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Topological Modeling for Visualization

  • Kartonierter Einband
  • 408 Seiten
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The flood of information through various computer networks such as the In ternet characterizes the world situation in which we liv... Weiterlesen
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Beschreibung

The flood of information through various computer networks such as the In ternet characterizes the world situation in which we live. Information worlds, often called virtual spaces and cyberspaces, have been formed on computer networks. The complexity of information worlds has been increasing almost exponentially through the exponential growth of computer networks. Such nonlinearity in growth and in scope characterizes information worlds. In other words, the characterization of nonlinearity is the key to understanding, utiliz ing and living with the flood of information. The characterization approach is by characteristic points such as peaks, pits, and passes, according to the Morse theory. Another approach is by singularity signs such as folds and cusps. Atoms and molecules are the other fundamental characterization ap proach. Topology and geometry, including differential topology, serve as the framework for the characterization. Topological Modeling for Visualization is a textbook for those interested in this characterization, to understand what it is and how to do it. Understanding is the key to utilizing information worlds and to living with the changes in the real world. Writing this textbook required careful preparation by the authors. There are complex mathematical concepts that require designing a writing style that facilitates understanding and appeals to the reader. To evolve a style, we set as a main goal of this book the establishment of a link between the theoretical aspects of modern geometry and topology, on the one hand, and experimental computer geometry, on the other.

Klappentext

The main goal of this textbook is to establish a bridge between the theoretical aspects of modern geometry and topology on the one hand and computer experimental geometry on the other. Thus the theory and application of mathematical visualization are given equal emphasis. This, along with the ample illustrations and the fact that each chapter is designed as an independent unit, makes Topological Modeling for Visualization a unique book in its field. The two internationally famous authors, A. T. Fomenko and T. L. Kunii, thoroughly explain the necessary mathematical techniques so that undergraduate students with only a grounding in high-school mathematics can benefit from using this book. While linear problems are covered, the emphasis is on nonlinear problems, with many examples relating to natural phenomena and todays abundant information sources. Students in the fields of mathematics and computing will find it rigorous enough to serve as a basic text in differential geometry and topology, while students from fields as diverse as cognitive science and economics who need to solve nonlinear problems will find this book indispensable.



Inhalt

Part I: Foundation: Curves. The Notion of a Riemannian Metric. Local Theory of Surfaces. The Classification of Surfaces. Abstract Manifolds. Critical Points and Morse Theory. Analyzing Human Body Motions Using Manifolds and Critical Points. Computer Examination of Surfaces and Morse Functions. Height Functions and Discrete Functions. Homotopies and Surface Generation. Homology. Geodesics. Transformation Groups.- Part II: Advanced Subjects: Hyperbolic Geometry and Topology. Hamiltonian System with Two Degrees of Freedom. Topological and Orbital Analysis of Integrable Problems. Orbital Invariant of Integrable Hamiltonian Systems. Ridges, Ravines and Singularities.- Bibliography.- Index.

Produktinformationen

Titel: Topological Modeling for Visualization
Autor:
EAN: 9784431669586
ISBN: 4431669582
Format: Kartonierter Einband
Herausgeber: Springer Japan
Anzahl Seiten: 408
Gewicht: 616g
Größe: H235mm x B155mm x T21mm
Jahr: 2013
Auflage: Softcover reprint of the original 1st ed. 1997