Subgrid modelling for the assignment of coordinates in phase space. The coordinates of the random tracers are modulated by the fraction f_col such that if d_r denotes the separation between the random particle and its closest dark matter particle, the new separation is f_cold_r. Velocities are modified in two steps: (i) an isotropic density-dependent correction γ(δ_dm) is applied to the velocities of both random tracers and dark matter tracers (), and (ii), after collapsing the random tracers, their velocities are modified using the parameters β (direction) and ζ (modulo). The angles α and β are defined on the plane generated by the vector joining random particles with their closest dark matter particle and the velocity of the random particle r_r.