[Insight-users] Weights1D matrix in itkBSplineInterpolationWeightFunction.txx ?

[motes motes]

In  the itkBSplineInterpolationWeightFunction.txx file a matrix
Weights1D is computed:

  Matrix<double,SpaceDimension,SplineOrder + 1> weights1D;
  for ( j = 0; j < SpaceDimension; j++ ) {
    double x = index[j] - static_cast<double>(startIndex[j]);
    for( k = 0; k <= SplineOrder; k++ ) {
      weights1D[j][k] = m_Kernel->Evaluate( x );
      x -= 1.0;
    }
  }


For a 2-order BSpline with (order+1*order+1) 9 coefficients/nodes this
results in a 2*3 matrix. This matrix is later used to compute the
final 1*9 weights array:

  for ( k = 0; k < m_NumberOfWeights; k++ ) {
    weights[k] = 1.0;
    for ( j = 0; j < SpaceDimension; j++ ) {
      weights[k] *= weights1D[j][ m_OffsetToIndexTable[k][j] ];
    }
  }

Is it correct that the Weights1D is the first order+1 nodes in the
first dimension and the second order+1 nodes in the second dimension
and that the final nodes are compute from these initial nodes?

I have not been able to find any documentation on how the
BSplineInterpolationWeightFunction actually computes these nodes (page
412 in the itkSoftwareGuide describes the process on a higher level).