A technique to derive the analytical form of convex envelopes for some bivariate functions

In the recent paper (Locatelli and Schoen in Math Program, 2013) it is shown that the value of the convex envelope of some bivariate functions over polytopes can be computed by solving a continuously differentiable convex problem. In this paper we show how this result can be exploited to derive in some cases the analytical form of the envelope. The technique is illustrated through two examples.