Polygon Mesh Processing (Hardcover)

Preface

1. Surface Representations
   Surface Definition and Properties
   Approximation Power
   Parametric Surface Representations
   Implicit Surface Representations
   Conversion Methods
   Summary and Further Reading
2. Mesh Data Structures
   Face-Based Data Structures
   Edge-Based Data Structures
   Halfedge-Based Data Structure
   Directed-Edge Data Structure
   Summary and Further Reading
3. Differential Geometry
   Curves
   Surfaces
   Discrete Differential Operators
   Summary and Further Reading
4. Smoothing
   Fourier Transform and Manifold Harmonics
   Diffusion Flow
   Fairing
   Summary and Further Reading
5. Parameterization
   General Goals
   Parameterization of a Triangulated Surface
   Barycentric Mapping
   Conformal Mapping
   Methods Based on Distortion Analysis
   Summary and Further Reading
6. Remeshing
   Local Structure
   Global Structure
   Correspondences
   Voronoi Diagrams and Delaunay Triangulations
   Triangle-Based Remeshing
   Quad-dominant Remeshing
   Summary and Further Reading
7. Simplification & Approximation
   Vertex Clustering
   Incremental Decimation
   Shape Approximation
   Out-of-Core Methods
   Summary and Further Reading
8. 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
9. 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