Triangulations and Applications

  • Øyvind Hjelle
  • Morten Dæhlen

Part of the Mathematics and Visualization book series (MATHVISUAL)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Øyvind Hjelle, Morten Dæhlen
    Pages 1-21
  3. Øyvind Hjelle, Morten Dæhlen
    Pages 23-45
  4. Øyvind Hjelle, Morten Dæhlen
    Pages 47-71
  5. Øyvind Hjelle, Morten Dæhlen
    Pages 73-93
  6. Øyvind Hjelle, Morten Dæhlen
    Pages 95-112
  7. Øyvind Hjelle, Morten Dæhlen
    Pages 113-129
  8. Øyvind Hjelle, Morten Dæhlen
    Pages 131-155
  9. Øyvind Hjelle, Morten Dæhlen
    Pages 157-192
  10. Øyvind Hjelle, Morten Dæhlen
    Pages 193-222
  11. Back Matter
    Pages 223-234

About this book

Introduction

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.

Keywords

Approximation Computational geometry Mesh generation Surface modeling Triangulation Triangulations algorithm algorithms data structure data structures optimization programming visualization

Authors and affiliations

  • Øyvind Hjelle
    • 1
  • Morten Dæhlen
    • 2
  1. 1.Simula Research Laboratory ASNorway
  2. 2.Department of InformaticsUniversity of OsloOsloNorway

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-33261-8
  • Copyright Information Springer 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-33260-2
  • Online ISBN 978-3-540-33261-9
  • Series Print ISSN 1612-3786
  • About this book