Guide to Computational Geometry Processing

Foundations, Algorithms, and Methods

  • Jakob Andreas Bærentzen
  • Jens Gravesen
  • François Anton
  • Henrik Aanæs

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Mathematical Preliminaries

    1. Front Matter
      Pages 11-11
    2. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 1-10
  3. Mathematical Preliminaries

    1. Front Matter
      Pages 11-11
    2. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 13-43
    3. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 45-64
    4. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 65-79
  4. Computational Geometry Processing

    1. Front Matter
      Pages 81-81
    2. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 83-97
    3. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 99-117
    4. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 119-141
    5. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 143-158
    6. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 159-177
    7. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 179-190
    8. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 191-211
    9. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 213-225
    10. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 227-240
    11. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 241-261
    12. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 263-275
    13. Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 277-286

About this book

Introduction

Optical scanning is rapidly becoming ubiquitous. From industrial laser scanners to medical CT, MR and 3D ultrasound scanners, numerous organizations now have easy access to optical acquisition devices that provide huge volumes of image data. However, the raw geometry data acquired must first be processed before it is useful.

This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages.

Topics and features:

  • Presents an overview of the underlying mathematical theory, covering vector spaces, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations
  • Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces
  • Examines techniques for computing curvature from polygonal meshes
  • Describes algorithms for mesh smoothing, mesh parametrization, and mesh optimization and simplification
  • Discusses point location databases and convex hulls of point sets
  • Investigates the reconstruction of triangle meshes from point clouds, including methods for registration of point clouds and surface reconstruction
  • Provides additional material at a supplementary website
  • Includes self-study exercises throughout the text

Graduate students will find this text a valuable, hands-on guide to developing key skills in geometry processing. The book will also serve as a useful reference for professionals wishing to improve their competency in this area.

Authors and affiliations

  • Jakob Andreas Bærentzen
    • 1
  • Jens Gravesen
    • 2
  • François Anton
    • 3
  • Henrik Aanæs
    • 4
  1. 1.Informatics and Mathematical ModellingTechnical University of DenmarkKongens LyngbyDenmark
  2. 2.Department of MathematicsTechnical University of DenmarkKongens LyngbyDenmark
  3. 3.Informatics and Mathematical ModellingTechnical University of DenmarkKongens LyngbyDenmark
  4. 4.Informatics and Mathematical ModellingTechnical University of DenmarkKongens LyngbyDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-4075-7
  • Copyright Information Springer-Verlag London 2012
  • Publisher Name Springer, London
  • eBook Packages Computer Science
  • Print ISBN 978-1-4471-4074-0
  • Online ISBN 978-1-4471-4075-7
  • About this book