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ESTS1197 WFSFIT.

WFSFIT, Wilson-Fowler Spline Fit Algorithm

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1. NAME OR DESIGNATION OF PROGRAM:  WFSFIT.
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2. COMPUTERS
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Program name Package id Status Status date
WFSFIT ESTS1197/01 Arrived 23-JAN-2001

Machines used:

Package ID Orig. computer Test computer
ESTS1197/01 Many Computers
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3. DESCRIPTION OF PROGRAM OR FUNCTION

WFSFIT is a legacy algorithm introduced in the early 1960s for passing a smooth curve through a planar set of design points.  WFSFIT predates b-spline methods, but is still used in some numeric control systems, e.g., APT.
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4. METHODS

In generating a smooth curve, the basic idea is to come as close as possible to the true spline which minimizes the energy of the curve with a curve composed of cubic segments which are joined together to achieve continuous tangent and curvatures. This is accomplished by introducing a local u,v-coordinate system for each segment with the independent variable running along the chord. The curvature matching conditions lead to a tridiagonal nonlinear system of equations which must be solved by an iterative method.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Numerical accuracy will vary with the format of floating point number representation.
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6. TYPICAL RUNNING TIME

Running time varies with input and is not particularly CPU intensive.
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7. UNUSUAL FEATURES:  WFSFIT implements an archaic algorithm.
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8. RELATED OR AUXILIARY PROGRAMS
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9. STATUS
Package ID Status date Status
ESTS1197/01 23-JAN-2001 Masterfiled Arrived
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10. REFERENCES
ESTS1197/01, included references:
- Fowler, A.H. and Wilson, C.W.:
Cubic Spline, A Curve Fitting Routine, Y-1400 (Revision 1) (June 28, 1966)
- Fritsch, F.N.:
History of the Wilson-Fowler Spline, UCID-20746 (April 1986)
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11. HARDWARE REQUIREMENTS
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
ESTS1197/01 FORTRAN-77
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13. SOFTWARE REQUIREMENTS:  WFSFIT runs on any FORTRAN 77 capable computer.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS
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15. NAME AND ESTABLISHMENT OF AUTHORS

                 F. Fritsch
                 Lawrence Livermore National Laboratory
                 Livermore, California, U. S. A.
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16. MATERIAL AVAILABLE
ESTS1197/01
Readme  Readme file
nwf03 Source code
nwf16 Source code
splin  data file
spline0.19 data file
splout0.19D
writup0.19  write up file
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17. CATEGORIES
  • I. Deformation and Stress Distributions, Structural Analysis and Engineering Design Studies
  • P. General Mathematical and Computing System Routines

Keywords: interpolation, mathematical routines, polynomials, series expansion, spline functions.