[Insight-users] Cubic BSpline kernel Theory?

[motes motes]

In the BSplineDeformableTransform a BSpline kernel is used which in
the Cubic case is:

::BSplineKernel( const double & u) const
{
  double absValue = vnl_math_abs( u );
  double sqrValue = vnl_math_sqr( u );

  if ( absValue  < 1.0 ) {
    return ( 4.0 - 6.0 * sqrValue + 3.0 * sqrValue * absValue ) / 6.0;
  } else if ( absValue < 2.0 ) {
    return ( 8.0 - 12 * absValue + 6.0 * sqrValue - sqrValue * absValue ) / 6.0;
  } else {
    return 0.0;
  }
}

But where does this expression come from? In the BSpline litterature I
have only found the basis functions expressed using the Cox De Boor
recursion formula. Where can I read up on the above explicit
expression?