Representing spherical functions with rhombic dodecahedron.

Ng Lai Sze.Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.Includes bibliographical references (leaves 135-140).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 2 --- Spherical Data Representation --- p.4Chapter 3 --- Rhombic Dodecahedron --- p.7Chapter 3.1 --- Introduction --- p.7Chapter 3.2 --- "Platonic Solids, Archimedean Solids and Dual Polyhedron" --- p.8Chapter 3.2.1 --- Platonic Solids --- p.8Chapter 3.2.2 --- Archimedean Solids --- p.10Chapter 3.2.3 --- Dual Polyhedron --- p.13Chapter 3.3 --- Rhombic Dodecahedron --- p.16Chapter 3.3.1 --- Basic Property of Rhombic Dodecahedron --- p.16Chapter 3.3.2 --- Construction of Rhombic Dodecahedron --- p.16Chapter 3.3.3 --- Advantages of Rhombic Dodecahedron --- p.16Chapter 3.4 --- Summary --- p.19Chapter 4 --- Subdivision Scheme --- p.21Chapter 4.1 --- Introduction --- p.21Chapter 4.2 --- Motivation --- p.22Chapter 4.3 --- Great Circle Subdivision --- p.22Chapter 4.3.1 --- Normal Space Analysis --- p.23Chapter 4.4 --- Small Circle Subdivision --- p.25Chapter 4.5 --- Skew Great Circle Subdivision --- p.27Chapter 4.6 --- Analysis --- p.28Chapter 4.6.1 --- Sampling Uniformity --- p.29Chapter 4.6.2 --- Area Uniformity --- p.32Chapter 4.6.3 --- Stretch Measurement --- p.35Chapter 4.6.4 --- Query Efficiency --- p.39Chapter 4.7 --- Summary --- p.40Chapter 5 --- Data Querying and Indexing --- p.42Chapter 5.1 --- Introduction --- p.42Chapter 5.2 --- Location of base polygon --- p.43Chapter 5.2.1 --- General Method --- p.43Chapter 5.2.2 --- Tailored Table Look Up Method --- p.45Chapter 5.3 --- Location of the subdivided area --- p.49Chapter 5.3.1 --- On Deriving the Indexing Equation --- p.50Chapter 5.4 --- Summary --- p.54Chapter 6 --- Environment Mapping --- p.56Chapter 6.1 --- Introduction --- p.56Chapter 6.2 --- Related Work --- p.57Chapter 6.3 --- Methodology --- p.58Chapter 6.4 --- Data Preparation --- p.59Chapter 6.4.1 --- Re-sampling of Data on Sphere --- p.60Chapter 6.4.2 --- Preparation of Texture --- p.65Chapter 6.5 --- Reflection and Refraction by environment mapping --- p.68Chapter 6.5.1 --- Location and Retrieval of Data --- p.68Chapter 6.5.2 --- Cg Implementation --- p.70Chapter 6.6 --- Experiments --- p.76Chapter 6.6.1 --- Experiment Setup --- p.76Chapter 6.6.2 --- Experiment Result and Analysis --- p.78Chapter 6.7 --- Summary --- p.89Chapter 7 --- Shadow Mapping --- p.92Chapter 7.1 --- Introduction --- p.92Chapter 7.2 --- Related Work --- p.93Chapter 7.3 --- Methodology --- p.95Chapter 7.4 --- Data Preparation --- p.97Chapter 7.5 --- Shadow Determination and Scene Illumination --- p.98Chapter 7.6 --- Experiments --- p.100Chapter 7.6.1 --- Experiment Setup --- p.100Chapter 7.6.2 --- Experiment Result and Analysis --- p.101Chapter 7.7 --- Summary --- p.107Chapter 8 --- Dynamic HDR Environment Sequences Sampling --- p.110Chapter 8.1 --- Introduction --- p.110Chapter 8.2 --- Related Work on HDR Distant Environment Map Sampling --- p.112Chapter 8.3 --- Static Sampling by Spherical Quad-Quad Tree --- p.114Chapter 8.3.1 --- Importance Metric --- p.117Chapter 8.4 --- Dynamic Sampling by Spherical Quad-Quad Tree --- p.121Chapter 8.5 --- Experiments --- p.125Chapter 8.5.1 --- Static Sampling --- p.125Chapter 8.5.2 --- Dynamic Sampling --- p.126Chapter 8.6 --- Summary --- p.132Chapter 9 --- Conclusion --- p.133Bibliography --- p.13