Scattering from specular surfaces produces complex optical effects that are frequently encountered in realistic scenes: intricate caustics due to focused reflection, multiple refraction, and high-frequency glints from specular microstructure. Yet, despite their importance and considerable research to this end, sampling of light paths that cause these effects remains a formidable challenge. In this article, we propose a surprisingly simple and general sampling strategy for specular light paths including the above examples, unifying the previously disjoint areas of caustic and glint rendering into a single framework. Given two path vertices, our algorithm stochastically finds a specular subpath connecting the endpoints. In contrast to prior work, our method supports high-frequency normal- or displacement-mapped geometry, samples specular-diffuse-specular ("SDS") paths, and is compatible with standard Monte Carlo methods including unidirectional path tracing. Both unbiased and biased variants of our approach can be constructed, the latter often significantly reducing variance, which may be appealing in applied settings (e.g. visual effects). We demonstrate our method on a range of challenging scenes and evaluate it against state-of-the-art methods for rendering caustics and glints.

Modern rendering systems are confronted with a dauntingly large and growing set of requirements: in their pursuit of realism, physically based techniques must increasingly account for intricate properties of light, such as its spectral composition or polarization. To reduce prohibitive rendering times, vectorized renderers exploit coherence via instruction-level parallelism on CPUs and GPUs. Differentiable rendering algorithms propagate derivatives through a simulation to optimize an objective function, e.g., to reconstruct a scene from reference images. Catering to such diverse use cases is challenging and has led to numerous purpose-built systems---partly, because retrofitting features of this complexity onto an existing renderer involves an error-prone and infeasibly intrusive transformation of elementary data structures, interfaces between components, and their implementations (in other words, everything). We propose Mitsuba 2, a versatile renderer that is intrinsically retargetable to various applications including the ones listed above. Mitsuba 2 is implemented in modern C++ and leverages template metaprogramming to replace types and instrument the control flow of components such as BSDFs, volumes, emitters, and rendering algorithms. At compile time, it automatically transforms arithmetic, data structures, and function dispatch, turning generic algorithms into a variety of efficient implementations without the tedium of manual redesign. Possible transformations include changing the representation of color, generating a "wide" renderer that operates on bundles of light paths, just-in-time compilation to create computational kernels that run on the GPU, and forward/reverse-mode automatic differentiation. Transformations can be chained, which further enriches the space of algorithms derived from a single generic implementation. We demonstrate the effectiveness and simplicity of our approach on several applications that would be very challenging to create without assistance: a rendering algorithm based on coherent MCMC exploration, a caustic design method for gradient-index optics, and a technique for reconstructing heterogeneous media in the presence of multiple scattering.

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color albedos, captured in five wavelength ranges covering the visible spectrum. We demonstrate usage of our data-driven pBRDF model in a physically based renderer that accounts for polarized interreflection, and we investigate the relationship of polarization and material appearance, providing insights into the behavior of characteristic real-world pBRDFs. CCS Concepts: • Computing methodologies → Image and video acquisition; Reflectance modeling.

Physically based differentiable rendering algorithms propagate derivatives through realistic light transport simulations and have applications in diverse areas including inverse reconstruction and machine learning. Recent progress has led to unbiased methods that can simultaneously compute derivatives with respect to millions of parameters. At the same time, elementary properties of these methods remain poorly understood. Current algorithms for differentiable rendering are constructed by mechanically differentiating a given primal algorithm. While convenient, such an approach is simplistic because it leaves no room for improvement. Differentiation produces major changes in the integrals that occur throughout the rendering process, which indicates that the primal and differential algorithms should be decoupled so that the latter can suitably adapt. This leads to a large space of possibilities: consider that even the most basic Monte Carlo path tracer already involves several design choices concerning the techniques for sampling materials and emitters, and their combination, e.g. via multiple importance sampling (MIS). Differentiation causes a veritable explosion of this decision tree: should we differentiate only the estimator, or also the sampling technique? Should MIS be applied before or after differentiation? Are specialized derivative sampling strategies of any use? How should visibility-related discontinuities be handled when millions of parameters are differentiated simultaneously? In this paper, we provide a taxonomy and analysis of different estimators for differential light transport to provide intuition about these and related questions.