  In this short note, we generalized the Tangential Cover used in Digital
Geometry in order to use very general geometric predicates. We present the
required notions of saturated $\alpha$-paths of a digital curve as well as
conservative predicates which indeed cover nearly all geometric digital
primitives published so far. The goal of this note is to prove that under a
very general situation, the size of the Tangential Cover is linear with the
number of points of the input curve. The computation complexity of the
Tangential Cover depends on the complexity of incremental recognition of
geometric predicates. Moreover, in the discussion, we show that our approach
does not rely on connectivity of points as it might be though first.
