Polygon mesh processing

Title:

Publication Information:

Natick, Mass. : A K Peters, c2010.

Physical Description:

xi, 230 p. : ill. (chiefly col.) ; 24 cm.

ISBN:

9781568814261

Subject Term:

Geometry -- Data processing.

Added Author:

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010265665	QA447 P62 2010	Open Access Book	Book	Searching... Unknown

Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing.

Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes.

A supplemental website contains downloads and additional information.

Author Notes

Leif Kobbelt is a professor of Computer Graphics & Multimedia at RWTH Aachen University in Germany. Mario Botsch is a professor of Computer Science at Bielefeld University and leads the Computer Graphics & Geometry Processing Group. Mark Pauly is an assistant professor in the computer science department of ETH Zurich, Switzerland. Pierre Alliez is a researcher in Computer Science at INRIA Sophia-Antipolis, in the GEOMETRICA group. Bruno Lvy is a senior researcher in INRIA-NGE, and a member of the LORIA lab. He is the scientific head of the ALICE project team.

Preface	p. ix
1 Surface Representations	p. 1
1.1 Surface Definition and Properties	p. 3
1.2 Approximation Power	p. 5
1.3 Parametric Surface Representations	p. 7
1.4 Implicit Surface Representations	p. 13
1.5 Conversion Methods	p. 15
1.6 Summary and Further Reading	p. 20
2 Mesh Data Structures	p. 21
2.1 Face-Based Data Structures	p. 22
2.2 Edge-Based Data Structures	p. 24
2.3 Halfedge-Based Data Structure	p. 25
2.4 Directed-Edge Data Structure	p. 27
2.5 Summary and Further Reading	p. 28
3 Differential Geometry	p. 29
3.1 Curves	p. 29
3.2 Surfaces	p. 31
3.3 Discrete Differential Operators	p. 40
3.4 Summary and Further Reading	p. 48
4 Smoothing	p. 49
4.1 Fourier Transform and Manifold Harmonics	p. 50
4.2 Diffusion Flow	p. 54
4.3 Fairing	p. 57
4.4 Summary and Further Reading	p. 61
5 Parameterization	p. 63
5.1 General Goals	p. 64
5.2 Parameterization of a Triangulated Surface	p. 66
5.3 Barycentric Mapping	p. 67
5.4 Conformal Mapping	p. 71
5.5 Methods Based on Distortion Analysis	p. 78
5.6 Summary and Further Reading	p. 82
6 Remeshing	p. 85
6.1 Local Structure	p. 86
6.2 Global Structure	p. 87
6.3 Correspondences	p. 89
6.4 Voronoi Diagrams and Delaunay Triangulations	p. 89
6.5 Triangle-Based Remeshing	p. 92
6.6 Quad-dominant Remeshing	p. 104
6.7 Summary and Further Reading	p. 110
7 Simplification & Approximation	p. 111
7.1 Vertex Clustering	p. 113
7.2 Incremental Decimation	p. 115
7.3 Shape Approximation	p. 122
7.4 Out-of-Core Methods	p. 127
7.5 Summary and Further Reading	p. 130
8 Model Repair	p. 131
8.1 Types of Artifacts: The "Freak Show"	p. 132
8.2 Types of Repair Algorithms	p. 132
8.3 Types of Input	p. 135
8.4 Surface-Oriented Algorithms	p. 139
8.5 Volumetric Repair Algorithms	p. 144
8.6 Summary and Further Reading	p. 150
9 Deformation	p. 151
9.1 Transformation Propagation	p. 153
9.2 Shell-Based Deformation	p. 155
9.3 Multi-Scale Deformation	p. 157
9.4 Differential Coordinates	p. 164
9.5 Freeform Deformation	p. 169
9.6 Radial Basis Functions	p. 173
9.7 Limitations of Linear Methods	p. 175
9.8 Summary and Further Reading	p. 177
A Numerics	p. 181
A.1 Discretizing Poisson and Laplace Equations	p. 181
A.2 Data Structures for Sparse Matrices	p. 184
A.3 Iterative Solvers	p. 187
A.4 Sparse Direct Cholesky Solver	p. 193
A.5 Non-Symmetric Indefinite Systems	p. 196
A.6 Comparison	p. 197
Bibliography	p. 203
Index	p. 226

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Table of Contents