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Homotopies and Surface Generation

  • Anatolij T. Fomenko
  • Tosiyasu L. Kinii

Abstract

Let f: XY and g: XY be two continuous maps between topological spaces X and Y. These maps are called homotopic if there exists a family φ t , for 0 ≤ t ≤ 1, of continuous maps
$${\varphi _t}:X \to Y$$
continuous with respect to t and xX simultaneously, and satisfying φ 0 = f, φ 1 = g. In words, two maps are homotopic if we can go from one to the other by means of a continuous deformation with parameter t ∈ [0, 1]. The family of maps φ t is called a homotopy between X and Y; it can also be regarded as a continuous map Φ :X × [0,1] → Y.

Keywords

Surface Generation Continuous Version Close Pair Triangulation Method Lower Contour 
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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