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Exploring high-dimensional data is a common task in many scientific disciplines. To address this task, two-dimensional embeddings, such as tSNE and UMAP, are widely used. While these determine the 2D position of data items, effectively encoding the first two dimensions, suitable visual encodings can be employed to communicate higher-dimensional features. To investigate such encodings, we have evaluated two commonly used glyph types, namely flower glyphs and star glyphs. To evaluate their capabilities for communicating higher-dimensional features in two-dimensional embeddings, we ran a large set of crowd-sourced user studies using real-world data obtained from data.gov. During these studies, participants completed a broad set of relevant tasks derived from related research. This paper describes the evaluated glyph designs, details our tasks, and the quantitative study setup before discussing the results. Finally, we will present insights and provide guidance on the choice of glyph encodings when exploring high-dimensional data., Peer Reviewed, Postprint (published version)

We propose an approach for verification of volume rendering correctness based on an analysis of the volume rendering integral, the basis of most DVR algorithms. With respect to the most common discretization of this continuous model (Riemann summation), we make assumptions about the impact of parameter changes on the rendered results and derive convergence curves describing the expected behavior. Specifically, we progressively refine the number of samples along the ray, the grid size, and the pixel size, and evaluate how the errors observed during refinement compare against the expected approximation errors. We derive the theoretical foundations of our verification approach, explain how to realize it in practice, and discuss its limitations. We also report the errors identified by our approach when applied to two publicly available volume rendering packages.

In this paper, we enable interactive volumetric global illumination by extending photon mapping techniques to handle interactive transfer function (TF) and material editing in the context of volume rendering. We propose novel algorithms and data structures for finding and evaluating parts of a scene affected by these parameter changes, and thus support efficient updates of the photon map. In direct volume rendering (DVR) the ability to explore volume data using parameter changes, such as editable TFs, is of key importance. Advanced global illumination techniques are in most cases computationally too expensive, as they prevent the desired interactivity. Our technique decreases the amount of computation caused by parameter changes, by introducing Historygrams which allow us to efficiently reuse previously computed photon media interactions. Along the viewing rays, we utilize properties of the light transport equations to subdivide a view-ray into segments and independently update them when invalid. Unlike segments of a view-ray, photon scattering events within the volumetric medium needs to be sequentially updated. Using our Historygram approach, we can identify the first invalid photon interaction caused by a property change, and thus reuse all valid photon interactions. Combining these two novel concepts, supports interactive editing of parameters when using volumetric photon mapping in the context of DVR. As a consequence, we can handle arbitrarily shaped and positioned light sources, arbitrary phase functions, bidirectional reflectance distribution functions and multiple scattering which has previously not been possible in interactive DVR., Funding Agencies|Excellence Center at Linkoping and Lund in Information Technology (ELLIIT)||Swedish e-Science Research Centre (SeRC), CADICS, CMIV

In this paper, we describe a novel approach for applying texture mapping to volumetric data sets. In contrast to previous approaches, the presented technique enables a unified integration of 2D and 3D textures and thus allows to emphasize material boundaries as well as volumetric regions within a volumetric data set at the same time. One key contribution of this paper is a parametrization technique for volumetric data sets, which takes into account material boundaries and volumetric regions. Using this technique, the resulting parametrizations of volumetric data sets enable texturing effects which create a higher degree of realism in volume rendered images. We evaluate the quality of the parametrization and demonstrate the usefulness of the proposed concepts by combining volumetric texturing with volumetric lighting models to generate photorealistic volume renderings. Furthermore, we show the applicability in the area of illustrative visualization., Funding Agencies|Deutsche Forschungsgemeinschaft (DFG)||ELLIIT||Strategic Area for ICT research||Swedish Government||ViMaL project (FWF)|P21695||SFB 656 MoBil

Finite element (FE) models are frequently used in engineering and life sciences within time-consuming simulations. In contrast with the regular grid structure facilitated by volumetric data sets, as used in medicine or geosciences, FE models are defined over a non-uniform grid. Elements can have curved faces and their interior can be defined through high-order basis functions, which pose additional challenges when visualizing these models. During ray-casting, the uniformly distributed sample points along each viewing ray must be transformed into the material space defined within each element. The computational complexity of this transformation makes a straightforward approach inadequate for interactive data exploration. In this paper, we introduce a novel coherency-based method which supports the interactive exploration of FE models by decoupling the expensive world-to-material space transformation from the rendering stage, thereby allowing it to be performed within a precomputation stage. Therefore, our approach computes view-independent proxy rays in material space, which are clustered to facilitate data reduction. During rendering, these proxy rays are accessed, and it becomes possible to visually analyze high-order FE models at interactive frame rates, even when they are time-varying or consist of multiple modalities. Within this paper, we provide the necessary background about the FE data, describe our decoupling method, and introduce our interactive rendering algorithm. Furthermore, we provide visual results and analyze the error introduced by the presented approach., Funding Agencies|Swedish Research Council (VR)|2011-4113|Excellence Center at Linkoping and Lund in Information Technology (ELLIIT)||Swedish e-Science Research Centre (SeRC)

In this paper, we present a user study in which we have investigated the influence of seven state-of-the-art volumetric illumination models on the spatial perception of volume rendered images. Within the study, we have compared gradient-based shading with half angle slicing, directional occlusion shading, multidirectional occlusion shading, shadow volume propagation, spherical harmonic lighting as well as dynamic ambient occlusion. To evaluate these models, users had to solve three tasks relying on correct depth as well as size perception. Our motivation for these three tasks was to find relations between the used illumination model, user accuracy and the elapsed time. In an additional task, users had to subjectively judge the output of the tested models. After first reviewing the models and their features, we will introduce the individual tasks and discuss their results. We discovered statistically significant differences in the testing performance of the techniques. Based on these findings, we have analyzed the models and extracted those features which are possibly relevant for the improved spatial comprehension in a relational task. We believe that a combination of these distinctive features could pave the way for a novel illumination model, which would be optimized based on our findings.