simulators [9] . There are two main ways of obtaining a DR of a real world object. One is by acquisition with a This paper presents the properties of the discrete analytical hyperplanes. They are defined analytically in the discrete dophysical device like a camera for a 2D DR, a CT or MR main by Diophantine equations. We show that the discrete scanner for a 3D DR, a PET scanner for a 4D DR, etc. hyperplane is a generalization of the classical digital hyper-The second one is by digitizing the

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... mitives forming planes. We present original properties such as exact point localits CAR. ization and space tiling. The main result is the links made Although many papers have dealt with the digitization between the arithmetical thickness of a hyperplane and its of primitives, the problems we have in handling the geome- topology. © 1997 Academic Press try and topology of the discrete world resulted in a predominant approach: "a digital primitive is the result of a local approximation process applied to the continuous primi-