  Discrete differential geometry aims to develop discrete equivalents of the
geometric notions and methods of classical differential geometry. In this
survey we discuss the following two fundamental Discretization Principles: the
transformation group principle (smooth geometric objects and their
discretizations are invariant with respect to the same transformation group)
and the consistency principle (discretizations of smooth parametrized
geometries can be extended to multidimensional consistent nets). The main
concrete geometric problem discussed in this survey is a discretization of
curvature line parametrized surfaces in Lie geometry. We find a discretization
of curvature line parametrization which unifies the circular and conical nets
by systematically applying the Discretization Principles.
