Examples

  inter1=SplineFit[{{0,0},{1,1},{2,4},{3,1},{4,0}},Cubic]

  plot6=ParametricPlot[inter1[x],{x,0,4},PlotRange->All,
     Compiled->False];

Let's compare this with what we found.

  Show[plot1,plot2,plot6];

This was our second example.

You will notice in the output SplineFunction[Cubic, {0., 3.}]. The parametrization goes from 0 to 3, 0 representing the first point, 3 the last. Notice also that 0 to 3 is the range we supply in the ParametricPlot command.

  inter2=SplineFit[{{0,0},{.1,.1125},{.25,.2763},{.35,.3794}},
    Cubic]

  plot7=ParametricPlot[inter2[x],{x,0,3},PlotRange->All,
    Compiled->False];

Let's compare with what we found. You will notice some error, which you may attribute to the fact that we rounded our piecewise cubics gc1, gc2, gc3, gc4.

  Show[plot3,plot4,plot7];

Let's compare Mathematica with the error function Erf[x]. It is pretty darn good!

  Show[plot5,plot7];

Up to Mathematica and Splines