The perception of transparency and the underlying neural mechanisms have been subject to extensive research in the cognitive sciences. However, we have yet to develop visualization techniques that optimally convey the inner structure of complex transparent shapes. In this paper, we apply the findings of perception research to develop a novel illustrative rendering method that enhances surface transparency nonlocally. Rendering of transparent geometry is computationally expensive since many optimizations, such as visibility culling, are not applicable and fragments have to be sorted by depth for correct blending. In order to overcome these difficulties efficiently, we propose the illustration buffer. This novel data structure combines the ideas of the A and G-buffers to store a list of all surface layers for each pixel. A set of local and nonlocal operators is then used to process these depth-lists to generate the final image. Our technique is interactive on current graphics hardware and is only limited by the available graphics memory. Based on this framework, we present an efficient algorithm for a nonlocal transparency enhancement that creates expressive renderings of transparent surfaces. A controlled quantitative double blind user study shows that the presented approach improves the understanding of complex transparent surfaces significantly.

We present a visualization tool for the real-time analysis of interactively steered ensemble-simulation runs, and apply it to flooding simulations. Simulations are performed on-the-fly, generating large quantities of data. The user wants to make sense of the data as it is created. The tool facilitates understanding of what happens in all scenarios, where important events occur, and how simulation runs are related. We combine different approaches to achieve this goal. To maintain an overview, data are aggregated and embedded into the simulation rendering, showing trends, outliers, and robustness. For a detailed view, we use information-visualization views and interactive visual analysis techniques. A selection mechanism connects the two approaches. Points of interest are selected by clicking on aggregates, supplying data for visual analysis. This allows the user to maintain an overview of the ensemble and perform analysis even as new data are supplied through simulation steering. Unexpected or unwanted developments are detected easily, and the user can focus the exploration on them. The solution was evaluated with two case studies focusing on placing and testing flood defense measures. Both were evaluated by a consortium of flood simulation and defense experts, who found the system to be both intuitive and relevant.

In this paper, we present a data-flow system which supports comparative analysis of time-dependent data and interactive simulation steering. The system creates data on-the-fly to allow for the exploration of different parameters and the investigation of multiple scenarios. Existing data-flow architectures provide no generic approach to handle modules that perform complex temporal processing such as particle tracing or statistical analysis over time. Moreover, there is no solution to create and manage module data, which is associated with alternative scenarios. Our solution is based on generic data-flow algorithms to automate this process, enabling elaborate data-flow procedures, such as simulation, temporal integration or data aggregation over many time steps in many worlds. To hide the complexity from the user, we extend the World Lines interaction techniques to control the novel data-flow architecture. The concept of multiple, special-purpose cursors is introduced to let users intuitively navigate through time and alternative scenarios. Users specify only what they want to see, the decision which data are required is handled automatically. The concepts are explained by taking the example of the simulation and analysis of material transport in levee-breach scenarios. To strengthen the general applicability, we demonstrate the investigation of vortices in an offline-simulated dam-break data set.

Artistic illustrations of important structures in fluid flow have a long-standing tradition and are appreciated as clearly perceivable, instructive, but still conveying all relevant information to the viewer. One important illustrative technique for such visualizations are cutaways. Currently cutaways are placed manually or using view-vector based approaches. We propose to optimize the visibility of important target features based on a degree-of-interest (DOI) function. The DOI is specified during interactive visual analysis, e.g., by brushing scatterplots. We show that the problem of placing cutaway boxes optimally is NP-hard in the number of boxes. To overcome this obstacle, we present an intelligent method to compute cutaways. Geometric cutaway objects are positioned using a view-dependent objective function which optimizes the visibility of all features. In order to approximate the optimal solution, we use a Monte Carlo method and exploit temporal coherence in dynamic scenes. Performance-critical parts are implemented on the GPU. The proposed method can be integrated easily into existing rendering frameworks and is general enough to be able to optimize other parameters besides cutaways as well. We evaluate the performance of the algorithm and provide a case study of vorticity visualization in a turbulent flow.

Abstract We present a dense visualization of vector fields on multi‐layered surfaces. The method is based on the illustration buffer, which provides a screen space representation of the surface, where each pixel stores a list of all surface layers. This representation is implemented on the GPU using shaders and leads to a fast output sensitive technique. In our approach, we first use procedural noise to create an initial spot pattern on the surface that has both an almost constant screen space frequency and is view independent. Then, we perform anisotropic diffusion simultaneously on all surface layers using a discretization scheme that maintains second order convergence while only accessing the four neighboring pixels. Finally, we enhance this result with illustrative techniques and composite the final image. Our method works with time‐evolving surfaces, time‐dependent vector fields, and moving cameras. We apply our method to CFD data sets from engineering and astronomy as well as synthetic velocity fields.

Room air flow and air exchange are important aspects for the design of energy-efficient buildings. As a result, simulations are increasingly used prior to construction to achieve an energy-efficient design. We present a visual analysis of air flow generated at building entrances, which uses a combination of revolving doors and air curtains. The resulting flow pattern is challenging because of two interacting flow patterns: On the one hand, the revolving door acts as a pump, on the other hand, the air curtain creates a layer of uniformly moving warm air between the interior of the building and the revolving door. Lagrangian coherent structures (LCS), which by definition are flow barriers, are the method of choice for visualizing the separation and recirculation behavior of warm and cold air flow. The extraction of LCS is based on the finite-time Lyapunov exponent (FTLE) and makes use of a ridge definition which is consistent with the concept of weak LCS. Both FTLE computation and ridge extraction are done in a robust and efficient way by making use of the fast Fourier transform for computing scale-space derivatives.

Abstract Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering. Methods based on vector field topology are known for their convenience for visualizing and analysing steady flows, but a counterpart for unsteady flows is still missing. However, a lot of good and relevant work aiming at such a solution is available. We give an overview of previous research leading towards topology‐based and topology‐inspired visualization of unsteady flow, pointing out the different approaches and methodologies involved as well as their relation to each other, taking classical (i.e. steady) vector field topology as our starting point. Particularly, we focus on Lagrangian methods, space–time domain approaches, local methods and stochastic and multifield approaches. Furthermore, we illustrate our review with practical examples for the different approaches.

Abstract In the visualization of flow simulation data, feature detectors often tend to result in overly rich response, making some sort of filtering or simplification necessary to convey meaningful images. In this paper we present an approach that builds upon a decomposition of the flow field according to dynamical importance of different scales of motion energy. Focusing on the high‐energy scales leads to a reduction of the flow field while retaining the underlying physical process. The presented method acknowledges the intrinsic structures of the flow according to its energy and therefore allows to focus on the energetically most interesting aspects of the flow. Our analysis shows that this approach can be used for methods based on both local feature extraction and particle integration and we provide a discussion of the error caused by the approximation. Finally, we illustrate the use of the proposed approach for both a local and a global feature detector and in the context of numerical flow simulations.

Flood disasters are the most common natural risk and tremendous efforts are spent to improve their simulation and management. However, simulation-based investigation of actions that can be taken in case of flood emergencies is rarely done. This is in part due to the lack of a comprehensive framework which integrates and facilitates these efforts. In this paper, we tackle several problems which are related to steering a flood simulation. One issue is related to uncertainty. We need to account for uncertain knowledge about the environment, such as levee-breach locations. Furthermore, the steering process has to reveal how these uncertainties in the boundary conditions affect the confidence in the simulation outcome. Another important problem is that the simulation setup is often hidden in a black-box. We expose system internals and show that simulation steering can be comprehensible at the same time. This is important because the domain expert needs to be able to modify the simulation setup in order to include local knowledge and experience. In the proposed solution, users steer parameter studies through the World Lines interface to account for input uncertainties. The transport of steering information to the underlying data-flow components is handled by a novel meta-flow. The meta-flow is an extension to a standard data-flow network, comprising additional nodes and ropes to abstract parameter control. The meta-flow has a visual representation to inform the user about which control operations happen. Finally, we present the idea to use the data-flow diagram itself for visualizing steering information and simulation results. We discuss a case-study in collaboration with a domain expert who proposes different actions to protect a virtual city from imminent flooding. The key to choosing the best response strategy is the ability to compare different regions of the parameter space while retaining an understanding of what is happening inside the data-flow system.

Abstract In this paper we present an extended critical point concept which allows us to apply vector field topology in the case of unsteady flow. We propose a measure forunsteadinesswhich describes the rate of change of the velocities in a fluid element over time. This measure allows us to select particles for which topological properties remain intact inside a finite spatio‐temporal neighborhood. One benefit of this approach is that the classification of critical points based on the eigenvalues of the Jacobian remains meaningful. In the steady case the proposed criterion reduces to the classical definition of critical points. As a first step we show that finding an optimal Galilean frame of reference can be obtained implicitly by analyzing the acceleration field. In a second step we show that this can be extended by switching to the Lagrangian frame of reference. This way the criterion can detect critical points moving along intricate trajectories. We analyze the behavior of the proposed criterion based on two analytical vector fields for which a correct solution is defined by their inherent symmetries and present results for numerical vector fields.

In this paper we present World Lines as a novel interactive visualization that provides complete control over multiple heterogeneous simulation runs. In many application areas, decisions can only be made by exploring alternative scenarios. The goal of the suggested approach is to support users in this decision making process. In this setting, the data domain is extended to a set of alternative worlds where only one outcome will actually happen. World Lines integrate simulation, visualization and computational steering into a single unified system that is capable of dealing with the extended solution space. World Lines represent simulation runs as causally connected tracks that share a common time axis. This setup enables users to interfere and add new information quickly. A World Line is introduced as a visual combination of user events and their effects in order to present a possible future. To quickly find the most attractive outcome, we suggest World Lines as the governing component in a system of multiple linked views and a simulation component. World Lines employ linking and brushing to enable comparative visual analysis of multiple simulations in linked views. Analysis results can be mapped to various visual variables that World Lines provide in order to highlight the most compelling solutions. To demonstrate this technique we present a flooding scenario and show the usefulness of the integrated approach to support informed decision making.

Abstract In this state‐of‐the‐art report we discuss relevant research works related to the visualization of complex, multi‐variate data. We discuss how different techniques take effect at specific stages of the visualization pipeline and how they apply to multi‐variate data sets being composed of scalars, vectors and tensors. We also provide a categorization of these techniques with the aim for a better overview of related approaches. Based on this classification we highlight combinable and hybrid approaches and focus on techniques that potentially lead towards new directions in visualization research. In the second part of this paper we take a look at recent techniques that are useful for the visualization of complex data sets either because they are general purpose or because they can be adapted to specific problems.

In this paper we describe a novel method to integrate interactive visual analysis and machine learning to support the insight generation of the user. The suggested approach combines the vast search and processing power of the computer with the superior reasoning and pattern recognition capabilities of the human user. An evolutionary search algorithm has been adapted to assist in the fuzzy logic formalization of hypotheses that aim at explaining features inside multivariate, volumetric data. Up to now, users solely rely on their knowledge and expertise when looking for explanatory theories. However, it often remains unclear whether the selected attribute ranges represent the real explanation for the feature of interest. Other selections hidden in the large number of data variables could potentially lead to similar features. Moreover, as simulation complexity grows, users are confronted with huge multidimensional data sets making it almost impossible to find meaningful hypotheses at all. We propose an interactive cycle of knowledge-based analysis and automatic hypothesis generation. Starting from initial hypotheses, created with linking and brushing, the user steers a heuristic search algorithm to look for alternative or related hypotheses. The results are analyzed in information visualization views that are linked to the volume rendering. Individual properties as well as global aggregates are visually presented to provide insight into the most relevant aspects of the generated hypotheses. This novel approach becomes computationally feasible due to a GPU implementation of the time-critical parts in the algorithm. A thorough evaluation of search times and noise sensitivity as well as a case study on data from the automotive domain substantiate the usefulness of the suggested approach.

In this paper we present a method for vortex core line extraction which operates directly on the smoothed particle hydrodynamics (SPH) representation and, by this, generates smoother and more (spatially and temporally) coherent results in an efficient way. The underlying predictor-corrector scheme is general enough to be applied to other line-type features and it is extendable to the extraction of surfaces such as isosurfaces or Lagrangian coherent structures. The proposed method exploits temporal coherence to speed up computation for subsequent time steps. We show how the predictor-corrector formulation can be specialized for several variants of vortex core line definitions including two recent unsteady extensions, and we contribute a theoretical and practical comparison of these. In particular, we reveal a close relation between unsteady extensions of Fuchs et al. and Weinkauf et al. and we give a proof of the Galilean invariance of the latter. When visualizing SPH data, there is the possibility to use the same interpolation method for visualization as has been used for the simulation. This is different from the case of finite volume simulation results, where it is not possible to recover from the results the spatial interpolation that was used during the simulation. Such data are typically interpolated using the basic trilinear interpolant, and if smoothness is required, some artificial processing is added. In SPH data, however, the smoothing kernels are specified from the simulation, and they provide an exact and smooth interpolation of data or gradients at arbitrary points in the domain.

Feature-based flow visualization is naturally dependent on feature extraction. To extract flow features, often higher-order properties of the flow data are used such as the Jacobian or curvature properties, implicitly describing the flow features in terms of their inherent flow characteristics (e.g., collinear flow and vorticity vectors). In this paper we present recent research which leads to the (not really surprising) conclusion that feature extraction algorithms need to be extended to a time-dependent analysis framework (in terms of time derivatives) when dealing with unsteady flow data. Accordingly, we present two extensions of the parallel vectors based vortex extraction criteria to the time-dependent domain and show the improvements of feature-based flow visualization in comparison to the steady versions of this extraction algorithm both in the context of a high-resolution dataset, i.e., a simulation specifically designed to evaluate our new approach, as well as for a real-world dataset from a concrete application.