A consistent formulation is presented for the direct numerical simulation of an arbitrarily shaped colloidal particle at a deformable fluidic interface. The rigid colloidal particle is decomposed into a collection of solid spherical beads and the three-phase boundaries are replaced with smoothly spreading interfaces. The major merit of the present formulation lies in the ease with which the geometrical decomposition of the colloidal particle is implemented, yet allows the dynamic simulation of intricate three-dimensional colloidal shapes in a binary fluid. The dynamics of a rodlike, a platelike, and a ringlike particle are presently tested. It is found that platelike particles attach more rapidly to a fluidic interface and are subsequently harder to dislodge when subject to an external force. Using the Bond number, i.e., the ratio of the gravitational force to the reference capillary force, a spherical particle with equal affinity for the two fluids breaks away from a fluidic interface at the critical value Bo = 0.75. This value is in line with our numerical experiments. It is here shown that a plate and a ring of equivalent masses detach at greater critical Bond numbers approximately equal to Bo = 1.3. Results of this study will find applications in the stabilization of emulsions by colloids and in the recovery of colloidal particles by rising bubbles.