  The scattering patterns near the primary rainbow of oblate drops are
simulated by extending the vectorial complex ray model (VCRM) [1] to
three-dimensional (3D) calculations. With the curvature of wavefront as
intrinsic property of a ray, this advanced ray model permits, in principle, to
predict the amplitudes and phases of all emergent rays with a rigorous
algebraic formalism. This letter reports a breakthrough of VCRM for 3D
scattering with a line-by-line triangulation interpolation algorithm allowing
to calculate the total complex amplitude of scattered f eld. This makes
possible to simulate not only the skeleton (geometrical rainbow angles,
hyperbolic-umbilic caustics), but also the coarse (Airy bows, lattice) and f ne
(ripple fringes) structures of the generalized rainbow patterns (GRPs) of
oblate drops. The simulated results are found qualitatively and quantitatively
in good agreement with experimental scattering patterns for drops of different
aspect ratios. The physical interpretation of the GRPs is also given. This work
opens up prominent perspectives for simulating and understanding the 3D
scattering of large particles of any shape with smooth surface by VCRM.
