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Computer Examination of Surfaces and Morse Functions

  • Anatolij T. Fomenko
  • Tosiyasu L. Kinii

Abstract

This chapter considers the problem of encoding essential information about a compact surface in terms of a finite amount of data that can be stored and manipulated by computer. If all we want is the topological type of a surface, the genus and the orientability are sufficient. But in many applications, we would like to have a rough version of the geometry, and yet we don’t have, or don’t care about, an exact geometric description of the surface. Using Morse theory, it is possible to assign a code, or schematic representation, to a surface. We consider three problems:
  1. (a)

    How to code a Morse function on a smooth manifold, and in particular on a surface.

     
  2. (b)

    How to code a surface using a Morse function defined on it.

     
  3. (c)

    How to reconstruct a surface if we know a coding of it.

     

Keywords

Height Function Compact Surface Morse Function Clinical Dentistry Klein Bottle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Japan 1997

Authors and Affiliations

  • Anatolij T. Fomenko
    • 1
  • Tosiyasu L. Kinii
    • 2
    • 3
  1. 1.Department of Differential Geometry and Application, Faculty of Mathematics and MechanicsMoscow State UniversityMoscowRussia
  2. 2.Laboratory of Digital Art and TechnologyTokyo, 113Japan
  3. 3.Senior Partner of MONOLITH Co. Ltd.Tokyo, 106Japan

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