Shape Analysis and Structuring (eBook)

Contents 8
List of Contributors 14
Shape Interrogation 16
1 Introduction 16
2 Differential Geometry of curves and surfaces 17
3 Interrogation of discrete shapes 20
4 First-Order Shape Analysis 24
5 Second-order shape analysis 28
6 Characteristic lines 35
7 Robust Symbolic based Shape Interrogation and Analysis 40
8 Interrogation of algebraic curves and surfaces 45
9 Conclusion 56
References 57
Recent Advances in Remeshing of Surfaces 67
1 Introduction 67
2 State of the Art 70
References 92
Multiresolution Analysis 97
1 Introduction 97
2 Hierarchical Freeform Representations 98
3 Multiresolution Methods for Freeform Representations 99
4 Multiresolution Analysis for Irregular Mesh-based Representations 116
5 Conclusions and Open Issues 123
References 124
Subdivision Surfaces and Applications 129
1 Introduction 129
2 Subdivision basics 130
3 Artifacts in subdivision surfaces 134
4 Implementation and usability issues 142
5 Constraint-based subdivision surfaces 145
6 Conclusions 152
References 154
Skeletal Structures 158
1 Introduction 158
2 Definitions of geometric medial structures 161
3 Exact representation of medial structures 163
4 Approximation of the medial axis 169
5 Skeletons from topological structures 181
6 Conclusions and future developments 188
References 190
Morphological Representations of Scalar Fields 197
1 Introduction 197
2 Background Notions 198
3 Extracting Critical Points 205
4 Extracting Approximations of a Morse-Smale Complex 209
5 Algorithms for Extracting a Contour Tree 214
6 Concluding Remarks 219
Acknowledgments 220
References 220
Topological Representations of Vector Fields 226
1 Introduction 226
2 Topological features of 2D vector fields 227
3 Topological Features of 3D Vector Fields 231
4 Topological features of time-dependent vector fields 237
5 Further applications of topological features 242
6 Conclusions 248
References 249
Control Structure and Multi-Resolution Techniques for Virtual Human Representation 252
1 Definitions and Background 252
2 Skeleton control methods 254
3 Skeleton skinning and skin mapping 258
4 Skeleton-driven deformation 260
5 Generation of Control Skeleton 264
6 Discussion on skeleton for Virtual Humans 270
7 Multi-Resolution Techniques 272
References 279
A Colour Plates: Shape Interrogation 286
B Colour Plates: Recent Advances in Remeshing of Surfaces 288
C Colour Plates of the Chapter: Multiresolution Analysis 290
D Colour Plates: Subdivision Surfaces and Applications 292
E Colour Plates: Skeletal Structures 295
F Colour Plates: Morphological Representations of Scalar Fields 297
G Colour Plates: Topological Representations of Vector Fields 298
Index 302