Transfer matrix based layered materials rendering

A statistical multi-lobe approach was recently introduced in order to efficiently handle layered materials rendering as an alternative to expensive general-purpose approaches. However, this approach poorly supports scattering volumes as the method does not account for back-scattering and resorts to single scattering approximations. In this paper, we address these limitations with an efficient solution based upon a transfer matrix approach which leverages the properties of the Henyey-Greenstein phase function. Under this formalism, each scattering component of the stack is described through a lightweight matrix, layering operations are reduced to simple matrix products and the statistics of each BSDF lobe accounting for multiple scattering effects are obtained through matrix operators. Based on this representation, we leverage the versatility of the transfer matrix approach to efficiently handle forward and backward scattering which occurs in arbitrary layered materials. The resulting model enables the reproduction of a wide range of layered structures embedding scattering volumes of arbitrary depth, in constant computation time and with low variance.