In the context of Ewald sum, truncation is often used to reduce the cost of the real-space sum. Traditionally, two types of truncations have been used to simplify the field evaluations and limit the long-range interactions in PBC, namely: the minimum image convention and spherical cutoffs, see Fig.(3).
Figure 3: Periodic Boundary Conditions: A 2D periodic lattice where the unit cell contains five
particles (adapted from [3]).
In the minimum image scheme,
each particle interacts with exactly N-1 particles that are inside a fictitious
box of size L centered on the particle.
The total number of interactions is therefore 
, which is prohibitive for
large systems.
A further simplification is achieved when a spherical cutoff radius is used.
In this scheme, a sphere of radius 
, typically
between 8-12Å, is centered at the particle of interest and particles outside the sphere
are excluded from interacting with the particle.
The total number of interactions is a function of the cutoff radius and is an 
operation
for 
.
Figure(3) illustrates both methods. In the spherical cutoff method, particle 5 in the original cell
O will only interact with particles 1A, 2G, 4A while in the minimum image scheme,
particle 5 in the original cell interacts with particles 1A, 2G, 3O, 4A.