Triangulations and Applications

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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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.

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

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)

• Simula Research Laboratory AS, Norway

  Øyvind Hjelle

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

  Morten Dæhlen

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