We propose a data reduction technique for scattered data based on statistical sampling. Our void-and-cluster sampling technique finds a representative subset that is optimally distributed in the spatial domain with respect to the blue noise property. In addition, it can adapt to a given density function, which we use to sample regions of high complexity in the multivariate value domain more densely. Moreover, our sampling technique implicitly defines an ordering on the samples that enables progressive data loading and a continuous level-of-detail representation. We extend our technique to sample time-dependent trajectories, for example pathlines in a time interval, using an efficient and iterative approach. Furthermore, we introduce a local and continuous error measure to quantify how well a set of samples represents the original dataset. We apply this error measure during sampling to guide the number of samples that are taken. Finally, we use this error measure and other quantities to evaluate the quality, performance, and scalability of our algorithm.Data reduction is thus a necessary means to reduce storage requirements for both simulation, measurement devices, and for subsequent data analysis.We specifically consider the reduction of large, spatio-temporal scattered data, i.e. unstructured points in space-time with an associated value domain. In particular, we investigate the use of statistical sampling to reduce large data sets to a representative subset. Sampling scales well to higher dimensional data and is well-suited for scattered data. Although simple random sampling gives decent results, recent work improves upon this using stratified [21, 28] and informationguided sampling [3,27]. These results emphasize the significance of 1 arXiv:1907.05073v1 [cs.GR]

Predictions of the primary breakup of fuel in realistic fuel spray nozzles for aero-enginecombustors by means of the SPH method are presented. Based on simulations in 2D, novel insightsinto the fundamental effects of primary breakup are established by analyzing the dynamics ofLagrangian-coherent structures (LCSs). An in-house visualization and data exploration platformis used in order to retrieve fields of the finite-time Lyapunov exponent (FTLE) derived from theSPH predictions aiming at the identification of time resolved LCSs. The main focus of this paperis demonstrating the suitability of FTLE fields to capture and visualize the interaction between thegas and the fuel flow leading to liquid disintegration. Aiming for a convenient illustration at a highspatial resolution, the analysis is presented based on 2D datasets. However, the method and theconclusions can analoguosly be transferred to 3D. The FTLE fields of modified nozzle geometriesare compared in order to highlight the influence of the nozzle geometry on primary breakup, whichis a novel and unique approach for this industrial application. Modifications of the geometry areproposed which are capable of suppressing the formation of certain LCSs, leading to less fluctuationof the fuel flow emerging from the spray nozzle.

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Physically based rendering is a well‐understood technique to produce realistic‐looking images. However, different algorithms exist for efficiency reasons, which work well in certain cases but fail or produce rendering artefacts in others. Few tools allow a user to gain insight into the algorithmic processes. In this work, we present such a tool, which combines techniques from information visualization and visual analytics with physically based rendering. It consists of an interactive parallel coordinates plot, with a built‐in sampling‐based data reduction technique to visualize the attributes associated with each light sample. Two‐dimensional (2D) and three‐dimensional (3D) heat maps depict any desired property of the rendering process. An interactively rendered 3D view of the scene displays animated light paths based on the user's selection to gain further insight into the rendering process. The provided interactivity enables the user to guide the rendering process for more efficiency. To show its usefulness, we present several applications based on our tool. This includes differential light transport visualization to optimize light setup in a scene, finding the causes of and resolving rendering artefacts, such as fireflies, as well as a path length contribution histogram to evaluate the efficiency of different Monte Carlo estimators.

Rapidly growing data sizes of scientific simulations pose significant challenges for interactive visualization and analysis techniques. In this work, we propose a compact probabilistic representation to interactively visualize large scattered datasets. In contrast to previous approaches that represent blocks of volumetric data using probability distributions, we model clusters of arbitrarily structured multivariate data. In detail, we discuss how to efficiently represent and store a high-dimensional distribution for each cluster. We observe that it suffices to consider low-dimensional marginal distributions for two or three data dimensions at a time to employ common visual analysis techniques. Based on this observation, we represent high-dimensional distributions by combinations of low-dimensional Gaussian mixture models. We discuss the application of common interactive visual analysis techniques to this representation. In particular, we investigate several frequency-based views, such as density plots in 1D and 2D, density-based parallel coordinates, and a time histogram. We visualize the uncertainty introduced by the representation, discuss a level-of-detail mechanism, and explicitly visualize outliers. Furthermore, we propose a spatial visualization by splatting anisotropic 3D Gaussians for which we derive a closed-form solution. Lastly, we describe the application of brushing and linking to this clustered representation. Our evaluation on several large, real-world datasets demonstrates the scaling of our approach.