PARabolic FILling midpoints: PARFIL

Inserts mid points ito each interval of x,y data: all(diff(x)>0)=true

FILls midpoints into vectors/matrices by PARabolic interpolation as would do Y=interp1(x,y,X,'parabolic')with X=sort([x;( x(1:end-1)+x(2:end) )/2];
For matrices PARFIL works on columns. If only rows match length(x),
then y will be transposed.
For regular data (equidistantly sampled, i.e. std(diff(x))=0),
Y is identical with INTERPOL(y,1,DEG) in inner intervals,(completely identical for DEG=3), but INTERPOL is somewhat
faster than PARFIL

DEMO is included in help and given by
parfil()

For very smooth data results are close to that of SPLINE

For somewhat noisy data can become method of choice (better than linear, pchip or spline interpolations)