If the mathematics of rational cubic curves is visualized via its homogeneous counterpart, it is required to establish some equivalent constraints on the homogeneous curves regarding continuity of the kind which is desired for the rational curve. The constraints on the homogeneous curves are derived that are exactly equivalent to the parametric and Cs-continuity of the rational cubic curves. For every degree of continuity, the rational continuity constraints contain a degree of freedom not present in the corresponding continuity constraints) for projected curves.