The renderings include color effects, softening of sharp features, and strong forward scattering that are not predicted by traditional ray-based models, though the two approaches produce similar appearance for complex fiber assemblies under many conditions.

To increase diversity and realism, surface bidirectional scattering distribution functions (BSDFs) are often modelled as consisting of multiple layers, but accurately evaluating layered BSDFs while accounting for all light transport paths is a challenging problem. Recently, Guo et al. [GHZ18] proposed an accurate and general position‐free Monte Carlo method, but this method introduces variance that leads to longer render time compared to non‐stochastic layered models. We improve the previous work by presenting two new sampling strategies, pair‐product sampling and multiple‐product sampling. Our new methods better take advantage of the layered structure and reduce variance compared to the conventional approach of sequentially sampling one BSDF at a time. Our pair‐product sampling strategy importance samples the product of two BSDFs from a pair of adjacent layers. We further generalize this to multiple‐product sampling, which importance samples the product of a chain of three or more BSDFs. In order to compute these products, we developed a new approximate Gaussian representation of individual layer BSDFs. This representation incorporates spatially varying material properties as parameters so that our techniques can support an arbitrary number of textured layers. Compared to previous Monte Carlo layering approaches, our results demonstrate substantial variance reduction in rendering isotropic layered surfaces.

Looking at a cup of hot tea, an observer can see color patterns and granular textures both on the water surface and in the steam. Motivated by this example, we model the appearance of iridescent water droplets. Mie scattering describes the scattering of light waves by individual spherical particles and is the building block for both effects, but we show that other mechanisms must also be considered in order to faithfully reproduce the appearance. Iridescence on the water surface is caused by droplets levitating above the surface, and interference between light scattered by drops and reflected by the water surface, known as Quetelet scattering, is essential to producing the color. We propose a model, new to computer graphics, for rendering this phenomenon, which we validate against photographs. For iridescent steam, we show that variation in droplet size is essential to the characteristic color patterns. We build a droplet growth model and apply it as a post‐processing step to an existing computer graphics fluid simulation to compute collections of particles for rendering. We significantly accelerate the rendering of sparse particles with motion blur by intersecting rays with particle trajectories, blending contributions along viewing rays. Our model reproduces the distinctive color patterns correlated with the steam flow. For both effects, we instantiate individual droplets and render them explicitly, since the granularity of droplets is readily observed in reality, and demonstrate that Mie scattering alone cannot reproduce the visual appearance.