Connections of Patches by Blending

  • Mamoru Hosaka
Part of the Computer Graphics — Systems and Applications book series (COMPUTER GRAPH.)


Generally, when we have to define a surface patch, its degree of freedom is not always equal to that of given external conditions. If the latter is greater than the former, there must be some relations among the given conditions, or some methods must be provided to increase the degree of freedom of the patch to satisfy the given conditions.


Tangent Vector Boundary Curve Contour Curve Convex Corner Triangular Patch 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Coons S.A.: Surfaces for computer aided design of space forms. MIT Project MAC TR-41 1967Google Scholar
  2. [2]
    Gregory J.A.: Smooth interpolation without twist constaints. In: Burnhill, R.E., Riesenfeld, R.F.(eds.): Computer aided geometrric design, New York: Academic Press 1974, pp. 71–87Google Scholar
  3. [3]
    Sabin, M.A.: The use of piecewise forms for the numerical representation of shape. Computer and Automation Inst. Hungarian Academy of Sci. 1977Google Scholar
  4. [4]
    Barnhill, R.E., Brown, J.H., Klucewicz I.M.: A new twist in computer aided geometric design. Computer Graphics and Image Processing 8: 78–91, 1978CrossRefGoogle Scholar
  5. [5]
    Higashi, M. et. al.: An interactive CAD systems for construction of shapes with high quality surface. In: Warman, E.A. (ed.): Proc. CAPE’83 IFIP 1983, pp. 371–390Google Scholar
  6. [6]
    Chiyokura, H., Kimura, F.: Design of solids with free-form surfaces. Computer Graphics 17 (3): 289–298, 1983CrossRefGoogle Scholar
  7. [7]
    Hosaka, M., Kimura, F.: Non-four-sided patch expressions with control. points. Computer Aided Geometric Design 1 (1): 75–86, 1984MATHCrossRefGoogle Scholar
  8. [8]
    Charrot, P., Gregory, J.A.: A pentagonal surface patch for CAGD. Computer Aided Geometric Design 1 (1): 87–94, 1984MATHCrossRefGoogle Scholar
  9. [9]
    Herron, G.: Smooth closed surface with triangular interpolants. Computer Aided Geometric Design 2 (4): 297–306, 1985MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    Farin G. Triangular Bernstein-Bezier patches. Computer Aided Geometric Design 3 (2): 83–127, 1986MathSciNetCrossRefGoogle Scholar
  11. [11]
    Sabin, M. A.: Some negtive results in N sided patches. Computer Aided Design 18 (1): 38–44, 1986CrossRefGoogle Scholar
  12. [12]
    Chiyokura, H.: Localized surface interpolation method for irregular meshes. In: Kunii, T. (ed.): Computer Graphics. Berlin: Springer-Verlag, 1986Google Scholar
  13. [13]
    Holmstroem, L.: Piecewise quadric blending of implicitly defined surface. Computer Aided Geometric Design 4: 171–189, 1987MathSciNetCrossRefGoogle Scholar
  14. [14]
    Shirman, L.A., Sequin, C.H.: Local surface interpolation with Bézier patches. Computer Aided Geometric Design 4 (4): 279–295, 1987MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    van Wijk J.J.: Bicubic patch for approximating non-rectangular meshes. Computer Aided Geometric Design 3 (1): 1–14, 1987CrossRefGoogle Scholar
  16. [16]
    Farin, G. et al.: The octant of a sphere as a non-degenerate triangular patch. Computer Aided Geometric Design 4 (4): 329–332, 1987MathSciNetMATHCrossRefGoogle Scholar
  17. [17]
    Storry, D.J.T., Ball, A.A.: Design of an n-sided surface patch from Her mite boundary data. Computer Aided Geometric Design 6 (2): 111–120, 1989MathSciNetMATHCrossRefGoogle Scholar
  18. [18]
    Kushimoto, T., Hosaka, M.: *Design methods of surface in non-four-sided regions. 1, J.JSPE 55(08): 55-60, 1989. 2, J.JSPE 55 (11): 119–124, 1989Google Scholar
  19. [19]
    Kushimoto, T., Hosaka, M.: *Connection of triangular patches and its application. J. JSPE 55 (10): 67–72, 1989Google Scholar
  20. [20]
    Saitoh, T., Hosaka, M.: Interpolating curve networks with new blending patches. In: Vandoni, C.E., Duce, D.A. (eds.): Proc. Eurographics’90, pp. 137–146Google Scholar
  21. [21]
    Hosaka, M.: *New solution of connection problem in free-form surfaces. J. IPS Japan 31 (5): 612–622, 1990Google Scholar
  22. [22]
    Peters, J.: Local cubic and bicubic C1 surface interpolation with linearly varying boundary normal. Computer Aided Geometric Design 7: 499–516, 1990MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Mamoru Hosaka
    • 1
  1. 1.Tokyo Denki UniversityChiyoda-ku, TokyoJapan

Personalised recommendations