Introduction xiii Chapter 1 Understanding the Relationship between Math and Art 1 Understanding How Math and Art Differ 2 Understanding How Math and Art Are Similar 4 Using Math to Create Digital Art 13 Using Math in Traditional Drawing 15 Using Math to Help You Draw 18 Examining Existing Drawing Methods 22 Stop Separating Math from Art 28 Chapter 2 Extracting Graphical Structures -- A Scientific Point of View 31 Introducing CG Concepts and Principles 32 Unifying 2D and 3D Cases 40 Understanding the Properties of Basic Shapes 43 Understanding Graphical Structures 47 Extracting GSs with Triangulation 54 Chapter 3 Drawing with the ABC Method 57 Meeting the Criteria for a New Drawing Method 58 Introducing the ABC Method 61 Chapter 4 Drawing Simple Objects 79 Preparing to Draw 80 Extracting Basic Information 80 Demonstrations of 3D Objects 85 Demonstrations of 2D Images 92 Exercises 97 Chapter 5 Drawing Complicated Objects 99 Breaking Down Complexity 100 Demonstrations 108 Exercises 120 Chapter 6 Drawing Complicated Scenes 121 Introducing Techniques for Merging Objects 122 Demonstrations 129 Exercises 138 Chapter 7 Using Advanced Techniques 141 Working with Curved Triangles and Polygons 142 Drawing a Group of Ovals 146 Using Shadow Maps 149 Using Rhythms for Partitioning 151 Exploring Trade-Offs between Accuracy and Speed 152 Demonstrations 153 Summary 161 Exercises 161 Chapter 8 Using Special Techniques for Drawing Human Bodies 163 General Tips 164 Tips for Drawing Faces 169 Tips for Quick Life Sketches 174 Demonstrations 180 Summary 186 Exercises 187 Post-Test: Drawing Van Gogh 188 Index 189.