Logo - springer
Slogan - springer

Mathematics - Computational Science & Engineering | Triangulations and Applications

Triangulations and Applications

Hjelle, Øyvind, Dæhlen, Morten

2006, XI, 229 p.

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$59.95

(net) price for USA

ISBN 978-3-540-33261-9

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$74.95

(net) price for USA

ISBN 978-3-540-33260-2

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$74.95

(net) price for USA

ISBN 978-3-642-06988-8

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

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.

Content Level » Research

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

Related subjects » Computational Intelligence and Complexity - Computational Science & Engineering - Earth Sciences & Geography - Image Processing

Table of contents 

1 Triangles and Triangulations 1.1 Triangles 1.2 Triangulations 1.3 Some properties of triangulations 1.4 A Triangulation Algorithm 1.5 Edge Insertion 1.6 Using Triangulations 1.7 Exercises 2 Graphs and Data Structures 2.1 Graph Theoretic Concepts 2.2 Generalized Maps (G-maps) 2.3 Data Structures for Triangulations 2.4 A Minimal Triangle-Based Data Structure 2.5 Triangle-Based Data Structure with neighbors 2.6 Vertex-Based Data Structure with neighbors 2.7 Half-Edge Data Structure 2.8 Dart-Based Data Structure 2.9 Triangles for visualization 2.10 Binary Triangulations 2.11 Exercises 3 Delaunay Triangulations and Voronoi Diagrams 3.1 Optimal Triangulations 3.2 The Neutral Case 3.3 Voronoi diagrams 3.4 Delaunay Triangulation as the Dual of the Voronoi Diagram 3.5 The Circle Criterion 3.6 Equivalence of the Delaunay Criteria for Strictly Convex Quadrilaterals 3.7 Computing the Circumcircle Test 3.8 The Local Optimization Procedure (LOP) 3.9 Global Properties of the Delaunay Triangulation 3.10 Exercises 4 Algorithms for Delaunay Triangulation 4.1 A Simple Algorithm Based on Previous Results 4.2 Radial Sweep 4.3 A Step-by-Step Approach for Making Delaunay Triangles 4.4 Incremental Algorithms 4.5 Inserting a Point into a Delaunay Triangulation 4.6 Point Insertion and Edge-Swapping 4.7 Running Time of Incremental Algorithms 4.8 Divide-and-Conquer 4.9 Exercises 5 Data Dependent Triangulations 5.1 Motivation 5.2 Optimal Triangulations Revisited 5.3 The General Concept 5.4 Data Dependent Swapping Criteria 5.5 On Implementation of the LOP 5.6 Modified Local Optimization Procedures (MLOP) 5.7 Simulated Annealing 5.8 Exercises 6 Constrained Delaunay Triangulation 6.1 Delaunay Triangulation of a Planar Straight-Line Graph 6.2 Generalization of Delaunay Triangulation 6.3 Algorithms for Constrained Delaunay Triangulation 6.4 Inserting an Edge into a CDT 6.5 Edge Insertion and Swapping 6.6 Inserting a Point into a CDT 6.7 Exercises 7 Delaunay Refinement Mesh Generation 7.1 Introduction 7.2 General Requirements for Meshes 7.3 Node Insertion 7.4 Splitting Encroached Segments 7.5 The Delaunay Refinement Algorithm 7.6 Minimum Edge Length and Termination 7.7 Corner-Lopping for Handling Small Input Angles 7.8 Spatial Grading 7.9 Exercises 8 Least Squares Approximation of Scattered Data 8.1 Another Formulation of Surface Triangulations 8.2 Approximation over Triangulations of Subsets of Data 8.3 Existence and Uniqueness 8.4 Sparsity and Symmetry 8.5 Penalized Least Squares 8.6 Smoothing Terms for Penalized Least Squares 8.7 Approximation over General Triangulations 8.8 Weighted Least Squares 8.9 Constrained Least Squares 8.10 Approximation over Binary Triangulations 8.11 Numerical Examples for Binary Triangulations 8.12 Exercises 9 Programming Triangulations: The Triangulation Template Library (TTL) 9.1 Implementation of the Half-Edge Data Structure 9.2 The Overall Design and the Adaptation Layer 9.3 Topological Queries and the Dart Class 9.4 Some Iterator Classes 9.5 Geometric Queries and the Traits Class 9.6 Geometric and Topological Modifiers 9.7 Generic Delaunay Triangulation 9.8 Exercises References Index

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Visualization.