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Height Functions and Distance Functions

  • Anatolij T. Fomenko
  • Tosiyasu L. Kinii

Abstract

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.

Keywords

Distance Function Focal Point Principal Curvature Measure Zero Regular Point 
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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