ABSTRACT
Historically, exponential spline interpolants ([148, 149, 162]) were considered before rational splines with parameter-controlled poles were. Their purpose is to be able to achieve a visually pleasing interpolating curve through the appropriate choice of certain tension parameters, pk > 0, which have the effect of "tightening" the curve on the corresponding intervals. The special case of all the pk = 0 results in ordinary cubic spline interpolation. Since they make use of exponential functions, their computational expense is considerably greater than that of rational splines whose complexity, as we saw in the last chapter, is already quite high. For this reason, exponential splines are not usually considered to be a competitive alternative.
