“…By the same theorem and Definition 2 the polynomials u, v, w -which we call the preimage polynomials -define a planar PH curve p(t) = t α h(u)du + const by prescribing its hodograph as h(t) = (w(t)(u 2 (t) − v 2 (t), 2w(t)u(t)v(t)), and vice-versa, i.e., for any planar PH curve there exist three preimage polynomials u, v, w that satisfy (4) for (a, b) = p . Therefore, any planar PH curve generates one polynomial minimal surface, and it is further shown in [4] that this generating curve lies on the minimal surface. Let us call the set of all minimal surfaces obtained from planar PH curves through Enneper-Weierstrass parameterization the class 1 minimal surfaces.…”