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To my nieces and nephews, Marrick, Hans, Max, Anna, Augustus, Presley, and Elyse CONTENTS Dedication v Acknowledgments xxii Introduction xxv Intended Audience xxvi Prerequisites xxvi Required Development Tools and Hardware xxvii Using the DirectX SDK Documentation and SDK Samples xxvii Clarity xxix Sample Programs and Online Supplements xxix Demo Project Setup in Visual Studio 2010 xxix Download the Book’s Source Code xxx Create a Win32 Project xxx Linking the DirectX Libraries xxxi Adding the Source Code and Building the Project xxxii PART I MATHEMATICAL PREREQUISITES Chapter 1 Vector Algebra 3 1.1 Vectors 4 1.1.1 Vectors and Coordinate Systems 5 1.1.2 Left-Handed Versus Right-Handed Coordinate Systems 6 1.1.3 Basic Vector Operations 7 1.2 Length and Unit Vectors 9 1.3 The Dot Product 10 1.3.1 Orthogonalization 13 1.4 The Cross Product 14 1.4.1 Pseudo 2D Cross Product 16 1.4.2 Orthogonalization with the Cross Product 16 viii INTRODUCTION TO 3D GAME PROGRAMMING WITH DIRECTX® 12 1.5 Points 17 1.6 DirectX Math Vectors 18 1.6.1 Vector Types 19 1.6.2 Loading and Storage Methods 21 1.6.3 Parameter Passing 21 1.6.4 Constant Vectors 23 1.6.5 Overloaded Operators 24 1.6.6 Miscellaneous 24 1.6.7 Setter Functions 25 1.6.8 Vector Functions 26 1.6.9 Floating-Point Error 30 1.7 Summary 31 1.8 Exercises 33 Chapter 2 Matrix Algebra 37 2.1 Defi nition 38 2.2 Matrix Multiplication 40 2.2.1 Defi nition 40 2.2.2 Vector-Matrix Multiplication 41 2.2.3 Associativity 42 2.3 The Transpose of a Matrix 42 2.4 The Identity Matrix 43 2.5 The Determinant of a Matrix 44 2.5.1 Matrix Minors 45 2.5.2 Defi nition 45 2.6 The Adjoint of a Matrix 47 2.7 The Inverse of a Matrix 47 2.8 DirectX Math Matrices 49 2.8.1 Matrix Types 50 2.8.2 Matrix Functions 52 2.8.3 DirectX Math Matrix Sample Program 53 2.9 Summary 54 2.10 Exercises 55 Chapter 3 Transformations 59 3.1 Linear Transformations 60 3.1.1 Defi nition 60 3.1.2 Matrix Representation 60 3.1.3 Scaling 61 3.1.4 Rotation 63 CONTENTS ix 3.2 Affi ne Transformations 66 3.2.1 Homogeneous Coordinates 66 3.2.2 Defi nition and Matrix Representation 67 3.2.3 Translation 67 3.2.4 Affi ne Matrices for Scaling and Rotation 70 3.2.5 Geometric Interpretation of an Affi ne Transformation Matrix 70 3.3 Composition of Transformations 72 3.4 Change of Coordinate Transformations 73 3.4.1 Vectors 74 3.4.2 Points 74 3.4.3 Matrix Representation 75 3.4.4 Associativity and Change of Coordinate Matrices 76 3.4.5 Inverses and Change of Coordinate Matrices 77 3.5 Transformation Matrix versus Change of Coordinate Matrix 78 3.6 DirectX Math Transformation Functions 79 3.7 Summary 80 3.8 Exercises 82 PART II DIRECT 3D FOUNDATIONS Chapter 4 Direct3D Initialization 89 4.1 Preliminaries 90 4.1.1 Direct3D 12 Overview 90 4.1.2 COM 90 4.1.3 Textures Formats 91 4.1.4 The Swap Chain and Page Flipping 93 4.1.5 Depth Buffering 93 4.1.6 Resources and Descriptors 96 4.1.7 Multisampling Theory 98 4.1.8 Multisampling in Direct3D 99 4.1.9 Feature Levels 101 4.1.10 DirectX Graphics Infrastructure 101 4.1.11 Checking Feature Support 105 4.1.12 Residency 107 4.2 CPU/GPU Interaction 107 4.2.1 The Command Queue and Command Lists 108 4.2.2 CPU/GPU Synchronization 112 x INTRODUCTION TO 3D GAME PROGRAMMING WITH DIRECTX® 12 4.2.3 Resource Transitions 114 4.2.4 Multithreading with Commands 116 4.3 Initializing Direct3D 116 4.3.1 Create the Device 117 4.3.2 Create the Fence and Descriptor Sizes 118 4.3.3 Check 4X MSAA Quality Support 119 4.3.4 Create Command Queue and Command List 119 4.3.5 Describe and Create the Swap Chain 120 4.3.6 Create the Descriptor Heaps 122 4.3.7 Create the Render Target View 123 4.3.8 Create the Depth/Stencil Buffer and View 125 4.3.9 Set the Viewport 129 4.3.10 Set the Scissor Rectangles 131 4.4 Timing and Animation 131 4.4.1 The Performance Timer 132 4.4.2 Game Timer Class 133 4.4.3 Time Elapsed Between Frames 134 4.4.4 Total Time 136 4.5 The Demo Application Framework 139 4.5.1 D3DApp 139 4.5.2 Non-Framework Methods 142 4.5.3 Framework Methods 143 4.5.4 Frame Statistics 145 4.5.5 The Message Handler 146 4.5.6 The “Init Direct3D” Demo 149 4.6 Debugging Direct3D Applications 153 4.7 Summary 155 Chapter 5 The Rendering Pipeline 159 5.1 The 3D Illusion 160 5.2 Model Representation 162 5.3 Basic Computer Color 163 5.3.1 Color Operations 164 5.3.2 128-Bit Color 165 5.3.3 32-Bit Color 165 5.4 Overview of the Rendering Pipeline 167 5.5 The Input Assembler Stage 168 5.5.1 Vertices 168 5.5.2 Primitive Topology 169 5.5.2.1 Point List 170 CONTENTS xi 5.5.2.2 Line Strip 170 5.5.2.3 Line List 170 5.5.2.4 Triangle Strip 170 5.5.2.5 Triangle List 171 5.5.2.6 Primitives with Adjacency 171 5.5.2.7 Control Point Patch List 172 5.5.3 Indices 172 5.6 The Vertex Shader Stage 175 5.6.1 Local Space and World Space 175 5.6.2 View Space 179 5.6.3 Projection and Homogeneous Clip Space 182 5.6.3.1 Defi ning a Frustum 183 5.6.3.2 Projecting Vertices 184 5.6.3.3 Normalized Device Coordinates (NDC) 185 5.6.3.4 Writing the Projection Equations with a Matrix 186 5.6.3.5 Normalized Depth Value 187 5.6.3.6 XMMatrixPerspectiveFovLH