Deforming Meyer sets

A linear deformation of a Meyer set M in Rd is the image of M under a group homomorphism of the group [M] generated by M into Rd. We provide a necessary and sufficient condition for such a deformation to be a Meyer set. In the case where the deformation is a Meyer set and the deformation is injective, the deformation is pure point diffractive if the original set M is pure point diffractive.