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Stochastic geometry models have enjoyed immense success in graphics for modeling interactions of light with complex phenomena such as participating media, rough surfaces, fibers, and more. Although each of these models operates on the same principle of replacing intricate geometry by a random process and deriving the average light transport across all instances thereof, they are each tailored to one specific application and are fundamentally distinct. Each type of stochastic geometry present in the scene is firmly encapsulated in its own appearance model, with its own statistics and light transport average, and no cross-talk between different models or deterministic and stochastic geometry is possible. In this paper, we derive a theory of light transport on stochastic implicit surfaces, a geometry model capable of expressing deterministic geometry, microfacet surfaces, participating media, and an exciting new continuum in between containing aggregate appearance, non-classical media, and more. Our model naturally supports spatial correlations, missing from most existing stochastic models. Our theory paves the way for tractable rendering of scenes in which all geometry is described by the same stochastic model, while leaving ample future work for developing efficient sampling and rendering algorithms. 

We propose a novel design for a do-it-yourself hyperspectral imaging system which operates by taking multiple photographs through tunable, polarization-induced, spectral filters. Prior approaches in this do-it-yourself arena achieve hyperspectral imaging by selecting from a discrete set of spectra baked into existing products. In contrast, our approach is capable of generating a continuous family of broadband transmission spectra by simple rotations of stacked polarizers and waveplates. This greatly expands the potential range of representable spectra from a fixed-dimensional to an arbitrary-dimensional space. We analyze the theoretical spectral gamut of our approach and demonstrate its viability for spectral surface reflectance reconstruction both in simulation and with a low-cost physical prototype. Our prototype demonstrates that our approach can achieve comparable quality to prior work at reduced cost, while the new design space holds ample opportunity for increased quality and flexibility with professional manufacturing. 

Partial differential equations (PDEs) with spatially varying coefficients arise throughout science and engineering, modeling rich heterogeneous material behavior. Yet conventional PDE solvers struggle with the immense complexity found in nature, since they must first discretize the problem---leading to spatial aliasing, and global meshing/sampling that is costly and error-prone. We describe a method that approximates neither the domain geometry, the problem data, nor the solution space, providing the exact solution (in expectation) even for problems with extremely detailed geometry and intricate coefficients. Our main contribution is to extend thewalk on spheres (WoS)algorithm from constant- to variable-coefficient problems, by drawing on techniques from volumetric rendering. In particular, an approach inspired bynull-scatteringyields unbiased Monte Carlo estimators for a large class of 2nd order elliptic PDEs, which share many attractive features with Monte Carlo rendering: no meshing, trivial parallelism, and the ability to evaluate the solution at any point without solving a global system of equations.