Algorithm 893: TSPACK: tension spline package for curve design and data fitting

ABSTRACT

TSPACK is a curve-fitting package based on exponential tension splines with automatic selection of tension factors. It serves both as a method for data fitting with preservation of shape properties or more general constraints, and as a means of computer aided geometric design of curves in two or three dimensions. The package is based on a translation of Algorithm 716 from Fortran 77 into MATLAB. The translation includes bug corrections, vectorization where possible, and extensions, including a B-spline representation, designed to facilitate curve design as opposed to data fitting. An interactive graphical user interface, not part of the algorithm, is available from the author.

REFERENCES

• 1: Kaklis, P. D. and Karavelas, M. I. 1997. Shape-preserving interpolation in R³. IMA J. Numer. Anal. 17, 373--419.
• 2: Koch, P. E. and Lyche, T. 1989. Exponential B-splines in tension. In Approximation Theory VI, C. K. Chui, L. L. Schumaker and J. D. Ward, Eds. Academic Press, New York, 361--364.
• 3: 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]
• 4: R. J. Renka, Algorithm 716: TSPACK: tension spline curve-fitting package, ACM Transactions on Mathematical Software (TOMS), v.19 n.1, p.81-94, March 1993 [doi>10.1145/151271.151277]
• 5: Schweikert, D. G. 1966. An interpolation curve using a spline in tension. J. Math. Phys. 45, 312--317.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.1 Interpolation

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
  G.4 MATHEMATICAL SOFTWARE

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