Multivariate spline and its applications in science and technology

  • Ren-Hong Wang


Algebraic Curve Algebraic Curf Interior Vertex Interior Edge Singular Vertex 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P. Alfeld, B. Piper, L.L. Schumaker, SIAM, J. Numer. Anal., Vol. 24, No. 4 (1987), pp. 891–911.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    P. Alfeld, B. Piper, L.L. Schumaker, CAGD, 4(1987), pp. 105–123.MATHMathSciNetGoogle Scholar
  3. [3]
    L.J. Billera, Trans. Amer. Math. Soc., 310(1988), pp. 325–340.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    L.J. Billera, L.L. Rose, Discrete Comp. Geom., 6(1991), pp. 107–128.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Y.S. Chui, L.Y. Su, R.H. WangIn Multivariate Approx. Theorey III, Birkhauser Basel, 1985, pp. 71–83Google Scholar
  6. [6]
    Y.S. Chui, T.X. He, R.H. Wang, Coll. Math. Soc. J. Bolyai 49, 1985.Google Scholar
  7. [7]
    Y.S. Chui, R.H. Wang, J. Math. Anal. Appl., 92(1983), pp. 533–551.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Y.S. Chui, R.H. Wang, ibid, J. Math. Anal. Appl., 101 (1984).Google Scholar
  9. [9]
    Y.S. Chui, R.H. Wang, Scientia Sinica (A), 27 (1984), pp. 1129–1142.MATHMathSciNetGoogle Scholar
  10. [10]
    G. Farin, Worsey,CAGD, 1987Google Scholar
  11. [11]
    D. Hong, Approx. Theory & Appl., 1(1991), pp. 56–75Google Scholar
  12. [12]
    Z.X. LuoResearch on non-linear spline functions, Ph.D. Thesis, Dalian Univ. of Tech., 1991Google Scholar
  13. [13]
    Z.X. Luo, R.H. Wang, J. Math. Res. Exposition, 12(1992), pp. 579–582.MATHMathSciNetGoogle Scholar
  14. [14]
    Z.X. Luo, R.H. Wang, J. Dalian Univ. of Tech., 33(1993), pp. 621–627.MATHMathSciNetGoogle Scholar
  15. [15]
    J. Morgan, R. ScottThe dimension of the space of C 1 piecewise polynomials, Unpublished manuscript.Google Scholar
  16. [16]
    J. Morgan, R. Scott, Math. Comp., 29(1975), pp. 736–740.MATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    G. Nürnberg, Th. RiessingerLagrange and Hermite interpolation by bivariate splines, report Univ. of Mannheim, No. 109, 1990.Google Scholar
  18. [18]
    M.J. Powell, M.A. Sabin, ACM Trans. Math. Software., 3(1977), pp. 316–325.MATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    X.Q. Shi, CAGD, 8(1991), pp. 201–206.MATHGoogle Scholar
  20. [20]
    X.Q. Shi, J. Comp. Math., 10(1992), pp. 224–230.MATHGoogle Scholar
  21. [21]
    X.Q. ShiHigher dimensional splines, Ph.D. Thesis, Jilin Univ., 1988.Google Scholar
  22. [22]
    X.Q. Shi, R.H. WangDecomposition method for studying multivariate splines, J. Math. Res. Exposition, to appear.Google Scholar
  23. [23]
    X.Q. ShiThe, piecewise algebraic curves, Surfaces, and their applications in CAGD, Ph.D. thesis, Dalian Univ. of tech., 1993.Google Scholar
  24. [24]
    R.H. Wang, Acta Math. Sinica, 18(1975), pp. 91–106.MATHMathSciNetGoogle Scholar
  25. [25]
    R.H. Wang, Scientitia Sinica, Math. I(1979), pp. 215–226.Google Scholar
  26. [26]
    R.H. Wang, Numer., Math. J. Chineese Univ., 1(1980), pp. 78–81.Google Scholar
  27. [27]
    R.H. Wang, Proc. Asian Math. Conf. 1990, World Sci. 1992, pp. 474–477.Google Scholar
  28. [28]
    R.H. Wang, Proc. of the 1st China-Japan Seminar on Numer. Math., Aug. 1992, World Sci. 1993, pp. 184–191.Google Scholar
  29. [29]
    R.H. Wang, X.Z. LiangApproximation of multivariate functions, Sci. Press, Beijing, 1988.Google Scholar
  30. [30]
    R.H. Wang, X.G. Lu, Scientitia Sinica (A), 6(1988), pp. 585–594.MathSciNetGoogle Scholar
  31. [31]
    R.H. Wang, X.Y. QianIntersection of two piecewise algebraic curves Google Scholar
  32. [32]
    R.H. Wang, X.Q. ShiA kind of cubic C 1 interpolation in the n-dimensional finite elements method, Res. Report, Inst. of Math., Jilin Univ. 1987; J. Math. Res. Exposition, 1989.Google Scholar
  33. [33]
    R.H. Wang, R. Van DammeCurve interpolation with constrained length, submitted.Google Scholar
  34. [34]
    R.H. Wang, B.Z. YinSequence decomposition method for computing a Gröbner basis and its application in bivariate splines. Submitted.Google Scholar
  35. [35]
    R.H. Wang, Y.W. ZhanOn the C 2 interpolation over Morgan-Scotl split. Submitted.Google Scholar
  36. [36]
    X.S. Wang, Northeastern Math. J., 2(1986), pp. 67–71.Google Scholar
  37. [37]
    P. Zwart, SIAM J. Numer. Anal. (1973).Google Scholar

Copyright information

© Birkhäuser-Verlag 1993

Authors and Affiliations

  • Ren-Hong Wang
    • 1
  1. 1.Dalian University oh TechnologyChina

Personalised recommendations