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On a planar representation of 3D figures commutative with respect to set and morphological operations

In order to reduce the amount of time required for computing set and morphological operations on 3D figures, we pose and solve the problem of finding such a planar representation of 3D figures, which is commutative with respect to these operations. The proposed representation is a generalization of the well known halftone technique, called ordered dithering, and thereby is a new kind of halftoning which can find applications elsewhere.