Piecewise-linear and nonlinear interpolators (PLI and NLI) for the generation of a function of one variable produce an output signal from two or more input signals which represent tangents to the function. They have the additional property that an additive signal which is simultaneously applied to all input terminals is transferred through them. This property is made use of in order to facilitate the generation of functions of two variables that can be written in the form F(x, y) = f(u)+g(v), where u and v are linear functions of x and y. The method is particularly suitable when f and g are convex or concave functions; the major applications are interpolating multipliers for which this paper provides a simple theory of operation.