5] Wenguang Zhai, On primitive lattice
points in planar domains.
Furthermore, as the cubic primitive lattice is common for inorganic materials, the above type of ambiguity can often present difficulties in common practice.
The above discussion has focused on the cubic crystals characterized by a primitive lattice.
In the case of a cubic primitive lattice which is highly symmetric, the pixel configurations [[xi].
For simplicity we restrict ourselves to the special case where X is observed on a cubic primitive lattice.
For the special case of a cubic primitive lattice [L.
Again, for the sake of simplicity we concentrate on samplings on cubic primitive lattices.
For cubic primitive lattices it is sufficient to restrict the following considerations to the congruence classes [D.
We are starting from the local knowledge represented by the numbers of 2 x 2 x 2 pixel configurations on cubic primitive lattices and ask for the best choice of surface weights.
Table 4 shows that most organic compounds crystallize in a triclinic, monoclinic, or orthorhombic Bravais lattice with the primitive lattice
We remark that the method of Ohser and Mucklich (2000) is designed for the general case of cuboidal lattices, while the restriction on the particular case of cubic primitive lattices allows to exploy symmetry properties (Ohser and Schladitz, 2009), and to present the weights in a very condensed form (depending on representatives of the 22 equivalence classes, as in Table 1).
First, the method can simply be extended to arbitrary homogeneous lattices so that we are no longer restricted to cubic primitive lattices (Ohseretal.