  There are several examples of spaces of univariate functions for which we
have a characterization of all sets of knots which are poised for the
interpolation problem. For the standard spaces of univariate polynomials, or
spline functions the mentioned results are well-known. In contrast with this
there are no such results in the bivariate case. As an exception one may
consider only the Pascal classic theorem, in the interpolation theory
interpretation. In this paper we consider a space of bivariate piecewise linear
functions, for which we can readily find out whether the given node set is
poised or not. The main tool we use for this purpose is the reduction by a
basic subproblem, introduced in this paper.
