A new approach presented here predicts and quantifies the nonuniform spatial distribution of passive interfaces in both periodic and aperiodic chaotic mixing processes, Based on a coarse-grained calculation of line element stretching, it bypasses the direct numerical simulation of continuous interfaces, which is computationally, impractical even in simple model flows. The evolution of the structures created by the Lagrangian displacement and deformation process is decoupled into the product of a time-in-variant, spatially-dependent function expressing the nonuniform density of interface throughout the flow domain and a temporally-dependent function expressing the exponential growth of the interface, characterized by a global exponent (topological entropy) unambiguously different from the Lyapunov exponent. Pie Sine Flow agreed excellently with the Journal Bearing, when results from direct tracking of the interface were compared to those using stretching calculations to predict interface density.