  Properties of 2-dimensional generalizations of sine functions that are
symmetric or antisymmetric with respect to permutation of their two variables
are described. It is shown that the functions are orthogonal when integrated
over a finite region $F$ of the real Euclidean space, and that they are
discretely orthogonal when summed up over a lattice of any density in $F$.
Decomposability of the products of functions into their sums is shown by
explicitly decomposing products of all types. The formalism is set up for
Fourier-like expansions of digital data over 2-dimensional lattices in $F$.
Continuous interpolation of digital data is studied.
