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Figure 3
Hyperplanar shear parallel to [{\bf p}_{1}]. The lattice is `stratified' into different layers parallel to [{\bf p}_{1}]. The layer to which the vector [{\bf b}_{1}] points is given by the integer [ q = {\bf p}_{1}^{\rm t}{\bf b}_{1}]. The hyperplanar shear is made by calculating the point H (marked by a little orange star) which is the orthogonal projection of the origin O onto the layer q. The node Z such that [{\bf b}_{1} = {\bf O}{\bf Z}] can be translated towards another node Z′ closer to H (see text). The vector [{\bf b}_{1}' = {\bf O}{\bf Z}'] has a lower norm and a better `orthogonality' with the hyperplane [{\bf p}_{1}].

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