  We present an ab-initio numerical investigation of the internal conical
refraction of structured light beams in a biaxial crystal. Starting from the
solutions of the Fresnel equation, a theoretical analysis is developed without
assuming any analytical approximation, thus obtaining a set of exact equations
that can be solved by standard methods of integration for any impinging light
beam. As examples of applications, we consider the particular cases of linearly
and circularly polarized Gaussian and Bessel beams inside a KTP crystal. The
numerical calculations follow the evolution of the refracted beam inside the
crystal. It is seen that for realistic boundary conditions, a refraction cone
appears in a certain range of distances within the crystal and its shape is
rather sensitive to the initial conditions.
