  This paper treats 6j symbols or their orthonormal forms as a function of two
variables spanning a square manifold which we call the "screen". We show that
this approach gives important and interesting insight. This two dimensional
perspective provides the most natural extension to exhibit the role of these
discrete functions as matrix elements that appear at the very foundation of the
modern theory of classical discrete orthogonal polynomials. Here we present 2D
and 1D recursion relations that are useful for the direct computation of the
orthonormal 6j, which we name U. We present a convention for the order of the
arguments of the 6j that is based on their classical and Regge symmetries, and
a detailed investigation of new geometrical aspects of the 6j symbols.
Specifically we compare the geometric recursion analysis of Schulten and Gordon
with the methods of this paper. The 1D recursion relation, written as a matrix
diagonalization problem, permits an interpretation as a discrete
Schr\"odinger-like equations and an asymptotic analysis illustrates
semiclassical and classical limits in terms of Hamiltonian evolution.
