Mathematical Insights into Advanced Computer Graphics Techniques (eBook)

oshinori Dobashi is an Associate Professor at the Graduate School of Information Science and Technology, Hokkaido University. He received his Ph.D. in Engineering from Hiroshima University, and his research interests center on computer graphics, including realistic rendering, fluid simulation and sound modeling. He has published numerous papers at leading computer graphics conferences and in respected journals, such as ACM SIGGRAPH. He has received several best paper awards from major computer graphics conferences, including EUROGRAPHICS. He also received a Commendation for Science and Technology (Research Category) from the Minister of Education, Culture, Sports, Science and Technology. He is one of the leading researchers in the computer graphics community in Japan.Shizuo Kaji is an Associate Professor at the Institute of Mathematics for Industry, Kyushu University.  He received Ph.D. from the Department of Mathematics, Kyoto University in 2007. His research interest is in topology and its applications in computer sciences. He is currently a PRESTO researcher at the Japan Science and Technology Agency (JST), working on a project on the mathematics of computer graphics.Kei Iwasaki is currently an Associate Professor at the Faculty of Systems Engineering at Wakayama University. He received his Ph.D. degree from The University of Tokyo in 2004. His research interests include computer graphics, real-time rendering and visual simulation.

Preface 6
Contents 7
Mathematics in Computer Graphics 9
1 Introduction 9
2 Appearance Modeling 10
3 Fluid Simulation 11
4 Digital Fabrication and Visualization 11
References 12
Part I Mathematics in Appearance Modeling 13
Micro-appearance Modeling of Fabrics 14
1 Introduction 14
2 Background: the Hierarchy of Fabric Structures 15
3 Fiber Light Scattering Models 16
4 Building Fabric Models Using Micro-CT Imaging 18
4.1 Building Volumetric Models 18
4.2 Building Fiber-Based Models 22
4.3 Appearance Matching 25
4.4 Data Replication 28
5 Procedural Modeling 28
5.1 Procedural Yarn Model 29
5.2 Fitting Procedural Parameters 32
6 Summary 39
References 39
Measuring the Light Reflectance with Mobile Devices 41
1 Introduction 41
2 Light Scattering 43
2.1 Bidirectional Reflectance Distribution Function 43
2.2 Obtaining HDR Intensity from RGB Colour 44
2.3 Conversion of Intensity to BRDF Values 45
3 Proposed Reflectance Measurements 47
3.1 Methodology 47
3.2 Calibration 48
3.3 Directions Vectors and Data Transfer Between Devices 50
3.4 Valid Combination of Directions 51
4 Results 51
4.1 Discussions 53
5 Conclusions 54
References 55
Sparkling Effect in Virtual Reality Device 56
1 Introduction 56
2 Depth Effect 56
3 Sparkle Modeling 57
3.1 Sparkle Normal Acquisition 58
3.2 Normal Texture Usage 59
4 Environment Mapping 59
5 Implementation and Results 60
6 Conclusions 63
References 63
Dappled Tiling 64
1 Introduction 64
2 The Algorithm 66
3 Extension 68
3.1 Non-uniform Condition 68
3.2 Cyclic Tiling 68
4 Example: Brick Wang Tiles 71
5 Example: Flow Tiles 74
6 Conclusion and Future Work 74
References 77
Procedural Non-Uniform Cellular Noise 78
1 Introduction 78
2 Related Work 79
3 Procedural Multi-scale Cellular Noise 80
3.1 Definitions and Notations 80
3.2 Grid Procedural Cellular Noise 82
3.3 Multi-level Grid Procedural Cellular Noise 84
4 Implementation Details 84
4.1 Distance to Squares 85
4.2 Neighbors Traversal Order: Depth 86
4.3 Iterative Traversal 86
5 Results 88
6 Conclusion 89
References 90
Part II Mathematics in Fluid Simulation 91
Just Enough Non-linearity 92
1 Introduction 92
2 Fluid Simulation 93
2.1 How Much Non-linearity? 93
2.2 Quasi-linear Approximations 94
3 Solid Simulation 95
3.1 Linear Materials 95
3.2 Neo-Hookean Materials 97
3.3 Overall Conclusions 98
4 Quaternion Julia Sets 99
4.1 How Much Non-linearity? 108
5 Discussion and Conclusions 109
References 110
An Efficient Cloud Simulation with Adaptive Grid Structure 112
1 Introduction 112
2 Related Work 113
3 Cloud Simulation 114
3.1 Governing Equations 114
3.2 Grid Structure 115
4 Proposed Method 116
4.1 Detecting the Region of Interest 117
4.2 Updating the Grid Structure 118
5 Experimental Results 118
6 Conclusions and Future Works 120
References 121
Recent Progress in Simulations of 3D Vortex Sheets with Surface Tension 122
1 Introduction 122
2 Related Works 123
3 Model and Numerics 124
3.1 Formulation 125
3.2 Topological Singularity 127
3.3 Controllability of Parametrization 128
3.4 Stiffness 128
4 Open Problems and Conclusion 131
References 132
Part III Mathematics in Digital Fabrication and Visualization 133
Physics-Based Computational Design for Digital Fabrication 134
1 Introduction 134
1.1 Presentation Overview 135
2 Physics-Based Simulation 136
2.1 Multi-scale Simulation of Liquid–Rod Interaction 136
2.2 Acoustic Simulation 137
3 Integrating Simulation in Design Cycles 139
3.1 Computational Hydrographic Printing 140
3.2 Physical Tags for Digital Fabrication 142
4 Search for Novel Designs 144
4.1 Computational Design of Modular Acoustic Filters 145
5 Conclusion 148
References 148
Design Tools in the Age of Personal Fabrication 151
1 Overview 151
2 Design Tools for Graphics 152
3 Design Tools for Fabrication 152
4 Smart Tools for Direct Fabrication 154
References 154
Clustering and Layout of Graphs with Attributed Nodes 155
1 Introduction 155
2 Background 156
2.1 Graph Clustering 156
2.2 Graph Layout 156
3 A Hybrid Graph Layout 156
4 A Key-Node-Separated Graph Visualization 159
5 Conclusion 163
References 163