# Triangulations and Applications

## Benefits

• Applications-oriented

• Well-written textbook on triangulations

Textbook

Part of the Mathematics and Visualization book series (MATHVISUAL)

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

### 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

1. 1.Simula Research Laboratory ASNorway
2. 2.Department of InformaticsUniversity of OsloOsloNorway

### Bibliographic information

• Book Title Triangulations and Applications
• Authors Øyvind Hjelle
Morten Dæhlen
• Series Title Mathematics and Visualization
• DOI https://doi.org/10.1007/3-540-33261-8
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Hardcover ISBN 978-3-540-33260-2
• Softcover ISBN 978-3-642-06988-8
• eBook ISBN 978-3-540-33261-9
• Series ISSN 1612-3786
• Edition Number 1
• Number of Pages XI, 229
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site

## 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)