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Triangulations and Applications

Øyvind Hjelle, Morten Dæhlen (Autoren)

Buch | Hardcover

XI, 229 Seiten

2006 | 2006
Springer Berlin (Verlag)
978-3-540-33260-2 (ISBN)

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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.

Triangles and Triangulations.- Graphs and Data Structures.- Delaunay Triangulations and Voronoi Diagrams.- Algorithms for Delaunay Triangulation.- Data Dependent Triangulations.- Constrained Delaunay Triangulation.- Delaunay Refinement Mesh Generation.- Least Squares Approximation of Scattered Data.- Programming Triangulations: The Triangulation Template Library (TTL).

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)

Erscheint lt. Verlag	13.9.2006
Reihe/Serie	Mathematics and Visualization
Zusatzinfo	XI, 229 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	563 g
Themenwelt	Informatik ► Software Entwicklung ► User Interfaces (HCI)
	Mathematik / Informatik ► Mathematik ► Graphentheorie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	algorithm • algorithms • Approximation • Computational Geometry • data structure • data structures • Mesh Generation • Optimization • programming • Surface modeling • Triangulation • triangulations • Visualization
ISBN-10	3-540-33260-X / 354033260X
ISBN-13	978-3-540-33260-2 / 9783540332602
Zustand	Neuware