Dobashi / Kaji / Iwasaki Mathematical Insights into Advanced Computer Graphics Techniques

1. Auflage 2018
ISBN: 978-981-13-2850-3
Verlag: Springer Nature Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 32, 163 Seiten

Reihe: Mathematics for Industry

This book presents cutting-edge developments in the advanced mathematical theories utilized in computer graphics research - fluid simulation, realistic image synthesis, and texture, visualization and digital fabrication. A spin-off book from the International Symposium on Mathematical Progress in Expressive Image Synthesis in 2016 and 2017 (MEIS2016/2017) held in Fukuoka, Japan, it includes lecture notes and an expert introduction to the latest research presented at the symposium. The book offers an overview of the emerging interdisciplinary themes between computer graphics and driven mathematic theories, such as discrete differential geometry. Further, it highlights open problems in those themes, making it a valuable resource not only for researchers, but also for graduate students interested in computer graphics and mathematics.

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.

Autoren/Hrsg.

Dobashi, Yoshinori

Kaji, Shizuo

Iwasaki, Kei

Inhaltsverzeichnis

1;Preface;6
2;Contents;7
3;Mathematics in Computer Graphics;9
3.1;1 Introduction;9
3.2;2 Appearance Modeling;10
3.3;3 Fluid Simulation;11
3.4;4 Digital Fabrication and Visualization;11
3.5;References;12
4;Part I Mathematics in Appearance Modeling;13
5;Micro-appearance Modeling of Fabrics;14
5.1;1 Introduction;14
5.2;2 Background: the Hierarchy of Fabric Structures;15
5.3;3 Fiber Light Scattering Models;16
5.4;4 Building Fabric Models Using Micro-CT Imaging;18
5.4.1;4.1 Building Volumetric Models;18
5.4.2;4.2 Building Fiber-Based Models;22
5.4.3;4.3 Appearance Matching;25
5.4.4;4.4 Data Replication;28
5.5;5 Procedural Modeling;28
5.5.1;5.1 Procedural Yarn Model;29
5.5.2;5.2 Fitting Procedural Parameters;32
5.6;6 Summary;39
5.7;References;39
6;Measuring the Light Reflectance with Mobile Devices;41
6.1;1 Introduction;41
6.2;2 Light Scattering;43
6.2.1;2.1 Bidirectional Reflectance Distribution Function;43
6.2.2;2.2 Obtaining HDR Intensity from RGB Colour;44
6.2.3;2.3 Conversion of Intensity to BRDF Values;45
6.3;3 Proposed Reflectance Measurements;47
6.3.1;3.1 Methodology;47
6.3.2;3.2 Calibration;48
6.3.3;3.3 Directions Vectors and Data Transfer Between Devices;50
6.3.4;3.4 Valid Combination of Directions;51
6.4;4 Results;51
6.4.1;4.1 Discussions;53
6.5;5 Conclusions;54
6.6;References;55
7;Sparkling Effect in Virtual Reality Device;56
7.1;1 Introduction;56
7.2;2 Depth Effect;56
7.3;3 Sparkle Modeling;57
7.3.1;3.1 Sparkle Normal Acquisition;58
7.3.2;3.2 Normal Texture Usage;59
7.4;4 Environment Mapping;59
7.5;5 Implementation and Results;60
7.6;6 Conclusions;63
7.7;References;63
8;Dappled Tiling;64
8.1;1 Introduction;64
8.2;2 The Algorithm;66
8.3;3 Extension;68
8.3.1;3.1 Non-uniform Condition;68
8.3.2;3.2 Cyclic Tiling;68
8.4;4 Example: Brick Wang Tiles;71
8.5;5 Example: Flow Tiles;74
8.6;6 Conclusion and Future Work;74
8.7;References;77
9;Procedural Non-Uniform Cellular Noise;78
9.1;1 Introduction;78
9.2;2 Related Work;79
9.3;3 Procedural Multi-scale Cellular Noise;80
9.3.1;3.1 Definitions and Notations;80
9.3.2;3.2 Grid Procedural Cellular Noise;82
9.3.3;3.3 Multi-level Grid Procedural Cellular Noise;84
9.4;4 Implementation Details;84
9.4.1;4.1 Distance to Squares;85
9.4.2;4.2 Neighbors Traversal Order: Depth;86
9.4.3;4.3 Iterative Traversal;86
9.5;5 Results;88
9.6;6 Conclusion;89
9.7;References;90
10;Part II Mathematics in Fluid Simulation;91
11;Just Enough Non-linearity;92
11.1;1 Introduction;92
11.2;2 Fluid Simulation;93
11.2.1;2.1 How Much Non-linearity?;93
11.2.2;2.2 Quasi-linear Approximations;94
11.3;3 Solid Simulation;95
11.3.1;3.1 Linear Materials;95
11.3.2;3.2 Neo-Hookean Materials;97
11.3.3;3.3 Overall Conclusions;98
11.4;4 Quaternion Julia Sets;99
11.4.1;4.1 How Much Non-linearity?;108
11.5;5 Discussion and Conclusions;109
11.6;References;110
12;An Efficient Cloud Simulation with Adaptive Grid Structure;112
12.1;1 Introduction;112
12.2;2 Related Work;113
12.3;3 Cloud Simulation;114
12.3.1;3.1 Governing Equations;114
12.3.2;3.2 Grid Structure;115
12.4;4 Proposed Method;116
12.4.1;4.1 Detecting the Region of Interest;117
12.4.2;4.2 Updating the Grid Structure;118
12.5;5 Experimental Results;118
12.6;6 Conclusions and Future Works;120
12.7;References;121
13;Recent Progress in Simulations of 3D Vortex Sheets with Surface Tension;122
13.1;1 Introduction;122
13.2;2 Related Works;123
13.3;3 Model and Numerics;124
13.3.1;3.1 Formulation;125
13.3.2;3.2 Topological Singularity;127
13.3.3;3.3 Controllability of Parametrization;128
13.3.4;3.4 Stiffness;128
13.4;4 Open Problems and Conclusion;131
13.5;References;132
14;Part III Mathematics in Digital Fabrication and Visualization;133
15;Physics-Based Computational Design for Digital Fabrication;134
15.1;1 Introduction;134
15.1.1;1.1 Presentation Overview;135
15.2;2 Physics-Based Simulation;136
15.2.1;2.1 Multi-scale Simulation of Liquid–Rod Interaction;136
15.2.2;2.2 Acoustic Simulation;137
15.3;3 Integrating Simulation in Design Cycles;139
15.3.1;3.1 Computational Hydrographic Printing;140
15.3.2;3.2 Physical Tags for Digital Fabrication;142
15.4;4 Search for Novel Designs;144
15.4.1;4.1 Computational Design of Modular Acoustic Filters;145
15.5;5 Conclusion;148
15.6;References;148
16;Design Tools in the Age of Personal Fabrication;151
16.1;1 Overview;151
16.2;2 Design Tools for Graphics;152
16.3;3 Design Tools for Fabrication;152
16.4;4 Smart Tools for Direct Fabrication;154
16.5;References;154
17;Clustering and Layout of Graphs with Attributed Nodes;155
17.1;1 Introduction;155
17.2;2 Background;156
17.2.1;2.1 Graph Clustering;156
17.2.2;2.2 Graph Layout;156
17.3;3 A Hybrid Graph Layout;156
17.4;4 A Key-Node-Separated Graph Visualization;159
17.5;5 Conclusion;163
17.6;References;163