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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.

 

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, Guoet 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 samplingandmultiple‐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. Ourpair‐product samplingstrategy importance samples the product of two BSDFs from a pair of adjacent layers. We further generalize this tomultiple‐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.

 

Traditional fiber scattering models, based on ray optics, are missing some important visual aspects of fiber appearance. Previous work [Xia et al. 2020] on wave scattering from ideal extrusions demonstrated that diffraction produces strong forward scattering and colorful effects that are missing from ray-based models. However, that work was unable to include some important surface characteristics such as surface roughness and tilted cuticle scales, which are known to be important for fiber appearance. In this work, we take an important step to study wave effects from rough fibers with arbitrary 3D microgeometry. While the full-wave simulation of realistic 3D fibers remains intractable, we developed a 3D wave optics simulator based on a physical optics approximation, using a GPU-based hierarchical algorithm to greatly accelerate the calculation. It simulates surface reflection and diffractive scattering, which are present in all fibers and typically dominate for darkly pigmented fibers. The simulation provides a detailed picture of first order scattering, but it is not practical to use for production rendering as this would require tabulation per fiber geometry. To practically handle geometry variations in the scene, we propose a model based on wavelet noise, capturing the important statistical features in the simulation results that are relevant for rendering. Both our simulation and practical model show similar granular patterns to those observed in optical measurement. Our compact noise model can be easily combined with existing scattering models to render hair and fur of various colors, introducing visually important colorful glints that were missing from all previous models.

 

Computing light reflection from rough surfaces is an important topic in computer graphics. Reflection models developed based on geometric optics fail to capture wave effects such as diffraction and interference, while existing models based on physical optics approximations give erroneous predictions under many circumstances (e.g. when multiple scattering from the surface cannot be ignored). We present a scalable 3D full-wave simulator for computing reference solutions to surface scattering problems, which can be used to evaluate and guide the development of approximate models for rendering. We investigate the range of validity for some existing wave optics based reflection models; our results confirm these models for low-roughness surfaces but also show that prior rendering methods do not accurately predict the scattering behavior of some types of surfaces.

Our simulator is based on the boundary element method (BEM) and accelerated using the adaptive integral method (AIM), and is implemented to execute on modern GPUs. We demonstrate the simulator on domains up to 60 × 60 × 10 wavelengths, involving surface samples with significant height variations. Furthermore, we propose a new system for efficiently computing BRDF values for large numbers of incident and outgoing directions at once, by combining small simulations to characterize larger areas. Our simulator will be released as an open-source toolkit for computing surface scattering.

 

Existing fiber scattering models in rendering are all based on tracing rays through fiber geometry, but for small fibers diffraction and interference are non-negligible, so relying on ray optics can result in appearance errors. This paper presents the first wave optics based fiber scattering model, introducing an azimuthal scattering function that comes from a full wave simulation. Solving Maxwell's equations for a straight fiber of constant cross section illuminated by a plane wave reduces to solving for a 3D electromagnetic field in a 2D domain, and our fiber scattering simulator solves this 2.5D problem efficiently using the boundary element method (BEM). From the resulting fields we compute extinction, absorption, and far-field scattering distributions, which we use to simulate shadowing and scattering by fibers in a path tracer. We validate our path tracer against the wave simulation and the simulation against a measurement of diffraction from a single textile fiber. Our results show that our approach can reproduce a wide range of fibers with different sizes, cross sections, and material properties, including textile fibers, animal fur, and human hair. 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.