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Topological Modeling for Visualization

  • Textbook
  • © 1997

Overview

Authors:
  1. Anatolij T. Fomenko

    1. Department of Differential Geometry and Applications, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, Russia

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  2. Tosiyasu L. Kunii

    1. Laboratory of Digital Art and Technology, Tokyo, 113, Japan
      Senior Partner of MONOLITH Co. Ltd., Tokyo, 106, Japan

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (18 chapters)

  1. Front Matter

    Pages ii-x
    Download chapter PDF

  2. Foundation

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Curves

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 3-24

    3. The Notion of a Riemannian Metric

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 25-33

    4. Local Theory of Surfaces

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 35-66

    5. The Classification of Surfaces

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 67-94

    6. Abstract Manifolds

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 95-104

    7. Critical Points and Morse Theory

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 105-125

    8. Application: Analyzing Human Body Motions Using Manifolds and Critical Points

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 127-137

    9. Computer Examination of Surfaces and Morse Functions

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 139-180

    10. Height Functions and Distance Functions

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 181-190

    11. Homotopies and Surface Generation

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 191-210

    12. Homology

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 211-244

    13. Geodesics

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 245-261

    14. Transformation Groups

      • Anatolij T. Fomenko, Tosiyasu L. Kinii
      Pages 263-286
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Differential Geometry and Applications, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, Russia

    Anatolij T. Fomenko

  • Laboratory of Digital Art and Technology, Tokyo, 113, Japan

    Tosiyasu L. Kunii

  • Senior Partner of MONOLITH Co. Ltd., Tokyo, 106, Japan

    Tosiyasu L. Kunii

Bibliographic Information

  • Book Title: Topological Modeling for Visualization

  • Authors: Anatolij T. Fomenko, Tosiyasu L. Kunii

  • DOI: https://doi.org/10.1007/978-4-431-66956-2

  • Publisher: Springer Tokyo

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Japan 1997

  • Softcover ISBN: 978-4-431-66958-6Published: 03 October 2013

  • eBook ISBN: 978-4-431-66956-2Published: 17 April 2013

  • Edition Number: 1

  • Number of Pages: X, 395

  • Number of Illustrations: 414 b/w illustrations, 16 illustrations in colour

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Visualization, Computer Graphics

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