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A Short Course in Computational Geometry and Topology

A Short Course in Computational Geometry and Topology

Autorzy
Wydawnictwo Springer International Publishing AG
Data wydania 12/05/2014
Liczba stron 110
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
ISBN 9783319059563
Kategorie Geometria analityczna, Topologia, Matematyka i naukowcy
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Opis książki

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.

A Short Course in Computational Geometry and Topology

Spis treści

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.

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