250 Pages
    by A K Peters/CRC Press

    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.


    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
      Discrete Differential Operators
      Summary and Further Reading
    4. Smoothing
      Fourier Transform and Manifold Harmonics
      Diffusion Flow
      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
      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


    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