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    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, Toshiya
    Far-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.
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    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, Toshiya
    Spectral 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.
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    Multiscale Visualization and Exploration of Large Bipartite Graphs
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Pezzotti, Nicola; Fekete, Jean-Daniel; Höllt, Thomas; Lelieveldt, Boudewijn P. F.; Eisemann, Elmar; Vilanova, Anna; Jeffrey Heer and Heike Leitte and Timo Ropinski
    A bipartite graph is a powerful abstraction for modeling relationships between two collections. Visualizations of bipartite graphs allow users to understand the mutual relationships between the elements in the two collections, e.g., by identifying clusters of similarly connected elements. However, commonly-used visual representations do not scale for the analysis of large bipartite graphs containing tens of millions of vertices, often resorting to an a-priori clustering of the sets. To address this issue, we present the Who's-Active-On-What-Visualization (WAOW-Vis) that allows for multiscale exploration of a bipartite socialnetwork without imposing an a-priori clustering. To this end, we propose to treat a bipartite graph as a high-dimensional space and we create the WAOW-Vis adapting the multiscale dimensionality-reduction technique HSNE. The application of HSNE for bipartite graph requires several modifications that form the contributions of this work. Given the nature of the problem, a set-based similarity is proposed. For efficient and scalable computations, we use compressed bitmaps to represent sets and we present a novel space partitioning tree to efficiently compute similarities; the Sets Intersection Tree. Finally, we validate WAOWVis on several datasets connecting Twitter-users and -streams in different domains: news, computer science and politics. We show how WAOW-Vis is particularly effective in identifying hierarchies of communities among social-media users.