  We give a full classification of continuous flexible discrete axial
cone-nets, which are called axial C-hedra. The obtained result can also be used
to construct their semi-discrete analogs. Moreover, we identify a novel
subclass within the determined class of (semi-)discrete axial cone-nets, whose
members are named axial P-nets as they fulfill the proportion (P) of the
intercept theorem. Known special cases of these axial P-nets are the smooth and
discrete conic crease patterns with reflecting rule lines. By using a
parallelism operation one can even generalize axial P-nets. The resulting
general P-nets constitute a rich novel class of continuous flexible
(semi-)discrete surfaces, which allow direct access to their spatial shapes by
three control polylines. This intuitive method makes them suitable for
transformable design tasks using interactive tools.
