Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering

[Dissertation] [Abstract] [Overview] [Contents] [Images]

Table of contents

• Chapter 1: Introduction ..... 3
  • 1.1 Rendering ..... 3
  • 1.2 The Input ..... 4
  • 1.3 The Output ..... 6
  • 1.4 Physically-Based Rendering Algorithms ..... 6
    • 1.4.1 Object-Based and Image-Based Algorithms ..... 7
    • 1.4.2 Deterministic and Monte Carlo Algorithms ..... 7
  • 1.5 Objectives of this Thesis ..... 8
  • 1.6 Overview ..... 9
• Chapter 2: The Global Illumination Problem ..... 11
  • 2.1 Concepts ..... 12
    • 2.1.1 Radiance ..... 12
    • 2.1.2 Radiant Flux ..... 14
    • 2.1.3 The Bidirectional Reflectance Distribution Function ..... 16
  • 2.2 The Rendering Equation ..... 18
  • 2.3 The Potential Equation ..... 20
  • 2.4 The Global Reflectance Distribution Function ..... 23
    • 2.4.1 Definition ..... 23
    • 2.4.2 Flux in Terms of the GRDF ..... 24
    • 2.4.3 Equations Defining the GRDF ..... 24
  • 2.5 Summary ..... 27
• Chapter 3: Monte Carlo Methods ..... 29
  • 3.1 Introduction ..... 29
  • 3.2 Monte Carlo Integration ..... 31
  • 3.3 Stratified Sampling ..... 34
  • 3.4 Importance Sampling ..... 38
  • 3.5 Combining Estimators ..... 42
  • 3.6 Control Variates ..... 54
  • 3.7 Monte Carlo Methods to Solve Integral Equations ..... 56
  • 3.8 Russian roulette ..... 57
  • 3.9 Next Event Estimation ..... 61
  • 3.10 Summary ..... 62
• Chapter 4: Monte Carlo Methods Applied to the Global Illumination Problem ..... 65
  • 4.1 Monte Carlo Methods Applied to the Rendering Equation -- Path Tracing ..... 68
    • 4.1.1 Basic Algorithm ..... 68
    • 4.1.2 Stratified Sampling ..... 72
    • 4.1.3 Importance Sampling ..... 73
    • 4.1.4 Next Event Estimation ..... 74
    • 4.1.5 Combining Estimators ..... 79
    • 4.1.6 Control Variates ..... 80
    • 4.1.7 Improved Importance Sampling and Control Variates ..... 81
  • 4.2 Monte Carlo Methods Applied to the Potential Equation -- Light Tracing ..... 84
    • 4.2.1 Basic Algorithm ..... 84
    • 4.2.2 Importance Sampling ..... 87
    • 4.2.3 Next Event Estimation ..... 87
  • 4.3 Monte Carlo Methods Applied to the Integral Equations of the GRDF -- Bidirectional Path Tracing ..... 91
    • 4.3.1 Basic Algorithm ..... 91
    • 4.3.2 Next Event Estimation ..... 92
    • 4.3.3 Importance Sampling ..... 100
    • 4.3.4 Combining Estimators ..... 101
  • 4.4 Summary ..... 102
• Chapter 5: Test Results ..... 103
  • 5.1 Implementation ..... 103
  • 5.2 Test Scenes ..... 105
  • 5.3 Stratified Sampling ..... 107
  • 5.4 Importance Sampling ..... 109
  • 5.5 Next Event Estimation ..... 110
  • 5.6 Combining Estimators ..... 113
  • 5.7 Control Variates ..... 114
  • 5.8 Bidirectional Path Tracing ..... 116
  • 5.9 Summary ..... 118
• Chapter 6: Summary and Conclusions ..... 119
  • 6.1 Summary ..... 119
  • 6.2 Conclusions ..... 121
  • 6.3 Future Work ..... 124
• Appendix A: Camera Models ..... 127
• List of Figures ..... 133
• Bibliography ..... 135