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1st Edition

Polygon Mesh Processing




ISBN 9781568814261
Published October 7, 2010 by A K Peters/CRC Press
250 Pages

 
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Book Description

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.

Table of Contents

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

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Author(s)

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.

Reviews

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