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

Drawing in the Digital Age

An Observational Method for Artists and Animators