1st Edition
Polygon Mesh Processing
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.Preface
- Surface Representations
Surface Definition and Properties
Approximation Power
Parametric Surface Representations
Implicit Surface Representations
Conversion Methods
Summary and Further Reading - Mesh Data Structures
Face-Based Data Structures
Edge-Based Data Structures
Halfedge-Based Data Structure
Directed-Edge Data Structure
Summary and Further Reading - Differential Geometry
Curves
Surfaces
Discrete Differential Operators
Summary and Further Reading - Smoothing
Fourier Transform and Manifold Harmonics
Diffusion Flow
Fairing
Summary and Further Reading - Parameterization
General Goals
Parameterization of a Triangulated Surface
Barycentric Mapping
Conformal Mapping
Methods Based on Distortion Analysis
Summary and Further Reading - Remeshing
Local Structure
Global Structure
Correspondences
Voronoi Diagrams and Delaunay Triangulations
Triangle-Based Remeshing
Quad-dominant Remeshing
Summary and Further Reading - Simplification & Approximation
Vertex Clustering
Incremental Decimation
Shape Approximation
Out-of-Core Methods
Summary and Further Reading - Model Repair
Types of Artifacts: The "Freak Show"
Types of Repair Algorithms
Types of Input
Surface-Oriented Algorithms
Volumetric Repair Algorithms
Summary and Further Reading - Deformation
Transformation Propagation
Shell-Based Deformation
Multi-Scale Deformation
Differential Coordinates
Freeform Deformation
Radial Basis Functions
Limitations of Linear Methods
Summary and Further Reading
A. Numerics
Discretizing Poisson and Laplace Equations
Data Structures for Sparse Matrices
Iterative Solvers
Sparse Direct Cholesky Solver
Non-Symmetric Indefinite Systems
Comparison
Bibliography
Index
Biography
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.
College-level collections strong in engineering and modeling science will find this [book] covers the entire geometry processing pipeline, covering all kinds of models acquired by 3D scanning techniques. The latest techniques using triangle meshes receive powerful, in-depth analysis in a pick for any college-level engineering collection.
—Midwest Book Review, January 2011
