Skip to main content
  • Textbook
  • © 2012

Guide to Computational Geometry Processing

Foundations, Algorithms, and Methods

  • Provides a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics
  • Presents an introduction to the theoretical and mathematical underpinnings of each technique
  • Includes self-study exercises throughout the text, and supplies additional material at a supplementary website
  • Includes supplementary material: sn.pub/extras

Buy it now

Buying options

eBook USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (18 chapters)

  1. Front Matter

    Pages I-XVIII
  2. Mathematical Preliminaries

    1. Front Matter

      Pages 11-11
  3. Introduction

    1. Introduction

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 1-10
  4. Mathematical Preliminaries

    1. Front Matter

      Pages 11-11
    2. Vector Spaces, Affine Spaces, and Metric Spaces

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 13-43
    3. Differential Geometry

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 45-64
    4. Finite Difference Methods for Partial Differential Equations

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 65-79
  5. Computational Geometry Processing

    1. Front Matter

      Pages 81-81
    2. Polygonal Meshes

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 83-97
    3. Splines

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 99-117
    4. Subdivision

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 119-141
    5. Curvature in Triangle Meshes

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 143-158
    6. Mesh Smoothing and Variational Subdivision

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 159-177
    7. Parametrization of Meshes

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 179-190
    8. Simplifying and Optimizing Triangle Meshes

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 191-211
    9. Spatial Data Indexing and Point Location

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 213-225
    10. Convex Hulls

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 227-240
    11. Triangle Mesh Generation: Delaunay Triangulation

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 241-261
    12. 3D Surface Registration via Iterative Closest Point (ICP)

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 263-275
    13. Surface Reconstruction using Radial Basis Functions

      • Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs
      Pages 277-286

About this book

This book 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. 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.

Reviews

From the book reviews:

“The book consists of two parts—Mathematical Preliminaries and Computational Geometry Processing. Almost 70 pages of linear algebra, differential geometry and finite difference methods comprise all the necessary concepts for the rest of the book. … the book fills a gap in the market for textbook-like publications on geometry processing topics. It could be a valuable source of initial ideas for people trying to extend their basic knowledge in the area.” (Pavel Chalmovianský, Mathematical Reviews, November, 2014)

“The book is brilliant in that it maintains a sane balance between theory and practice. It is written by practitioners, for practitioners--the authors are experienced programmers who have developed the geometry and linear algebra (GEL) library, which is being used in real-world applications--without losses in mathematical rigor or theoretical details. This elegant style enables both students and professionals to use it as a reference guide for fundamental topics in geometry processing. … The book is a handy companion for students and practitioners working in computer graphics and computer vision fields, but will also appeal to people working in any computational science and engineering field.” (Alin Anton, Computing Reviews, January, 2013)

“It focuses on the important techniques not covered by traditional courses on computer vision and computer graphics. … The book is presented in an accessible fashion full of images, examples, pseudocodes and exercises. … The book is suitable for professionals or graduate students who want to understand the theory and implement algorithms of geometry processing. It can be used for a self studing and as a course book as well.” (Agnieszka Lisowska, Zentralblatt MATH, Vol. 1252, 2012)

Authors and Affiliations

  • Informatics and Mathematical Modelling, Technical University of Denmark, Kongens Lyngby, Denmark

    Jakob Andreas Bærentzen, François Anton, Henrik Aanæs

  • Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark

    Jens Gravesen

Bibliographic Information

Buy it now

Buying options

eBook USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access