In this article, we propose SpongeCake: A layered BSDF model where each layer is a volumetric scattering medium, defined using microflake or other phase functions. We omit any reflecting and refracting interfaces between the layers. The first advantage of this formulation is that an exact and analytic solution for single scattering, regardless of the number of volumetric layers, can be derived. We propose to approximate multiple scattering by an additional single-scattering lobe with modified parameters and a Lambertian lobe. We use a parameter mapping neural network to find the parameters of the newly added lobes to closely approximate the multiple scattering effect. Despite the absence of layer interfaces, we demonstrate that many common material effects can be achieved with layers of SGGX microflake and other volumes with appropriate parameters. A normal mapping effect can also be achieved through mapping of microflake orientations, which avoids artifacts common in standard normal maps. Thanks to the analytical formulation, our model is very fast to evaluate and sample. Through various parameter settings, our model is able to handle many types of materials, like plastics, wood, cloth, and so on, opening a number of practical applications.

Digitally reproducing the appearance of woven fabrics is important in many applications of realistic rendering, from interior scenes to virtual characters. However, designing realistic shading models and capturing real fabric samples are both challenging tasks. Previous work ranges from applying generic shading models not meant for fabrics, to data-driven approaches scanning fabrics requiring expensive setups and large data. In this paper, we propose a woven fabric material model and a parameter estimation approach for it. Our lightweight forward shading model treats yarns as bent and twisted cylinders, shading these using a microflake-based bidirectional reflectance distribution function (BRDF) model. We propose a simple fabric capture configuration, wrapping the fabric sample on a cylinder of known radius and capturing a single image under known camera and light positions. Our inverse rendering pipeline consists of a neural network to estimate initial fabric parameters and an optimization based on differentiable rendering to refine the results. Our fabric parameter estimation achieves high-quality recovery of measured woven fabric samples, which can be used for efficient rendering and further edited.

Bidirectional Scattering Distribution Functions (BSDFs) encode how a material reflects or transmits the incoming light. The most commonly used model is the microfacet BSDF. It computes the material response from the microgeometry of the surface assuming a single bounce on specular microfacets. The original model ignores multiple bounces on the microgeometry, resulting in an energy loss, especially for rough materials. In this paper, we present a new method to compute the multiple bounces inside the microgeometry, eliminating this energy loss. Our method relies on a position-free formulation of multiple bounces inside the microgeometry. We use an explicit mathematical definition of the path space that describes single and multiple bounces in a uniform way. We then study the behavior of light on the different vertices and segments in the path space, leading to a reciprocal multiple-bounce description of BSDFs. Furthermore, we present practical, unbiased Monte Carlo estimators to compute multiple scattering. Our method is less noisy than existing algorithms for computing multiple scattering. It is almost noise-free with a very-low sampling rate, from 2 to 4 samples per pixel (spp).