A Short Course in Computational Geometry and Topology (eBook)

Herbert Edelsbrunner (Autor)

eBook Download: PDF

2014 | 2014
IX, 110 Seiten
Springer International Publishing (Verlag)
978-3-319-05957-0 (ISBN)

Infos

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.

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.

Produkt-Details

• Erscheint lt. Verlag: 28.4.2014
• Reihe/Serie: SpringerBriefs in Applied Sciences and Technology
• Reihe/Serie: SpringerBriefs in Applied Sciences and Technology
• Reihe/Serie: SpringerBriefs in Mathematical Methods
• Reihe/Serie: SpringerBriefs in Mathematical Methods
• Zusatzinfo: IX, 110 p. 64 illus., 60 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Schlagworte: Alpha Complexes • Computational Biology • Delaunay Triangulations • Persistent Homology • Protein Folding and Protein Docking • Simplicial Complexes • Voronoid Diagrams
• ISBN-10: 3-319-05957-2 / 3319059572
• ISBN-13: 978-3-319-05957-0 / 9783319059570