What do you mean by parabolic splines?
For parabolic splines a parabola is fitted by the first three points p1, p2,p3 of the data array of kot points. Then a second parabolic arc is found to fit the sequence of point's p2, p3, p4. This continues in this way unless a parabolic arc is found to fit by points pn-2, pn-1 and pn. The final plotted curve is a meshing together of all these parabolic arcs.