  We provide a method for the generation of effective continuum Hamiltonians
that goes beyond the well known k.p method in being equally effective in both
high, and low (or no) symmetry situations. Our approach is based on a
surprising exact map of the two-centre tight-binding method onto a compact
continuum Hamiltonian, with a precise condition given for the hermiticity of
the latter object. We apply this method to a broad range of low dimensional
systems of both high and low symmetry: graphene, graphdiyne, {\gamma}-graphyne,
6,6,12-graphyne, twist bilayer graphene, and partial dislocation networks in
Bernal stacked bilayer graphene. For the single layer systems the method yields
Hamiltonians for the ideal lattices, as well as a systematic theory for
corrections due to deformation. In the case of bilayer graphene we provide a
compact expression for an effective field capable of describing any stacking
deformation of the bilayer; twist bilayer graphene, as well as the partial
dislocation network in AB stacked graphene, emerge as special cases of this
field. For the latter system we find (i) charge pooling on the mosaic of AB and
AC segments near the Dirac point and (ii) localized current carrying states on
the partials with the current density characterized by both intralayer and
interlayer components.
