Edelsbrunner A Short Course in Computational Geometry and Topology

1. Auflage 2014
ISBN: 978-3-319-05957-0
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 110 Seiten

Reihe: Mathematics and Statistics (R0)

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.

Zielgruppe

Research

Autoren/Hrsg.

Edelsbrunner, Herbert

Inhaltsverzeichnis

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.