Skip to main content
Log in

Surfaces Generation by Blending Interpolation on a Triangle with One Curved Side

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

We use some interpolation operators and some Bernstein type operators for construction of surfaces which satisfy some given conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Barnhill, R.E.: Blending function interpolation: a survey and some new results. In: Collatz, L., et al. (eds.) Numerishe Methoden der Approximationstheorie, vol. 30, pp. 43–89. Birkhauser, Basel (1976)

  2. Barnhill, R.E.: Representation and approximation of surfaces. In: Rice, J.R. (ed.) Mathematical Software III, pp. 68–119. Academic Press, New-York (1977)

  3. Barnhill R.E., Birkhoff G., Gordon W.J.: Smooth interpolation in triangles. J. Approx. Theory 8, 114–128 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  4. Barnhill R.E., Gregory J.A.: Polynomial interpolation to boundary data on triangles. Math. Comp 29(131), 726–735 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  5. Barnhill R.E., Gregory J.A.: Compatible smooth interpolation in triangles. J. Approx. Theory 15, 214–225 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  6. Barnhill R.E., Gregory J.A.: Sard kernels theorems on triangular domains with applications to finite element error bounds. Numer. Math. 25, 215–229 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  7. Barnhill R.E., Mansfield L.: Error bounds for smooth interpolation in triangles. J. Approx. Theory 11, 306–318 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  8. Birkhoff G.: Interpolation to boundary data in triangles. J. Math. Anal. Appl. 42, 474–484 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  9. Blaga P., Cătinaş T., Coman Gh.: Bernstein-type operators on triangle with one curved side. Mediterr. J. Math. 9(4), 843–855 (2012)

    Article  Google Scholar 

  10. Blaga P., Cătinaş T., Coman Gh.: Bernstein-type operators on triangle with all curved sides. Appl. Math. Comput. 218, 3072–3082 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Böhmer, K., Coman, Gh., Blending interpolation schemes on triangle with error bounds. In: Lecture Notes in Mathematics, vol. 571, pp. 14–37. Springer, Berlin (1977)

  12. Coman Gh., Cătinaş T.: Interpolation operators on a triangle with one curved side. BIT Numer. Math. 50(2), 243–267 (2010)

    Article  MATH  Google Scholar 

  13. Coman Gh., Gânscă I.: Blending approximation with applications in constructions. Buletinul Ştiinţific al Institutului Politehnic Cluj-Napoca 24, 35–40 (1981)

    MATH  Google Scholar 

  14. Coman, Gh., Gânscă. I.: Some practical application of blending approximation II. In: Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca (1986)

  15. Coman Gh., Gânscă I., Ţâmbulea L.: Some new roof-surfaces generated by blending interpolation technique. Stud. Univ. Babeş-Bolyai Math 36(1), 119–130 (1991)

    MATH  Google Scholar 

  16. Coman Gh., Gânscă I., Ţâmbulea L.: Surfaces generated by blending interpolation. Stud. Univ. Babeş-Bolyai Math 38(3), 39–48 (1993)

    MATH  Google Scholar 

  17. Gordon W.J., Wixom J.A.: Pseudo-harmonic interpolation on convex domains. SIAM J. Numer. Anal. 11(5), 909–933 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  18. Gregory, J.A.: A blending function interpolant for triangles. In: Handscomb, D.C. (ed.) Multivariate Approximation, pp. 279–287, Academic Press, London (1978)

  19. Nielson G.M.: The side-vertex method for interpolation in triangles. J. Approx. Theory 25, 318–336 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  20. Nielson G.M.: Minimum norm interpolation in triangles. SIAM J. Numer. Anal. 17(1), 44–62 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  21. Nielson G.M., Thomas D.H., Wixom J.A.: Interpolation in triangles. Bull. Aust. Math. Soc. 20(1), 115–130 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  22. Schumaker, L.L.: Fitting surfaces to scattered data. In: Lorentz, G.G., Chui, C.K., Schumaker, L.L. (eds.) Approximation Theory II, pp. 203–268. Academic Press, London (1976)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Teodora Cătinaş.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cătinaş, T., Blaga, P. & Coman, G. Surfaces Generation by Blending Interpolation on a Triangle with One Curved Side. Results. Math. 64, 343–355 (2013). https://doi.org/10.1007/s00025-013-0318-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00025-013-0318-6

Mathematics Subject Classification (2000)

Keywords

Navigation