The Visual Computer

, Volume 11, Issue 10, pp 513–525 | Cite as

Variable-radius blending of parametric surfaces

  • Jung-Hong Chuang
  • Ching-Huei Lin
  • Wei-Chung Hwang
Orginal Articles

Abstract

The radius blend is a popular surface blending because of its geometric simplicity. A radius blend can be seen as the envelope of a rolling sphere or sweeping circle that centers on a spine curve and touches the surface to be blended along the linkage curves. For a given pair of base surfaces in parametric form, a reference curve, and a radius function of the rolling sphere, we present an exact representation for the variable-radius spine curve and propose a marching procedure. We describe methods that use the derived spine curve and linkage curves to compute a parametric form of the variable-radius sphearical and circular blends.

Key words

Geometric modeling Blending Variable-radius spherical and circular blend 

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References

  1. 1.
    Bajaj CL, Hoffmann CM, Lynch RE, Hopcroft J (1988) Tracing surface intersections. Comput Aided Geometric Design 5:285–307MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Bardis L, Patrikalakis NM (1989) Blending rational B-spline surfaces. In: Hansmann W, Hopgood FRA, Strasser W (eds) Proceedings of Eurographics '89. North-Holland, Amsterdam, pp 453–462.Google Scholar
  3. 3.
    Barnhill RE, Farin GE, Chen Q (1993) Constant-radius blending of parametric surfaces. In: Farin GE, Hagen H, Noltemeier H (eds) Geometric Modeling. Springer, Berlin Heidelberg New York, pp 1–20Google Scholar
  4. 4.
    Buchberger B (1985) Gröbner basis: an algorithmic method in polynomial ideal theory. In: Bose NK (ed) Multidimensional systems theory. Reidel, Holland, pp. 184–232Google Scholar
  5. 5.
    Chandru V, Dutta, D., Hoffmann CM (1990) Variable radius blending using Dupin cyclides. In: Wozny MJ, Turner JU, Preiss K (eds) Geometric modeling for product engineering. North-Holland, Amsterdam, pp 39–57Google Scholar
  6. 6.
    Chiyokura H (1988) Solid modelling with DESIGNBASE. Addison Wesley, SingaporeGoogle Scholar
  7. 7.
    Choi BK (1991) Surface modeling for CAD/CAM. Elsevier, AmsterdamGoogle Scholar
  8. 8.
    Choi BK, Ju SY (1989) Constant-radius blending in surface modelling. Comput Aided Design 21:213–220MATHCrossRefGoogle Scholar
  9. 9.
    Chuang JH, Lien FL (1995) One and two-parameter blending for parametric surfaces. In: Shin SY, Kunii TL (eds) Computer graphics and applications. World Scientific, Singapore, pp 333–347.Google Scholar
  10. 10.
    Filip DJ (1989) Blending parametric surfaces. ACM Trans Graph 8:164–173MATHCrossRefGoogle Scholar
  11. 11.
    Harada T, Konno K, and Chiyokura H (1991) Variableradius blending by using Gregory patches in geometric modeling. Proceedings of Eurographics '91. North-Holland, Amsterdam, pp 507–518Google Scholar
  12. 12.
    Hoffmann CM (1990) A dimensionality paradigm for surface interrogations. Comput Aided Geometric Design 7:517–532MATHCrossRefGoogle Scholar
  13. 13.
    Hoffmann CM, Hopcroft J (1987) The potential method for blending surfaces and corners. In: Farin G (ed) Geometric modeling: algorithms and new trends. SIAM Publications, USA, pp 347–365Google Scholar
  14. 14.
    Klass R, Kuhn B (1992) Fillet and surface intersections defined by rolling balls. Comput Aided Geometric Design 9:185–193MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Koparkar P (1991) Designing parametric blends: surface model and geometric correspondence. Visual Comput 7:39–58CrossRefGoogle Scholar
  16. 16.
    Lee T, Bedi S, Dubey RN (1993) A parametric surface blending method for complex engineering objects. In: Rossignac J, Turner J, Allen G (eds) Proceeding of the 2nd Symposium on Solid Modeling and Applications, Montreal, Canada, ACM, New York, pp 179–188Google Scholar
  17. 17.
    Middleditch AE, Sears KH (1985) Blend surfaces for set theoretic volume modelling systems. Comput Graph 19:161–170Google Scholar
  18. 18.
    Pegna J, Wilde DJ (1990) Spherical and circular blending of functional surfaces. Transactions of the ASME. J Offshore Mech Arctic Eng 112:134–142Google Scholar
  19. 19.
    Plass M, Stone M (1983) Curve-fitting with piecewise parametric curves. Comput Graph 17:229–239Google Scholar
  20. 20.
    Rockwood AP, Owen JC (1987) Blending surfaces in solid modeling. In: Farin GE (ed) Geometric modeling: algorithms and new trends. SIAM Publications. USA, pp 367–383Google Scholar
  21. 21.
    Sanglikar MA, Koparkar P, Joshi VN (1990) Modelling rolling ball blends for computer aided geometric design. Comput Aided Geometric Design 7:399–414MATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    Vaishnav H, rockwood A (1993) Blending parametric objects by implicit techniques. In: Rossignac J, Turner J, Allen G (ed) Proceeding of 2nd Symposium on Solid Modeling and Applications, Montreal, Canada, ACM, New York, pp 165–168Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Jung-Hong Chuang
    • 1
  • Ching-Huei Lin
    • 1
  • Wei-Chung Hwang
    • 1
  1. 1.Department of Computer Science and Information EngineeringNational Chiao Tung UniversityHsinchuTaiwan, Republic of China

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