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