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.
By:
Herbert Edelsbrunner Imprint: Springer International Publishing AG Country of Publication: Switzerland Dimensions:
Height: 235mm,
Width: 155mm,
Spine: 7mm
Weight: 1.942kg ISBN:9783319059563 ISBN 10: 3319059564 Series:SpringerBriefs in Applied Sciences and Technology Pages: 110 Publication Date:12 May 2014 Audience:
Professional and scholarly
,
College/higher education
,
Undergraduate
,
Primary
Format:Paperback Publisher's Status: Active
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.