  In order to deal with the interaction of an electromagnetic wave with large
homogeneous objects of arbitrary shape with smooth surface we develop the ray
theory of waves (RTW) which is composed of the vectorial complex ray model
(VCRM) and VCRM based singularity theory. By introducing the wavefront
curvature as an intrinsic property of rays, VCRM permits to predict the
amplitude and the phase of field at any point rigorously in the sense of ray
model. Its combination with the singularity theory remedies the discontinuity
in the ray model. In this letter, the wavefront equation, key physical law of
VCRM describing the relation between the wavefront curvatures of the incident
wave and the refracted/reflected wave, is derived for the most general case of
three dimension scattering. The strategy of the calculation scheme in RTW is
described. Typical applications to the prediction of the rainbow patterns of a
spheroidal drop are presented. The comparison to a rigorous numerical method,
multilevel fast multipole algorithm, shows that RTW can predict very fast and
precisely the scattered field even in the vicinity of caustics.
