In this work, we introduce an extension to microfacet theory for the rendering of iridescent effects caused by thin-films of varying thickness (such as oil, grease, alcohols, etc) on top of an arbitrarily rough base layer. Our material model is the first to produce a consistent appearance between tristimulus (e.g., RGB) and spectral rendering engines by analytically pre-integrating its spectral response. The proposed extension works with any microfacet-based model: not only on reflection over dielectrics or conductors, but also on transmission through dielectrics. We adapt its evaluation to work in multi-scale rendering contexts, and we expose parameters enabling artistic control over iridescent appearance. The overhead compared to using the classic Fresnel reflectance or transmittance terms remains reasonable enough for practical uses in production.

Fig. 1. We introduce a BSDF model to render plane-parallel layered materials using an analysis of the directional statistics of light interaction with microfacet geometry and participating media. Our model closely matches the reference and supports an arbitrary number of textured layers while being energy conserving, free from heavy per-material precomputation, and compatible with real-time constraints.We derive a novel framework for the e cient analysis and computation of light transport within layered materials. Our derivation consists of two steps. First, we decompose light transport into a set of atomic operators that act on its directional statistics. Speci cally, our operators consist of re ection, refraction, sca ering, and absorption, whose combinations are su cient to describe the statistics of light sca ering multiple times within layered structures. We show that the rst three directional moments (energy, mean and variance) already provide an accurate summary. Second, we extend the adding-doubling method to support arbitrary combinations of such operators e ciently. During shading, we map the directional moments to BSDF lobes. We validate that the resulting BSDF closely matches the ground truth in a lightweight and e cient form. Unlike previous methods, we support an arbitrary number of textured layers, and demonstrate a practical and accurate rendering of layered materials with both an o ine and real-time implementation that are free from per-material precomputation.

The rendering of effects such as motion blur and depth-of-field requires costly 5D integrals. We dramatically accelerate their computation through adaptive sampling and reconstruction based on the prediction of the anisotropy and bandwidth of the integrand. For this, we develop a new frequency analysis of the 5D temporal light-field, and show that first-order motion can be handled through simple changes of coordinates in 5D. We further introduce a compact representation of the spectrum using the covariance matrix and Gaussian approximations. We derive update equations for the 5 × 5 covariance matrices for each atomic light transport event, such as transport, occlusion, BRDF, texture, lens, and motion. The focus on atomic operations makes our work general, and removes the need for special-case formulas. We present a new rendering algorithm that computes 5D covariance matrices on the image plane by tracing paths through the scene, focusing on the single-bounce case. This allows us to reduce sampling rates when appropriate and perform reconstruction of images with complex depth-of-field and motion blur effects.

(presented at SIGGRAPH 2014)International audienceRendering participating media requires significant computation, but the effect of volumetric scattering is often eventually smooth. This article proposes an innovative analysis of absorption and scattering of local light fields in the Fourier domain and derives the corresponding set of operators on the covariance matrix of the power spectrum of the light field. This analysis brings an efficient prediction tool for the behavior of light along a light path in participating media. We leverage this analysis to derive proper frequency prediction metrics in 3D by combining per-light path information in the volume.We demonstrate the use of these metrics to significantly improve the convergence of a variety of existing methods for the simulation of multiple scattering in participating media. First, we propose an efficient computation of second derivatives of the fluence, to be used in methods like irradiance caching. Second, we derive proper filters and adaptive sample densities for image-space adaptive sampling and reconstruction. Third, we propose an adaptive sampling for the integration of scattered illumination to the camera. Finally, we improve the convergence of progressive photon beams by predicting where the radius of light gathering can stop decreasing. Light paths in participating media can be very complex. Our key contribution is to show that analyzing local light fields in the Fourier domain reveals the consistency of illumination in such media and provides a set of simple and useful rules to be used to accelerate existing global illumination methods.Une nouvelle analyse locale de la diffusion et de l'absorption de la lumière dans l'espace de Fourier est combinée avec le tracé de covariance et permet une estimation rapide du contenu fréquentiel local; cette approche permet l'amélioration de nombreux algorithmes de rendu de milieux participants tels que Progressive Photon Beams et l'integration d'effets de diffusion simple et l'échantillonnage et la reconstruction d'effets de simple diffusion simple en espace image

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Real-time: analytic spherical-cap integration Joint MIS (ours) 64spp MIS (previous) 64spp O ine: joint BRDF/spherical-cap sampling Fig. 1. Real-time application (le ). We approximate BRDFs with our distributions and shade with sphere lights in real-time using their analytic spherical-cap integral. The scene is rendered at 1080p and runs at 60fps on an NVIDIA 980 GTX. O line application (right). We compute the reference image with the exact BRDFs using importance sampling techniques. We use our distribution as a proxy for the BRDF and generate be er samples that are distributed jointly inside the lights and close to the BRDFs. This joint sampling scheme is unbiased and has lower variance than multiple importance sampling with separate BRDF and light sampling.We introduce a novel parameterization for spherical distributions that is based on a point located inside the sphere, which we call a pivot. The pivot serves as the center of a straight-line projection that maps solid angles onto the opposite side of the sphere. By transforming spherical distributions in this way, we derive novel parametric spherical distributions that can be evaluated and importance-sampled from the original distributions using simple, closedform expressions. Moreover, we prove that if the original distribution can be sampled and/or integrated over a spherical cap, then so can the transformed distribution. We exploit the properties of our parameterization to derive e cient spherical lighting techniques for both real-time and o ine rendering. Our techniques are robust, fast, easy to implement, and achieve quality that is superior to previous work.

We compare the performance of various analytical retroreflecting bidirectional reflectance distribution function (BRDF) models to assess how they reproduce accurately measured data of retroreflecting materials. We introduce a new parametrization, the back vector parametrization, to analyze retroreflecting data, and we show that this parametrization better preserves the isotropy of data. Furthermore, we update existing BRDF models to improve the representation of retroreflective data.

Many applications in rendering rely on integrating functions over spherical polygons. We present a new numerical solution for computing the integral of spherical harmonics (SH) expansions clipped to polygonal domains. Our solution, based on zonal decompositions of spherical integrands and discrete contour integration, introduces an important numerical operating for SH expansions in rendering applications. Our method is simple, efficient, and scales linearly in the bandlimited integrand’s harmonic expansion. We apply our technique to problems in rendering, including surface and volume shading, hierarchical product importance sampling, and fast basis projection for interactive rendering. Moreover, we show how to handle general, nonpolynomial integrands in a Monte Carlo setting using control variates. Our technique computes the integral of bandlimited spherical functions with performance competitive to (or faster than) more general numerical integration methods for a broad class of problems, both in offline and interactive rendering contexts. Our implementation is simple, relying only on self-contained SH evaluation and discrete contour integration routines, and we release a full source CPU-only and shader-based implementations (<750 lines of commented code).