Polygon Mesh Processing: 1st Edition (Hardback) book cover

Polygon Mesh Processing

1st Edition

By Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre Alliez, Bruno Levy

A K Peters/CRC Press

250 pages

Purchasing Options:$ = USD
Hardback: 9781568814261
pub: 2010-10-07
eBook (VitalSource) : 9780429195709
pub: 2010-10-07
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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.


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

Table of Contents


  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




About the Authors

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.

Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Computer Graphics
COMPUTERS / Programming / Games