Homotopies and Surface Generation

  • Anatolij T. Fomenko
  • Tosiyasu L. Kinii


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.


Surface Generation Continuous Version Close Pair Triangulation Method Lower Contour 


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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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