Tor Olav Kristensen fixed one problem with my sinespline and then I saw
that what I really needed was a CosineSpline!
Here is a test scene, all fixed up!
Red dots:    linear poitns
Yellow curve: #init_spline
Blue curve: Cosine spline

The yellow #init_spline gives the most smooth curve, but it's not too
proud to stay within the range of original points. The blue curve isn't
the smoothest or prettiest, but it behaves.

-------------------------------------
test scene

#version 3.1;
#include "colors.inc"
//by Greg M. Johnson and improved by Tor Olav Kristensen

#macro sinespline(xgive, ptArray)

  #local jj = 0;
  #local nextx = ptArray[jj].x;
  #local Found = false;
  #while (!Found & (jj < dimension_size(ptArray, 1) - 1))
    #local lastx = nextx;
    #local jj = jj+1;
    #local nextx = ptArray[jj].x;
    #local Found = ((xgive >= lastx) & (xgive < nextx) ? true : false);
  #end // while

  (Found ? ptArray[jj].y +
           (ptArray[jj-1] - ptArray[jj]).y*
           0.5*(
                cos
                       (pi*
                        (xgive - lastx)/(nextx - lastx)
                       )+1
               )
         : 0)

#end // macro sinespline

#init_spline {"initspline",
  < 0.000,  -15.0 >,
  < 0.250, -125.0 >,
  < 0.450, -110.0 >,
  < 0.500,  -10.0 >,
  < 0.750,  -25.0 >,
  < 1.000,  -15.0 >
}


#declare pn =
array[6] {
  < 0.000,  -15.0 >,
  < 0.250, -125.0 >,
  < 0.450, -110.0 >,
  < 0.500,  -10.0 >,
  < 0.750,  -25.0 >,
  < 1.000,  -15.0 >
}



#declare Radius = 3;
#declare sc = <300, 1, -3>;
#declare Cnt = 0;
#while(Cnt < 1)
  sphere {
    <Cnt, sinespline(Cnt, pn), 1>*sc, Radius
    pigment{ Blue }
    finish{ ambient 1 }
  }
  #declare Cnt = Cnt + .002;
#end
#declare Cnt = 0;
#while(Cnt < 1)
  sphere {
    <Cnt, eval_spline ("initspline",Cnt), 4>*sc, Radius*0.5
    pigment{ Yellow }
    finish{ ambient 1 }
  }
  #declare Cnt = Cnt + .006;
#end

#declare Cnt = 0;
#while(Cnt < dimension_size(pn, 1))
  sphere {
    <pn[Cnt].x, pn[Cnt].y, 1>*sc, Radius*1.25
    pigment{ Red }
    finish{ ambient 1 }
  }
  #declare Cnt = Cnt + 1;
#end


camera {
  location  <130, -75, -300>
  look_at   <130, -75,  0.0>
}

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