Advances in Multiresolution for Geometric Modelling (eBook)

Neil Dodgson took his BSc in Computer Science and Physics at Massey University in New Zealand (1988) and his PhD in image processing at the University of Cambridge (1992). He is a Senior Lecturer in the Computer Laboratory at the University of Cambridge and is co-leader of the Rainbow Research Group. He has over fifty refereed publications in the areas of modelling for 3D computer graphics, human-figure animation, 3D displays, and image processing.   Malcolm Sabin worked on representation of aircraft shapes at British Aircraft Corporation in the late 1960s, there developing one of the earliest modern surface systems. He has been active in CAD, CAM and CAE ever since, especially in the field of surface representations and in subdivision in particular.  He is employed by his own company, Numerical Geometry Ltd. which sells his time as a consultant, and maintains close contact with the Computer Laboratory and the Department of Applied Mathematics at the University of Cambridge.      

Preface 5
Contents 8
Part I — Compression 11
Recent Advances in Compression of 3D Meshes 12
Shape Compression using Spherical Geometry Images 36
Part II — Data Structures 56
A Survey on Data Structures for Level- of- Detail Models 57
An Algorithm for Decomposing Multi- dimensional Non- manifold Objects into Nearly Manifold Components 83
Encoding Level-of-Detail Tetrahedral Meshes 96
Multi-Scale Geographic Maps 108
Part III — Modelling 123
Constrained Multiresolution Geometric Modelling 124
Multi-scale and Adaptive CS-RBFs for Shape Reconstruction from Clouds of Points 148
Part IV — Parameterization 160
Surface Parameterization: a Tutorial and Survey 161
Variations on Angle Based Flattening 191
Part V — Subdivision 204
Recent Progress in Subdivision: a Survey 205
Optimising 3D Triangulations: Improving the Initial Triangulation for the Butterfly Subdivision Scheme 233
Simple Computation of the Eigencomponents of a Subdivision Matrix in the Fourier Domain 247
Subdivision as a Sequence of Sampled Cp Surfaces 260
Reverse Subdivision 272
v 5-subdivision 285
Geometrically Controlled 4-Point Interpolatory Schemes 300
Part VI — Thinning 315
Adaptive Thinning for Terrain Modelling and Image Compression 316
Simplification of Topologically Complex Assemblies 336
Topology Preserving Thinning of Vector Fields on Triangular Meshes 350
Part VII — Wavelets 364
Periodic and Spline Multiresolution Analysis and the Lifting Scheme 365
Nonstationary Sibling Wavelet Frames on Bounded Intervals: the Duality Relation 387
Haar Wavelets on Spherical Triangulations 400
Author Index 413
Colour Plates 414