Height Functions and Distance Functions

  • Anatolij T. Fomenko
  • Tosiyasu L. Kinii


We now restrict our attention to two classes of functions on surfaces, which have particular importance in computer geometry: height functions and distance functions. In particular, we investigate when such functions are Morse functions. We consider a solid, bounded, connected object in ℝ3, as in Figure 9.1, and assume that it has a smooth boundary. The boundary, therefore, is an orientable compact surface embedded in ℝ3.


Distance Function Focal Point Principal Curvature Measure Zero Regular Point 
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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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