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Item Quad-Based Fourier Transform for Efficient Diffraction Synthesis(The Eurographics Association and John Wiley & Sons Ltd., 2018) Scandolo, Leonardo; Lee, Sungkil; Eisemann, Elmar; Jakob, Wenzel and Hachisuka, ToshiyaFar-field diffraction can be evaluated using the Discrete Fourier Transform (DFT) in image space but it is costly due to its dense sampling. We propose a technique based on a closed-form solution of the continuous Fourier transform for simple vector primitives (quads) and propose a hierarchical and progressive evaluation to achieve real-time performance. Our method is able to simulate diffraction effects in optical systems and can handle varying visibility due to dynamic light sources. Furthermore, it seamlessly extends to near-field diffraction. We show the benefit of our solution in various applications, including realistic real-time glare and bloom rendering.Item Spectral Gradient Sampling for Path Tracing(The Eurographics Association and John Wiley & Sons Ltd., 2018) Petitjean, Victor; Bauszat, Pablo; Eisemann, Elmar; Jakob, Wenzel and Hachisuka, ToshiyaSpectral Monte-Carlo methods are currently the most powerful techniques for simulating light transport with wavelengthdependent phenomena (e.g., dispersion, colored particle scattering, or diffraction gratings). Compared to trichromatic rendering, sampling the spectral domain requires significantly more samples for noise-free images. Inspired by gradient-domain rendering, which estimates image gradients, we propose spectral gradient sampling to estimate the gradients of the spectral distribution inside a pixel. These gradients can be sampled with a significantly lower variance by carefully correlating the path samples of a pixel in the spectral domain, and we introduce a mapping function that shifts paths with wavelength-dependent interactions. We compute the result of each pixel by integrating the estimated gradients over the spectral domain using a onedimensional screened Poisson reconstruction. Our method improves convergence and reduces chromatic noise from spectral sampling, as demonstrated by our implementation within a conventional path tracer.