  Homogeneous Hilbert curves (HHC) in two dimensions are generalized by
introducing the construction of the space filling curves from the same affine
transformations but using an arbitrary kernel, we call such curves HHCK. The
new curves are still space filling that comply with the nesting condition but
violates the adjacency property. The freedom of building new HHC curves with
arbitrary kernels, is only limited by the constrain that the chosen kernel must
allow a well behaved connectivity between quadrants. Two examples of such
curves are discussed.
  The important property of locality preservation in space filling curve
mapping is discussed. Besides the common used dilation factor, the paper
introduces and discuss difference map as a site locality measure, allowing to
describe locality preservation in a more detailed way than dilation factors.
The strength of such analysis is proven and global descriptors from the
difference map are derived. Locality of all HHC curves and the two discussed
HHCK curves are studied by difference map.
