Algorithm 752: SRFPACK: software for scattered data fitting with a constrained surface under tension

ABSTRACT

SRFPACK is a Fortran 77 software package that constructs a smooth interpolatory or approximating surface to data values associated with arbitrarily distributed points in the plane. It employs automatically selected tension factors to preserve shape properties of the data and to avoid overshoot and undershoot associated with steep gradients. The domain of the fitting function may be nonconvex or multiply connected, and the surface may be constrained to have discontinuous value or derivative across a user-specified curve representing, for example, a geological fault line. Although triangle based, the method provides a means of avoiding the inaccuracy associated with long thin triangles on the boundary of the convex hull of the data abscissae.

REFERENCES

• 1: CLOUCH, R. W. AND TOCHER, J.L. 1965. Finite element stiffness matrices for analysis of plates in bending. In Proceedings of the Conference on Matrix Methods in Structural Mechanics. Air Force Inst. of Technology, Wright Patterson A.F.B., Dayton, Ohio.
• 2: F~.~KE, R. AND NIrLSON, G. M. 1983. Surface approximation with imposed conditions. In Surfaces in Computer Aided Geometric Design, R. E. Barnhill and W. Boehm, Eds. North Holland, Amsterdam, 135-146.
• 3: LAWSON, C. L, 1984. Cl surface interpolation for scattered data on a sphere. Rocky Mount. J. Math. 14, 1 (Winter), 177-202.
• 4: PRUESS, S.1978. An algorithm for computing smoothing splines in tension. Computing 19, 4, 365 373.
• 5: REINSCH, C.H. 1967. Smoothing by spline functions, Num. Math. 10, 177-183.
• 6: REtNSCH, C.H. 1971. Smoothing by spline functions IL Num. Math. 16, 451-454.
• 7: Robert J. Renka, Algorithm 624: Triangulation and Interpolation at Arbitrarily Distributed Points in the Plane, ACM Transactions on Mathematical Software (TOMS), v.10 n.4, p.440-442, Dec. 1984 [doi>10.1145/2701.356108]
• 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: 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]
• 10: R. J. Renka, Algorithm 751: TRIPACK: a constrained two-dimensional Delaunay triangulation package, ACM Transactions on Mathematical Software (TOMS), v.22 n.1, p.1-8, March 1996 [doi>10.1145/225545.225546]
• 11: RENKn, R. J. AND CLINE, A.K. 1984. A triangle-based Cl interpolation method. Rocky Mount. J. Math. 14, 1 (Winter)223-237.
• 12: RENKA, R. J. AND CLINE, A. K. 1992. Scattered data fitting using a constrained Delaunay triangulation. In IMACS Transactions on Scientific Computing 91. Vol. 3, Aft, Expert Systems, and Symbolic Computation. North Holland, Amsterdam.

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: FORTRAN

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.1 Interpolation
      G.1.2 Approximation
  G.4 MATHEMATICAL SOFTWARE

General Terms:
Algorithms

Keywords:
interpolation, scattered data fitting, smoothing, surface under tension