SIGMA(*) may fall within the range (0-infinity); its sign is ignored. The effect of the parameter is independent of the scale of the coordinates. For small SIGMA (0-5), the fitting function is a cubic in the coordinate u (= x or y) divided by a term linear in u; for SIGMA = 0, the function is exactly a cubic spline. As SIGMA becomes large (>25), the fit approaches a straight-line interpolation. For SIGMA larger than approximately 10**t (with t-digit floating-point arithmetic) the fit becomes exact linear interpolation, so there is no advantage to making SIGMA extremely large. In fact, values of SIGMA near the machine overflow limit can lead to overflows in function evaluations. Large SIGMA values can also lead to underflows, but such underflows are harmless provided the host system quietly sets them to zero.
The code employing this tensioning parameter was developed according to the discussion in S. Pruess, "Alternatives to the Exponential Spline in Tension", Math. Comp. 33, 1273-1281 (1979).
Center for Scientific Computing
South Physics Building
University of Utah
Salt Lake City, UT 84112
Tel: (801) 581-5254
(Manual page by R. P. C. Rodgers, Computer Applications in Laboratory Medicine Project, UCSF, San Francisco, CA 94143).