Advances in Geometric Modeling and Processing: 6th International Conference, GMP 2010, Castro Urdiales, Spain, June 16-18, 2010, Proceedings

Cover......Page 1
Advances in
Geometric Modeling
and Processing......Page 3
Lecture Notes in Computer Science 6130......Page 2
ISBN-10 3642134106......Page 4
Preface......Page 5
Conference Organization......Page 6
Table of Contents......Page 8
Introduction and Previous Work......Page 10
Solving Well-Constrained Transcendental Systems......Page 12
Single Solution Termination Criterion for Transcendental Systems......Page 13
Truncated Bounding Cones and Their Bounding Polytopes......Page 15
Bounding Cone's Arithmetic......Page 17
No Root Exclusion Test......Page 19
Analysis of the Bounding Cone's Tightness......Page 20
Examples......Page 22
Conclusion and Future Work......Page 26
References......Page 27
Introduction......Page 28
Preliminaries......Page 29
Construction of RCL Surfaces......Page 32
Properties and Examples of RCL Surfaces......Page 34
Conclusion......Page 36
References......Page 37
Introduction......Page 38
Preliminaries......Page 39
Support Function of the Tschirnhausen Cubic......Page 40
$G$^{1} Data on the Tschirnhausen Cubic......Page 42
Hermite Interpolation with PH Cubics and Their Offsets......Page 46
Existence and Number of Solutions......Page 47
Computation of Interpolants and Examples......Page 48
Conclusion......Page 50
References......Page 51
Introduction......Page 52
Multi-material Contouring......Page 55
Defining contours......Page 56
Characterization of the Contours......Page 57
Evaluating Contours......Page 58
Set Operations on Multi-material Contours......Page 60
Implementation......Page 61
Results......Page 62
References......Page 64
Introduction......Page 66
Basic Observations......Page 67
Related Work......Page 68
Computational Models and Representations of Polynomials......Page 69
Computational Models......Page 70
Representation of the Polynomials......Page 73
The Dialytic Method to Solve the Sign Condition Problem......Page 74
Lower Bounds for the Sign Condition Problem......Page 77
The Algebraic Model......Page 78
The Dialytic Method for Point Location......Page 82
References......Page 83
Smooth Network Interpolation......Page 86
Notation and Constraints......Page 88
Constraints on Boundary Curves Arising from $G$^{2} Continuity......Page 89
References......Page 95
Introduction......Page 97
Cone-Spheres and Their Distance Computation......Page 99
Computing Bounding Cone-Spheres......Page 101
Segmentation of a Canal Surface......Page 104
Pruning Irrelevant Pairs......Page 105
Algorithm......Page 107
Experimental Results......Page 108
Conclusion......Page 110
References......Page 111
Introduction......Page 113
Representation......Page 115
Subdivision Process......Page 117
Region Recovery......Page 119
Following the Boundary Curves around a Region......Page 121
Regularity Test......Page 123
The General Case......Page 124
Implementation and Demonstration......Page 125
References......Page 131
Introduction......Page 133
Related Work......Page 135
Medial Surface Reconstruction from Medial Voxels......Page 136
Sub-sampling of Medial Voxels......Page 137
Building a Voronoi Diagram on Medial Voxels......Page 138
Non-manifold Meshing from Vertex Connectivity......Page 139
Result and Discussion......Page 140
References......Page 143
Topology Classification of Voxels......Page 145
Introduction......Page 146
Periodicity Recognition......Page 147
Decomposition of 3D Models into Parts......Page 148
An Overview of Our Method......Page 149
Curvature Estimation and Segmentation......Page 152
Planar Parameterization......Page 153
Sub Grouping......Page 154
Initial Estimation and Assignment of Indices......Page 155
Optimal Estimation......Page 157
Region Growing......Page 158
Geometric Synthesis......Page 160
Evaluation of Gear Teeth Contact......Page 161
Results......Page 163
Conclusion and Future Works......Page 167
References......Page 168
Introduction......Page 170
Contribution......Page 171
Theoretical Background......Page 172
Visualization of Holomorphic Functions......Page 173
Branch Points and Branch Graph......Page 174
Shifts......Page 175
Cutting the Base Geometry......Page 177
Boundary Constraints for the Height Function......Page 178
Riemann Surface Models......Page 180
Domain Coloring on Riemann Surfaces......Page 183
References......Page 186
Introduction......Page 188
T-Junction on a Boundary Curve......Page 189
T-Junction at a 3-Valent Vertex......Page 195
Results......Page 198
References......Page 199
Introduction......Page 201
Related Work and Our Basic Idea......Page 204
Clipping Circle/Sphere and Clipping Lines/Planes......Page 206
Uniqueness of Solution......Page 207
Experimental Results......Page 208
Conclusions......Page 212
Squared Distance Functions for Cubic Bézier Curves......Page 213
Differential of Squared Distance Functions......Page 214
Introduction......Page 215
Evaluation of Catmull-Clark's Subdivision Surfaces......Page 217
Evaluation of Standard Catmull-Clark's Subdivision Surface......Page 218
Evaluation of Nonstandard Catmull-Clark's Subdivision Surface......Page 220
Finite Element Method for the Mean Curvature Flow......Page 221
Definition of Basis Functions......Page 222
Graphical Examples......Page 223
Conclusions......Page 226
References......Page 227
Introduction......Page 228
Previous Work......Page 230
Theoretic Foundation......Page 231
Volume Parameterization Using Green's Functions......Page 232
Parameterizing a Star Shape to a Ball......Page 233
Parameterizing a Star Shape to a Polycube......Page 236
Experimental Results and Applications......Page 237
Conclusion and Future Work......Page 240
References......Page 241
Introduction......Page 245
A Linear Sufficient Condition for Injectivity of Planar B-spline Parameterization......Page 247
Test Model — Heat Conduction Problem......Page 250
Isogeometric Analysis with Different Parameterization......Page 252
Shape Optimization Method......Page 255
Examples and Comparison......Page 257
References......Page 261
Introduction......Page 264
Notations......Page 266
Used Geometric PDEs......Page 267
Mixed Variational Formulations......Page 268
Basis Functions and Their Properties......Page 269
Spatial Discretizations......Page 271
Temporal Direction Discretization......Page 273
Illustrative Examples......Page 274
References......Page 276
Introduction......Page 278
Previous Work......Page 279
Problem Formulation......Page 280
Algorithm Overview......Page 281
Surface RVD Computation......Page 282
Clipped Voronoi Cells Construction......Page 283
Tetrahedral Mesh Generation......Page 284
Optimization......Page 285
Final Mesh Extraction......Page 286
Experimental Results......Page 287
References......Page 290
Introduction......Page 292
Basic Idea......Page 294
Computing Knots from Neighboring Data Points......Page 295
Merging Local Knots Sequences......Page 299
Experiments......Page 301
Conclusions and Future Work......Page 303
References......Page 304
Introduction......Page 305
Deformation Energies......Page 308
Modes of Deformation Energies......Page 309
Quadratic Energies......Page 313
Modal Signatures......Page 315
Results and Discussion......Page 317
References......Page 322
Author Index......Page 324