Computational Topology Iisc
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A Short Course in Computational Geometry and Topology
Author: Herbert Edelsbrunner
language: en
Publisher: Springer Science & Business
Release Date: 2014-04-28
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.
Geometric Approximation Algorithms
Author: Sariel Har-Peled
language: en
Publisher: American Mathematical Soc.
Release Date: 2011
Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.
Topology Optimization
Author: Martin Philip Bendsoe
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-04-17
"The art of structure is where to put the holes" Robert Le Ricolais, 1894-1977 This is a completely revised, updated and expanded version of the book titled "Optimization of Structural Topology, Shape and Material" (Bends0e 1995). The field has since then developed rapidly with many new contributions to theory, computational methods and applications. This has that a simple editing of Bends0e (1995) had to be superseded by what meant is to a large extent a completely new book, now by two authors. This work is an attempt to provide a unified presentation of methods for the optimal design of topology, shape and material for continuum and discrete structures. The emphasis is on the now matured techniques for the topology design of continuum structures and its many applications that have seen the light of the day since the first monograph appeared. The technology is now well established and designs obtained with the use of topology optimization methods are in production on a daily basis. The efficient use of materials is important in many different settings. The aerospace industry and the automotive industry, for example, apply sizing and shape optimization to the design of structures and mechanical elements.