# Triangulations and Applications

• Øyvind Hjelle
• Morten Dæhlen
Book

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

• 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