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Visualization and analysis techniques play a key role in the discovery of relevant features in ensemble data. Trends, in the form of persisting commonalities or differences in time-varying ensemble datasets, constitute one of the most expressive feature types in ensemble analysis. We develop a flow-graph representation as the core of a system designed for the visual analysis of trends in time-varying ensembles. In our interactive analysis framework, this graph is linked to a representation of ensemble parameter-space and the ensemble itself. This facilitates a detailed examination of trends and their correlations to properties of input-space. We demonstrate the utility of the proposed trends analysis framework in several benchmark data sets, highlighting its capability to support goal-driven design of time-varying simulations.

The simulation of complex events is a challenging task and often requires careful selection of simulation parameters. With the availability of vast computation resources, it has become possible to run several alternative parameter settings or simulation models in parallel, creating an 'ensemble' of possible outcomes for a given event of interest. Recently, the visual analysis of such ensemble data has repeatedly come up as one of the most important new areas of visualization and it is expected to have a wide impact on the field of visualization in the next few years. The main challenge is to develop expressive visualizations of properties of this set of solutions, the ensemble, to support scientists in this challenging parameter-space exploration task. This paper presents and explores future challenges for ensemble visualization.

Numerical ensemble forecasting is a powerful tool that drives many risk analysis efforts and decision making tasks. These ensembles are composed of individual simulations that each uniquely model a possible outcome for a common event of interest: e.g., the direction and force of a hurricane, or the path of travel and mortality rate of a pandemic. This paper presents a new visual strategy to help quantify and characterize a numerical ensemble's predictive uncertainty: i.e., the ability for ensemble constituents to accurately and consistently predict an event of interest based on ground truth observations. Our strategy employs a Bayesian framework to first construct a statistical aggregate from the ensemble. We extend the information obtained from the aggregate with a visualization strategy that characterizes predictive uncertainty at two levels: at a global level, which assesses the ensemble as a whole, as well as a local level, which examines each of the ensemble's constituents. Through this approach, modelers are able to better assess the predictive strengths and weaknesses of the ensemble as a whole, as well as individual models. We apply our method to two datasets to demonstrate its broad applicability.

Liquid–liquid extraction is a typical multi-fluid problem in chemical engineering where two types of immiscible fluids are mixed together. Mixing of two-phase fluids results in a time-varying fluid density distribution, quantitatively indicating the presence of liquid phases. For engineers who design extraction devices, it is crucial to understand the density distribution of each fluid, particularly flow regions that have a high concentration of the dispersed phase. The propagation of regions of high density can be studied by examining the topology of isosurfaces of the density data. We present a topology-based approach to track the splitting and merging events of these regions using the Reeb graphs. Time is used as the third dimension in addition to two-dimensional (2D) point-based simulation data. Due to low time resolution of the input data set, a physics-based interpolation scheme is required in order to improve the accuracy of the proposed topology tracking method. The model used for interpolation produces a smooth time-dependent density field by applying Lagrangian-based advection to the given simulated point cloud data, conforming to the physical laws of flow evolution. Using the Reeb graph, the spatial and temporal locations of bifurcation and merging events can be readily identified supporting in-depth analysis of the extraction process.

The input–output behavior or flow transfer function of typical mixing processes is highly relevant to the analysis of the dynamic system and its mixing quality. We aim to visualize this behavior by extracting topologically relevant flow volumes from statistics accumulated during particle traversal of the flow field. To guarantee a sufficiently dense sampling of the flow field, we use adaptive time-surfaces for the computation of these trajectory statistics. The proposed volume extraction technique operates in parameter space of the computed time-surfaces and facilitates fast extraction of boundary geometry at different levels of detail. Our results visualize flow transfer functions in the form of volumes for extrema of different time-surface statistics and demonstrate their benefit for flow analysis.

Moment tensors are indefinite tensors derived from seismic measurements and encode important information about earthquakes and surface displacement in the earth's mantle. Appropriate analysis of scattered moment tensor fields requires multi-scale visualization to identify related seismic events. For this matter we provide a visualization of the tensor field at different scales based on multivariate tensor clustering. The resulting visualization allows interactive analysis of individual tensors, analysis of tensor groups and clustering behavior as well as examination of the complete tensor field. Our results show the benefit of mutti-scate earthquake and displacement analysis and demonstrate the advantages over classic tensor visualization and univariate, static cluster visualization.

Advances in computational power now enable domain scientists to address conceptual and parametric uncertainty by running simulations multiple times in order to sufficiently sample the uncertain input space. While this approach helps address conceptual and parametric uncertainties, the ensemble datasets produced by this technique present a special challenge to visualization researchers as the ensemble dataset records a distribution of possible values for each location in the domain. Contemporary visualization approaches that rely solely on summary statistics (e.g., mean and variance) cannot convey the detailed information encoded in ensemble distributions that are paramount to ensemble analysis; summary statistics provide no information about modality classification and modality persistence. To address this problem, we propose a novel technique that classifies high-variance locations based on the modality of the distribution of ensemble predictions. Additionally, we develop a set of confidence metrics to inform the end-user of the quality of fit between the distribution at a given location and its assigned class. Finally, for the special application of evaluating the stability of bimodal regions, we develop local and regional metrics.

The evolution of strain and development of material anisotr opy in models of Earth’s mantle flow convey important information about how to interpret the geometric relations hip between observation of seismic anisotropy and the actual mantle flow field. By combining feature extraction techniques such as path line integration and tensor accumulation, we compute time-varying strain vector fields thatbuild the foundation for a number of feature extraction and visualization techniques. The proposed field segmentat ion, clustering, histograms, and multi-volume visualization techniques facilitate an intuitive understandingof three-dimensional strain in such flow fields, overcoming limitations of previous methods such as 2D line plots and sli cing. We present applications of our approach to an artificial time varying flow data set and a real world example of stationary flow in a subduction zone and discuss the challenges of processing these geophysical data sets aswell as the insights gained.

This paper presents a novel method for the extraction and visualization of volume deformations in grid-less point based flow simulations. Our primary goals are the segmentation of different paths through a mixing device and the visualization of ellipsoidal particle deformations. The main challenges are the numerically efficient processing of deformation tensors and the robust integration of stream- and streaklines at boundaries of the dataset such that closed segments are obtained. Our results show two- and three-dimensional particle deformations as well as the segmentation of volumes in stationary fields and areas in time-dependent datasets taking consistent paths through a mixing device.

Effective display and visual analysis of complex 3D data is a challenging task. Occlusions, overlaps, and projective distortions—as frequently caused by typical 3D rendering techniques—can be major obstacles to unambiguous and robust data analysis. Slicing planes are a ubiquitous tool to resolve several of these issues. They act as simple clipping geometry to provide clear cut-away views of the data. We propose to enhance the visualization and analysis process by providing methods for automatic placement of such slicing planes based on local optimization of gradient vector flow. The final obtained slicing planes maximize the total amount of information displayed with respect to a pre-specified importance function. We demonstrate how such automated slicing plane placement is able to support and enrich 3D data visualization and analysis in multiple scenarios, such as volume or surface rendering, and evaluate its performance in several benchmark data sets.

Integral flow surfaces constitute a widely used flow visualization tool due to their capability to convey important flow information such as fluid transport, mixing, and domain segmentation. Current flow surface rendering techniques limit their expressiveness, however, by focusing virtually exclusively on displacement visualization, visually neglecting the more complex notion of deformation such as shearing and stretching that is central to the field of continuum mechanics. To incorporate this information into the flow surface visualization and analysis process, we derive a metric tensor field that encodes local surface deformations as induced by the velocity gradient of the underlying flow field. We demonstrate how properties of the resulting metric tensor field are capable of enhancing present surface visualization and generation methods and develop novel surface querying, sampling, and visualization techniques. The provided results show how this step towards unifying classic flow visualization and more advanced concepts from continuum mechanics enables more detailed and improved flow analysis.

Time surfaces are a versatile tool to visualise advection and deformation in flow fields. Due to complex flow behaviours involving stretching, shearing, and folding, straightforward mesh-based representations of these surfaces can develop artefacts and degenerate quickly. Common counter-measures rely on refinement and adaptive insertion of new particles which lead to an unpredictable increase in memory requirements. We propose a novel time surface extraction technique that keeps the number of required flow particles constant, while providing a high level of fidelity and enabling straightforward load balancing. Our solution implements a 2D particle relaxation procedure that makes use of local surface metric tensors to model surface deformations. We combine this with an accurate bicubic surface representation to provide an artefact-free surface visualisation. We demonstrate and evaluate benefits of the proposed method with respect to surface accuracy and computational efficiency.

Where the computation of particle trajectories in classic vector field representations includes computationally involved numerical integration, a Lagrangian representation in the form of a flow map opens up new alternative ways of trajectory extraction through interpolation. In our paper, we present a novel re-organization of the Lagrangian representation by sub-sampling a pre-computed set of trajectories into multiple levels of resolution, maintaining a bound over the amount of memory mapped by the file system. We exemplify the advantages of replacing integration with interpolation for particle trajectory calculation through a real-time, low memory cost, interactive exploration environment for the study of flow fields. Beginning with a base resolution, once an area of interest is located, additional trajectories from other levels of resolution are dynamically loaded, densely covering those regions of the flow field that are relevant for the extraction of the desired feature. We show that as more trajectories are loaded, the accuracy of the extracted features converges to the accuracy of the flow features extracted from numerical integration with the added benefit of real-time, non-iterative, multi-resolution path and time surface extraction.

Evaluation, solved and unsolved problems, and future directions are popular themes pervading the visualization community over the last decade. The top unsolved problem in both scientific and information visualization was the subject of an IEEE Visualization Conference panel in 2004. The future of graphics hardware was another important topic of discussion the same year. The subject of how to evaluate visualization returned a few years later. Chris Johnson published a list of 10 top problems in scientific visualization research. This was followed up by report of both past achievements and future challenges in visualization research as well as financial support recommendations to the National Science Foundation (NSF) and National Institute of Health (NIH). Chen recently published the first list of top unsolved information visualization problems. Future research directions of topology-based visualization was also a major theme of a workshop on topology-based methods. Laramee and Kosara published a list of top future challenges in human-centered visualization.

Feature-based techniques are one of the main categories of methods used in scientific visualization. Features are structures in a dataset that are meaningful within the scientific or engineering context of the dataset. Extracted features can be visualized directly, or they can be used indirectly for modifying another type of visualization. In multifield data, each of the component fields can be searched for features, but in addition, there can be features of the multifield which rely on information form several of its components and which cannot be found by searching in a single field. In this chapter we give a survey of feature-based visualization of multifields, taking both of these feature types into account.

This chapter introduces a novel method for vortex detection in flow fields based on the corotation of line segments and glyph rendering. The corotation measure is defined as a point-symmetric scalar function on a sphere, suitable for direct representation in the form of a three-dimensional glyph. Appropriate placement of these glyphs in the domain of a flow field makes it possible to depict vortical features present in the flow. We demonstrate how topological analysis of this novel glyph-based representation of vortex features can reveal vortex characteristics that lie beyond the capabilities of visualization techniques that consider vortex direction and magnitude information only.

Sets of simulation runs based on parameter and model variation, so-called ensembles, are increasingly used to model physical behaviors whose parameter space is too large or complex to be explored automatically. Visualization plays a key role in conveying important properties in ensembles, such as the degree to which members of the ensemble agree or disagree in their behavior. For ensembles of time-varying vector fields, there are numerous challenges for providing an expressive comparative visualization, among which is the requirement to relate the effect of individual flow divergence to joint transport characteristics of the ensemble. Yet, techniques developed for scalar ensembles are of little use in this context, as the notion of transport induced by a vector field cannot be modeled using such tools. We develop a Lagrangian framework for the comparison of flow fields in an ensemble. Our techniques evaluate individual and joint transport variance and introduce a classification space that facilitates incorporation of these properties into a common ensemble visualization. Variances of Lagrangian neighborhoods are computed using pathline integration and Principal Components Analysis. This allows for an inclusion of uncertainty measurements into the visualization and analysis approach. Our results demonstrate the usefulness and expressiveness of the presented method on several practical examples.

Integration-based flow visualization provides important visual cues about fluid transport. Analyzing the behavior of infinitesimal volumes as opposed to the behavior of rigid particles provides additional details valuable to flow visualization research. Our work concentrates on examining the local velocity gradient tensor along the path of a particle seeded within time-varying flow to produce a visualization highlighting temporal characteristics of particle behaviors, such as deformation. We present a framework for the analysis and visualization of such characteristics, focused on providing concise representations of physically meaningful flow features such as separation regions and vorticity. We apply the derived techniques to two data sets, highlighting the importance of such higher order Lagrangian analysis techniques to time-varying flow analysis.

Material interfaces and free surfaces are a topic of increasing interest in the field of computational fluid dynamics. In parts, reconstructed interfaces from such multi-fluid simulations behave like classic integral surfaces as known in the visualization community, while other regions of the surface undergo topological changes or behave orthogonally to what is expected by the underlying flow field. Thus, the analysis of the flow field in connection with material interface shape and topology is a challenging task. We develop a technique that facilitates visualization and analysis of such complex material interface behavior over time. For this matter, we track a surface parametrization of time-varying material interfaces and identify locations of interaction between material interfaces and fluid particles. Splatting and surface visualization techniques produce an intuitive representation of the derived interface stability. Our results demonstrate, how the interaction of the flow field with the material interface can be highlighted by appropriate extraction and visualization techniques and how the developed techniques can aid analysis of mixing and material interface consistency.

Crease surfaces describe extremal structures of 3D scalar fields. We present a new region-growing-based approach to the meshless extraction of adaptive nonmanifold valley and ridge surfaces that overcomes limitations of previous approaches by decoupling point seeding and triangulation of the surface. Our method is capable of extracting valley surface skeletons as connected minimum structures. As our algorithm is inherently mesh-free and curvature adaptive, it is suitable for surface construction in fields with an arbitrary neighborhood structure. As an application for insightful visualization with valley surfaces, we choose a low frequency acoustics simulation. We use our valley surface construction approach to visualize the resulting complex-valued scalar pressure field for arbitrary frequencies to identify regions of sound cancellation. This provides an expressive visualization of the topology of wave node and antinode structures in simulated acoustics.

Moment tensors derived from seismic measurements during earthquakes are related to stress tensors and keep important information about surface displacement in the earth's mantle. We present methods facilitating an interactive visualization of scattered moment data to support earthquake and displacement analysis. For this goal, we combine and link visualizations of spatial location and orientation information derived from moment tensor decompositions. Furthermore, we contribute new tensor glyphs highlighting the indefinite character of moment tensors as well as novel tensor clustering and averaging techniques to aid interactive visual analysis and ease the challenges of interpreting moment tensor data.

We present a novel algorithm for the geometric extraction of stream volume segmentation for visualization of grid-less flow simulations. Our goal is the segmentation of different paths through a mixing tube where the flow is represented by scattered point sets approximated with moving least squares. The key challenges are thewatertight construction of boundary representations from separatrices. These are obtained by integrating and intersectingstream surfaces starting at separation and attachment lines at boundaries of flow obstacles. A major challenge is the robust integration of stream lines at boundaries with no-slip condition such that closed volume segments are obtained. Our results show the segmentation of volumes taking consistent paths through a mixing tube with six partitioning blades. Slicing these volumes provides valuable insight into the quality of the mixing process.