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 line. 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 any intersection of
the line and one of the vectors, the method computes a cost. The method also computes
a cost at any endpoint of the line that does not intersect one of the vectors.
Based on the computed costs, the method then specifies a second PLF that is defined
over the second state.
