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We consider a task of surveillance-evading path-planning in a continuous setting. An Evader strives to escape from a 2D domain while minimizing the risk of detection (and immediate capture). The probability of detection is path-dependent and determined by the spatially inhomogeneous surveillance intensity, which is fixed but a priori unknown and gradually learned in the multi-episodic setting. We introduce a Bayesian reinforcement learning algorithm that relies on a Gaussian Process regression (to model the surveillance intensity function based on the information from prior episodes), numerical methods for Hamilton-Jacobi PDEs (to plan the best continuous trajectories based on the current model), and Confidence Bounds (to balance the exploration vs exploitation). We use numerical experiments and regret metrics to highlight the significant advantages of our approach compared to traditional graph-based algorithms of reinforcement learning. 

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.