A Short Course in Computational Geometry and Topology

Başlık:

Yazar:

Edelsbrunner, Herbert. author.

ISBN:

9783319059570

Ek Yazar:

Edelsbrunner, Herbert. author.

Fiziksel Tanım:

IX, 110 p. 64 illus., 60 illus. in color. online resource.

Series:

SpringerBriefs in Applied Sciences and Technology,

Contents:

Roots of Geometry and Topology -- Voronoi and Delaunay Diagrams -- Weighted Diagrams -- Three Dimensions -- Alpha Complexes -- Holes -- Area Formulas -- Topological Spaces -- Homology Groups -- Complex Construction -- Filtrations -- PL Functions -- Matrix Reduction -- Epilogue.

Abstract:

With the aim to bring the subject of Computational Geometry and Topology closer to the scientific audience, this book is written in thirteen ready-to-teach sections organized in four parts: TESSELLATIONS, COMPLEXES, HOMOLOGY, PERSISTENCE. To speak to the non-specialist, detailed formalisms are often avoided in favor of lively 2- and 3-dimensional illustrations. The book is warmly recommended to everybody who loves geometry and the fascinating world of shapes.

Konu Terimleri:

Mathematics.

Computer mathematics.

Manifolds (Mathematics).

Complex manifolds.

Biomathematics.

Biomedical engineering.

Computational Science and Engineering.

Manifolds and Cell Complexes (incl. Diff.Topology).

Mathematical and Computational Biology.

Added Corporate Author:

SpringerLink (Online service)

Electronic Access:

http://dx.doi.org/10.1007/978-3-319-05957-0

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Library	Materyal Türü	Barkod	Yer Numarası	Durum
Searching... Pamukkale Merkez Kütüphanesi	E-Kitap	76145-1001	QA71 -90	Searching... Unknown

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Özet

This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.