Algorithm 716: TSPACK: tension spline curve-fitting package

ABSTRACT

The primary purpose of TSPACK is to construct a smooth function which interpolates a discrete set of data points. The function may be required to have either one or two continuous derivatives. If the accuracy of the data does not warrant interpolation, a smoothing function (which does not pass through the data points) may be constructed instead. The fitting method is designed to avoid extraneous inflection points (associated with rapidly varying data values) and preserve local shape properties of the data (monotonicity and convexity), or to satisfy the more general constraints of bounds on function values or first derivatives. The package also provides a parametric representation for construction general planar curves and space curves.

REFERENCES

• 1: A. K. Cline, Scalar- and planar-valued curve fitting using splines under tension, Communications of the ACM, v.17 n.4, p.218-220, April 1974 [doi>10.1145/360924.360971]
• 2: DE BOOR, C. A Practical Guide to Spltnes. Springer-Verlag, New York, 1978.
• 3: FRITSCH, F. N., AND BUTLAND, J. A method for constructing local monotone p~ecewise cubic interpolants. SIAM J. Sct. Stat. Comput. 5, 2 (June 1984), 300 304.
• 4: FRITSCH, F. N., AND CARLSON, R. E. Monotone piecewise cubic interpolation. SIAM J. Numer. Anal 17, 2 (Apr. 1988), 238-246.
• 5: David Kahaner , Cleve Moler , Stephen Nash, Numerical methods and software, Prentice-Hall, Inc., Upper Saddle River, NJ, 1989
• 6: RE~NSC}t, C.H. Smoothing by spline functions. Numer. Math. lO (1967), 177-183.
• 7: REINSCH, C.H. Smoothing by spline functions II. Numer. Math. 16 (1971), 451-454.
• 8: R. J. Renka, Interpolatory tension splines with automatic selection of tension factors, SIAM Journal on Scientific and Statistical Computing, v.8 n.3, p.393-415, May 1, 1987 [doi>10.1137/0908041]
• 9: SCHWEIKERT, D. G. An lnterpolatory curve using a spline in tension. J Math. Phys. 45 (1966), 312-317.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Algorithms

Keywords:
convexity preserving, cubic spline, exponential spline, interpolation, monotonicity preserving, parametric curve, piecewise polynomial, shape preserving, smoothing, spline under tension, tension factor