A Short Course in Computational Geometry and Topology

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Beschreibung

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.

Presents a short course in computational geometry and topology

Provides exercises at the end of each chapter

Written by an expert in the field



Klappentext

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.



Inhalt
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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Produktinformationen

Titel
A Short Course in Computational Geometry and Topology
Autor
EAN
9783319059563
ISBN
3319059564
Format
Kartonierter Einband
Herausgeber
Springer International Publishing
Anzahl Seiten
120
Gewicht
195g
Größe
H235mm x B155mm x T6mm
Jahr
2014
Untertitel
Englisch
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