Digital planarity of rectangular surface segments

We generalize the concept of evenness which has been developed for digital straight lines. Evenness is a necessary and sufficient condition for a digital arc segment to be a digital straight line segment. We prove that evenness is also a necessary and sufficient condition for a rectangular surface segment to be a digital plane segment. This is not true for surface segments of arbitrary shape. To clarify the relation between shape and evenness we introduce the notion of a regular shape and of an arbitrarily extendable even set