A Short Course In Computational Geometry And Topology (springerbriefs In Applied Sciences And Technology / Springerbriefs In Mathematical Methods)
by Herbert Edelsbrunner /
2014 / English / PDF
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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.
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.