On a Possibility of Classification of Part Surfaces

  • Stephen P. RadzevichEmail author


This chapter is devoted to the analysis of a possibility of classification of part surfaces. Irrespective of no scientific classification of smooth regular surfaces in global sense is feasible in nature, local part surface patches can be classified. For the investigation of geometry of local part surface patches planar characteristic images are employed. In this analysis Dupin indicatrix, curvature indicatrix, and circular diagrams at a part surface point are covered in detail. Base on the obtained results of the analysis two more circular charts are developed. One of them employs the part surface curvature indicatrices, while another one is based on the properties of circular diagrams at a current part surface point. This section of the book ends with a brief consideration of one more useful characteristic curve, which can be helpful for analytical description of geometry of a part surface locally.


  1. 1.
    Radzevich, S. P. (1988). Classification of surfaces, Monograph, Kiev, UkrNIINTI, No. 1440-Ук88, 185p.Google Scholar
  2. 2.
    Radzevich, S. P. (2001). Fundamentals of surface generation, monograph, Kiev, Rastan, 592p.Google Scholar
  3. 3.
    Koenderink, J. J. (1990). Solid Shape (p. 699). Cambridge, Massachusetts: The MIT Press.Google Scholar
  4. 4.
  5. 5.
    Radzevich, S. P. (1991). Differential-geometrical method of surface generation (Doctoral Thesis), Tula, Tula Polytechnic Institute, 300p.Google Scholar
  6. 6.
    Radzevich, S. P. (1991). Sculptured Surface Machining on Multi-Axis NC Machine, Monograph, Kiev, Vishcha Schola, 192p.Google Scholar
  7. 7.
    Miron, R. (1958). Observatii a Supra Unor Formule din Geometria Varietatilor Neonolonome \( E_{3}^{2} \).—Bulletinul Institutuini Politechnic din Iasi.Google Scholar
  8. 8.
    Lowe, P. G. (1980). A note on surface geometry with special reference to twist. Mathematical Proceedings of the Cambridge Philosophical Society, 87, 481–487.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lowe, P. G. (1982). Basic principles of plate theory. Surrey University.Google Scholar
  10. 10.
    Nutbourn, A. W. (1986). A circle diagram for local differential geometry. In J. Gregory (Ed.), Mathematics of surfaces, conference proceedings, institute of mathematics and its application, 1984. Oxford: Oxford University Press.Google Scholar
  11. 11.
    Nutbourn, A. W. & Martin, R. R. (1988). Differential geometry applied to curve and surface design, Volume 1: Foundations. Chichester: Ellis Horwood Ltd. Publishers, 282p.Google Scholar
  12. 12.
    Böhm, W. (1990). Differential geometry II, In: Curves and surfaces for computer aided geometric design. A practical guide (2nd edn., pp. 367–383) Boston: Academic Press, Inc. 444p.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Southfield Innovation CenterEaton CorporationSouthfieldUSA

Personalised recommendations