Some embodiments of the invention provide a method for propagating a first piecewise linear function (PLF), which is defined over a first state, to a second state, which is a surface. In some embodiments, the space includes a set of states and a transition map that specifies a set of states that can be reached from each particular state. For instance, in some embodiments, the space is a graph that includes points, lines, and surfaces. The method projects vectors from points on the first state that are locations of inflection points in the first PLF. At each intersection of the boundary of the surface and one of the vectors, the method computes a cost. Based on the computed costs, the method specifying a second PLF that is defined over the second state.