An analytical method is proposed for the study of all-dielectric photonic metamaterials (ADPMs). By introducing the long-wavelength approximation into the equations of Hamiltonian Optics, a master relationship is obtained for the refractive index distribution needed to make light follow prescribed paths. Furthermore, this approach is in good agreement with numerical calculations performed with Finite Different Time Domain (FDTD) simulation. It is an alternative solution to the use of coordinate transforms for the study of ADPMs and can be used for a versatile design of new optical functions.