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Triangulations and Applications

  • Textbook
  • © 2006

Overview

Authors:
  1. Øyvind Hjelle

    1. Simula Research Laboratory AS, Norway

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    You can also search for this author in PubMed   Google Scholar

  2. Morten Dæhlen

    1. Department of Informatics, University of Oslo, Oslo, Norway

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    You can also search for this author in PubMed   Google Scholar

  • Applications-oriented
  • Well-written textbook on triangulations

Part of the book series: Mathematics and Visualization (MATHVISUAL)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XI
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  2. Triangles and Triangulations

    • Øyvind Hjelle, Morten Dæhlen
    Pages 1-21

  3. Graphs and Data Structures

    • Øyvind Hjelle, Morten Dæhlen
    Pages 23-45

  4. Delaunay Triangulations and Voronoi Diagrams

    • Øyvind Hjelle, Morten Dæhlen
    Pages 47-71

  5. Algorithms for Delaunay Triangulation

    • Øyvind Hjelle, Morten Dæhlen
    Pages 73-93

  6. Data Dependent Triangulations

    • Øyvind Hjelle, Morten Dæhlen
    Pages 95-112

  7. Constrained Delaunay Triangulation

    • Øyvind Hjelle, Morten Dæhlen
    Pages 113-129

  8. Delaunay Refinement Mesh Generation

    • Øyvind Hjelle, Morten Dæhlen
    Pages 131-155

  9. Least Squares Approximation of Scattered Data

    • Øyvind Hjelle, Morten Dæhlen
    Pages 157-192

  10. Programming Triangulations: The Triangulation Template Library (TTL)

    • Øyvind Hjelle, Morten Dæhlen
    Pages 193-222

  11. Back Matter

    Pages 223-234
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Keywords

About this book

This book is entirely about triangulations. With emphasis on computational issues, we present the basic theory necessary to construct and manipulate triangulations. In particular, we make a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. We also discuss various data structures used for the representation of triangulations. Throughout the book we relate the theory to selected applications, in part- ular surface construction, meshing and visualization. The ?eld of triangulation is part of the huge area of computational ge- etry, and over many years numerous books and articles have been written on the subject. Important results on triangulations have appeared in theore- cal books and articles, mostly within the realm of computational geometry. However, many important results on triangulations have also been presented in publications within other research areas, where they have played and play an important role in solving speci?c scienti?c and applied problems. We will touch upon some of these areas in this book. Triangulations, almost everywhere. The early development of triangulation comes from surveying and the art of constructing maps – cartography. S- veyors and cartographers used triangles as the basic geometric feature for calculating distances between points on the Earth’s surface and a position’s elevation above sea level.

Reviews

From the reviews:

"The overall flavor of the book reflects the use of triangulations for the description of planar objects and as the domain for bivariate functions. … The book is meant as a text for a graduate class on triangulations." (Gerald Farin, SIAM Review, Vol. 49 (2), 2007)

Authors and Affiliations

  • Simula Research Laboratory AS, Norway

    Øyvind Hjelle

  • Department of Informatics, University of Oslo, Oslo, Norway

    Morten Dæhlen

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