In the trajectory-based approach, the relation between x and C is known at a given time only through the discrete values, x i (C i , t). Hence, interpolation is needed to estimate the density at arbitrary x. Our interpolation procedure is as follows: we first generate a monotonic interpolation of C(x, t) by the means of a monotone quintic splines interpolation algorithm. Then, taking the derivative of the resulting interpolating function yields the density at arbitrary points, thanks to the definition of C as ρ(x, t) = ∂C/∂x. The resulting density synthesis strictly obeys norm conservation, which is implicitly guaranteed by the definition of quantum trajectories and use of the trajectory labelling coordinate C. This method is favored over using finite differences to estimate the density from the spacing of trajectories [i.e., taking ρ(x i , t) ≈ 2∆C/(x i+1 -x i-1 ), then interpolating ln [ρ(x, t)] using cubic splines] as that procedure might violate the conservation law because of spline oscillations or "ringing".