of subset in the internal space $\mathsf{H}$, usually called a *window*, which consists of a compact and topologicaly regular subset $W$, supposed *irredundant* in the sense that the compact subgroup of elements of $w\in \mathsf{H}$ which satisfy $W+w = W$ is trivial.

Now if we are given a cut $\&$ project scheme together with a window $W$ in its internal space, we may form a certain point pattern $\mathfrak{P}(W)$ of $\mathbb{R}^d$ by projecting into the physical space the subset of points of the lattice $\Sigma$ lying within the *strip* $W\times \mathbb{R}^d$. To illustrate this we consider the following picture (see also [@BaaHePl])

(-1.2,1.3)(12.37,7.2) (3,7.5)(3,1.5) (1,3)(8.6,3) (1,2.17)(8.54,5.3) (1,3.17)(8.54,6.3) (1,1.75)(8.52,4.78) (2,3)(2.15,2.65) (4,3)(3.83,3.37) (4.21,3.5)(4,4) (5.06,3.86)(5,4) (6,4)(5.91,4.21) (6.27,4.36)(6,5) (7,5)(7.12,4.71) (7.97,5.06)(8,5) (8,6)(8.33,5.21) (3,4)(3.35,3.15) (1.15,7.45)(3.66,1.5) (2.64,3.85)(3.16,2.62)

(3,3) (4,3) (5,3) (6,3) (7,3) (8,3) (3,4) (4,4) (5,4) (6,4) (7,4) (8,4) (3,5) (4,5) (5,5) (6,5) (7,5) (8,5) (3,6) (4,6) (5,6) (6,6) (7,6) (8,6) (3,7) (5,7) (6,7) (7,7) (8,7) (2,3) (2,4) (2,5) (2,6) (2,7) (2,2) (3,2) (4,2) (5,2) (6,2) (7,2) (8,2) (4,7) (1,3.17) (8.54,6.3) (8.52,4.78) (8.52,5.3) (8.57,5.32)[$\mathbb{R}^d=\mathbb{R}$]{} (1.26,7.18) (1.6,6.5)[$\mathsf{H}=\mathbb{R}$]{} (2.78,3.53) (2.45,3.2)[$W$]{}

The above picture presents the most simple real cut $\&$ project scheme one may consider, that is, with physical and internal spaces being $1$-dimensional, and with a lattice $\Sigma 