In many multiphase systems (e.g. gas-liquid-solid) where surface tension forces dominate over viscous forces, the model can be reduced to a surface interface curvature-driven mechanical problem. In such systems an accurate estimate of the mean curvature of phase interfaces is essential. Conventional numerical methods are incapable of simulating certain complex systems over the space and timespans of interest due to the large number of discrete elements needed. Here we demonstrate how modern developments in the field of discrete differential geometry can be used in a generalised formulation building on the conventional cotan-formula. This can be used to reconstruct the exact mean normal- and geodesic curvatures of discretised interfaces. This result is essential to many scalable systems of interest, with a particular application focussed on restructuring in mesoporous nanoparticle films due to fluid imbibition and drying. An essential extension of conventional formulations is a discrete differential geometric formulation of three-phase contact angles which is accomplished through the Gauss-Bonnet Theorem.