................................233
Working with Input..............................................................234
Summary....................................................................................238
Part II 3D Math and Transformation
4 It’s a Math, Math, Math World—Trigonometry, Vectors, Matrices, and
Quaternions 241
Mathematical Notation.................................................................242
2D Coordinate Systems.................................................................243
2D Cartesian Coordinates......................................................243
2D Polar Coordinates............................................................246
3D Coordinate Systems.................................................................249
3D Cartesian Coordinates......................................................249
3D Cylindrical Coordinates............................................................252
Converting Between 3D Cartesian and Polar Coordinates............253
3D Spherical Coordinates...............................................................253
Trigonometry...............................................................................256
The Right Triangle................................................................256
Inverse Trigonometric Functions.............................................259
Trigonometric Identities.........................................................259
Vectors.......................................................................................261
Vector Length......................................................................262
Normalization......................................................................263
Scalar Multiplication.............................................................263
Vector Addition....................................................................265
Vector Subtraction................................................................265
The Inner Product, or the “Dot” Product..................................266
The Cross Product.................................................................270
The Zero Vector....................................................................272
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viii Tricks of the 3D Game Programming Gurus: Advanced 3D Graphics and Rasterization
Position and Displacement Vectors..........................................272
Vectors as Linear Combinations..............................................273
Matrices and Linear Algebra...........................................................273
The Identity Matrix...............................................................275
Matrix Addition...................................................................276
Transpose of a Matrix............................................................276
Matrix Multiplication............................................................277
Laws for Matrix Operations....................................................279
Computing the Inverse and Solving Systems.....................................279
Cramer’s Rule.......................................................................282
Transformations Using Matrices..............................................285
Homogeneous Coordinates ....................................................286
Applied Matrix Transformations..............................................287
Basic Geometric Entities................................................................296
Points.................................................................................297
Lines..................................................................................297
Lines in 3D Space.........................................................................300
Planes.................................................................................302
Using Parametric Equations............................................................307
2D and 3D Parametric Lines...................................................307
Parametric Line Segments with Standard Direction Vector v.........308
Parametric Line Segments with Unit Direction Vector |v| = 1........309
Parametric Lines in 3D..........................................................311
Introduction to Quaternions..........................................................317
Complex Number Theory......................................................318
Hyper-Complex Numbers.......................................................325
Applications of Quaternions...................................................333
Basic Calculus..............................................................................337
The Concept of Infinity.........................................................337
Limits.................................................................................340
Summation and Finite Series..................................................341
Infinite Series.......................................................................344
Derivatives..........................................................................345
Integrals..............................................................................355
Summary....................................................................................361
5 Building a Math Engine 363
Brief Overview of the Math Engine..................................................364
File Structure of the Math Engine............................................364
Naming Conventions............................................................365
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Contents ix
Error Handling.....................................................................366
My Final Word on C++..........................................................366
Data Structures and Types..............................................................367
Vectors and Points................................................................367
Parametric Lines...................................................................369
3D Planes............................................................................371
Matrices..............................................................................372
Quaternions.........................................................................376
Angular Coordinate System Support........................................377
Polar 2D..............................................................................378
Cylindrical 3D .....................................................................379
Spherical 3D........................................................................380
Fixed-Point Numbers.............................................................381
Math Constants...........................................................................382
Macros and Inline Functions..........................................................384
General Utility and Conversion...............................................390
Points and Vectors................................................................390
Matrices..............................................................................392
Quaternions.........................................................................394
Fixed-Point Math..................................................................395
Prototypes...................................................................................395
Globals.......................................................................................400
Math Engine API Listing................................................................401
Trigonometric Functions........................................................401
Coordinate System Support Functions......................................403
Vector Support Functions.......................................................407
Matrix Support Functions......................................................418
2D and 3D Parametric Line Support Functions..........................434
3D Plane Support Functions...................................................440
Quaternion Support Functions................................................446
Fixed-Point Math Support Functions........................................458
Equation Solving Support.......................................................464
Floating-Point Unit Math Primer.....................................................468
The FPU Architecture............................................................469
The FPU Stack......................................................................470
The FPU Instruction Set.........................................................472
Classical Instruction Format...................................................475
Memory Instruction Format...................................................475
Register Instruction Format....................................................476
Register Pop Instruction Format..............................................477
FPU Examples......................................................................477
