Aortic dissection is a life-threatening cardiovascular disease characterized by blood entering the media layer of the aortic vessel wall. This creates a second flow channel, known as the false lumen, which weakens the aortic wall and can potentially lead to fatal aortic rupture. Current risk stratification of aortic dissections is primarily based on morphological features of the aorta. However, hemodynamics also play a significant role in disease progression, though their investigation and visualization remain challenging. Common flow visualizations often experience visual clutter, especially when dealing with the intricate morphologies of aortic dissections. In this work, we implement and evaluate different approaches to visualizing the flow in aortic dissections effectively. We employ three techniques, namely streaklines with depth-dependent halos, transparent streaklines, and smoke surfaces. The latter is a technique based on streak surfaces, enhanced with opacity modulations, to produce a smoke-like appearance that improves visual clarity. We adapt the original opacity modulation of smoke surfaces to visualize flow even within the complex geometries of aortic dissections, thereby enhancing visual fidelity. To effectively capture dissection hemodynamics, we developed customized seeding structures that adapt to the shape of the surrounding lumen. Our evaluation, conducted via an online questionnaire, included medical professionals, fluid simulation experts, and visualization specialists. By analyzing results across these groups, we highlight differences in preference and interpretability, offering insight into domain-specific needs. No single visualization technique emerged as the best overall. Smoke surfaces provide the best overall clarity and visual realism. However, participants found streaklines with halos to be the best for quantifying flow, dispite them introducing significant visual clutter. Transparent streaklines serve as a middle ground, offering improved clarity over halos while maintaining some level of detail. Across all participant groups, smoke surfaces were rated as the most visually appealing and lifelike, with medical professionals highlighting their resemblance to contrast-agent injections used in clinical practice.

Principal Component Analysis (PCA) is perhaps the most popular linear projection technique for dimensionality reduction. We consider PCA under the assumption that the high-dimensional data points are equipped with Gaussian uncertainty. Several approaches to such uncertainty-aware PCA have been developed recently in the visualization community. Since PCA is a discontinuous map, a small uncertainty in the data points can result in a huge uncertainty in the projected points. We show that the uncertainty of the data points also creates uncertainty in the eigenvectors of the covariance matrix that defines the PCA projection. We present a closed-form expression to quantify eigenvector uncertainty. Based on this, we propose a 3D glyph that supports the decision whether existing solutions for uncertainty-aware PCA are sufficient, or whether a more expensive sampling-based approach is required. We apply our approach to several test data sets.

Finding projections of multidimensional data domains to the 2D screen space is a well-known problem. Multidimensional data often comes with the property that the dimensions are measured in different physical units, which renders the ratio between dimensions, i.e., their scale, arbitrary. The result of common projections, like PCA, t-SNE, or MDS, depends on this ratio, i.e., these projections are variant to scaling. This results in an undesired subjective view of the data, and thus, their projection. Simple solutions like normalization of each dimension are widely used, but do not always give high-quality results. We propose to visually analyze the space of all scalings and to find optimal scalings w.r.t. the quality of the visualization. For this, we evaluate different quality criteria on scatter plots. Given a quality criterion, our approach finds scalings that yield good visualizations with little to no user input using numerical optimization. Simultaneously, our method results in a scaling invariant projection, proposing an objective view to the projected data. We show for several examples that such an optimal scaling can significantly improve the visualization quality.

Interpolation between camera positions is a standard problem in computer graphics and can be considered the foundation of camera path planning. As the basis for a new interpolation method, we introduce a new Riemannian metric in camera space, which measures the 3D image flow under a small movement of the camera. Building on this, we define a linear interpolation between two cameras as shortest geodesic in camera space, for which we provide a closed-form solution after a mild simplification of the metric. Furthermore, we propose a geodesic Catmull-Rom interpolant for keyframe camera animation. We compare our approach with several standard camera interpolation methods and obtain consistently better camera paths especially for cameras with extremely varying scales.

We introduce a representation of a 2D steady vector field ${{\mathbf v}}$ by two scalar fields $a$, $b$, such that the isolines of $a$ correspond to stream lines of ${{\mathbf v}}$, and $b$ increases with constant speed under integration of ${{\mathbf v}}$. This way, we get a direct encoding of stream lines, i.e., a numerical integration of ${{\mathbf v}}$ can be replaced by a local isoline extraction of $a$. To guarantee a solution in every case, gradient-preserving cuts are introduced such that the scalar fields are allowed to be discontinuous in the values but continuous in the gradient. Along with a piecewise linear discretization and a proper placement of the cuts, the fields $a$ and $b$ can be computed. We show several evaluations on non-trivial vector fields.

The numerical extraction of vortex cores from time-dependent fluid flow attracted much attention over the past decades. A commonly agreed upon vortex definition remained elusive since a proper vortex core needs to satisfy two hard constraints: it must be objective and Lagrangian. Recent methods on objectivization met the first but not the second constraint, since there was no formal guarantee that the resulting vortex coreline is indeed a pathline of the fluid flow. In this paper, we propose the first vortex core definition that is both objective and Lagrangian. Our approach restricts observer motions to follow along pathlines, which reduces the degrees of freedoms: we only need to optimize for an observer rotation that makes the observed flow as steady as possible. This optimization succeeds along Lagrangian vortex corelines and will result in a non-zero time-partial everywhere else. By performing this optimization at each point of a spatial grid, we obtain a residual scalar field, which we call vortex deviation error. The local minima on the grid serve as seed points for a gradient descent optimization that delivers sub-voxel accurate corelines. The visualization of both 2D and 3D vortex cores is based on the separation of the movement of the vortex core and the swirling flow behavior around it. While the vortex core is represented by a pathline, the swirling motion around it is visualized by streamlines in the correct frame. We demonstrate the utility of the approach on several 2D and 3D time-dependent vector fields.

Recirculation in flows is an important phenomenon of dynamical systems as it is linked to numerous further properties and behaviors. A formal definition of recirculation surfaces has been introduced in previous work. However, the extraction and visualization of such surfaces is a highly complex challenge as they are 2-manifolds in the 5D space. Although an approach for the geometry extraction exists, there are still several unsolved problems, mainly connected to the computational effort and surface reconstruction. In this work, we propose a fundamentally different idea: Instead of extracting an explicit geometry, we apply a direct ray tracing approach. This way, we effectively circumvent the challenge of reconstructing the geometry. Additionally, we implement multiple strategies for an efficient computation. Due to this, we are able to provide a visualization of recirculation surfaces in a fraction of the computation time of existing approaches.

Lagrangian coherent structures (LCS) is an important concept for the visualization of unsteady flows. They describe the boundaries of regions for which material transport stays mostly coherent over time which can help for a better understanding of dynamical systems. One of the most common techniques for their computation is the extraction of ridges from the finite-time Lyapunov exponent (FTLE) field. FTLE ridges are challenging to extract, both in terms of accuracy and performance, because they expose strong gradients of the underlying field, tend to come close to each other and are dynamic with respect to different time parameters. We present a new method for extracting FTLE ridges for series of integration times which is able to show how coherent regions and their borders evolve over time. Our techniques mainly build on a particle system which is used for sampling the ridges uniformly. This system is highly optimized for the challenges of FTLE ridge extraction. Further, it is able to take advantage of the continuous evolvement of the ridges which makes their sampling for multiple integration times much faster. We test our method on multiple 3D datasets and compare it to the standard Marching Ridges technique. For the extraction examples our method is 13 to over 300 times faster, suggesting a significant advantage. We efficiently extract Lagrangian coherent structures (LCS) as ridges of the finite-time Lyapunov Exponent (FTLE) for series of integration times. Our methods build on a particle system which is highly optimized for the challenges of the FTLE ridge extraction and takes advantage of the continuous evolvement of ridges over time. image

Trajectory data consisting of a low number of smooth parametric curves are standard data sets in visualization. For a visual analysis, not only the behavior of the individual trajectories is of interest but also the relation of the trajectories to each other. Moving objects represented by the trajectories may rotate around each other or around a moving center. We present an approach to compute and visually analyze such rotational behavior in an objective way. We introduce trajectory vorticity (TRV), a measure of rotational behavior of a low number of trajectories. We show that it is objective and that it can be introduced in two independent ways: by approaches for unsteadiness minimization and by considering the relative spin tensor. We compare TRV against single-trajectory methods and apply it to a number of constructed and real trajectory data sets, including drifting buoys in the Atlantic, midge swarm tracking data, pedestrian tracking data, pigeon flocks, and a simulated vortex street

FTLE (Finite Time Lyapunov Exponent) computation is one of the standard approaches to Lagrangian flow analysis. The main features of interest in FTLE fields are ridges that represent hyperbolic Lagrangian Coherent Structures. FTLE ridges tend to become sharp and crisp with increasing integration time, where the sharpness of the ridges is an indicator of the strength of separation. The additional consideration of uncertainty in flows leads to more blurred ridges in the FTLE fields. There are multiple causes for such blurred ridges: either the locations of the ridges are uncertain, or the strength of the ridges is uncertain, or there is low uncertainty but weak separation. Existing approaches for uncertain FTLE computation are unable to distinguish these different sources of uncertainty in the ridges. We introduce a new approach to define and visualize FTLE fields for flow ensembles. Before computing and comparing FTLE fields for the ensemble members, we compute optimal displacements of the domains to mutually align the ridges of the ensemble members as much as possible. We do so in a way that an explicit geometry extraction and alignment of the ridges is not necessary. The additional consideration of these displacements allows for a visual distinction between uncertainty in ridge location, ridge sharpness, and separation strength. We apply the approach to several synthetic and real ensemble data sets.

We analyze two recently-introduced flow measured that are based on a single trajectory only: trajectory stretching exponent (TSE) to detect hyperbolic (stretching) behavior, and trajectory angular velocity (TRA) to detect elliptic (rotation) behavior. Haller et al. [$\href{https://doi.org/10.1063/5.0044151}{2021}$] and Haller et al. [$\href{https://doi.org/10.1063/5.0090124}{2022}$] introduced TSE, TRA as well as the concept of quasi-objectivity, and formulated theorems about the objectivity and quasi-objectivity of TSE and TRA. In this paper, we present two counter-examples showing that all theorems in Haller et al. [$\href{https://doi.org/10.1063/5.0044151}{2021}$] and Haller et al. [$\href{https://doi.org/10.1063/5.0090124}{2022}$] are incorrect

Combustion processes taking place in large-scale burners may need to consider the impact of the recently identified very-large-scale motions (VLSM) appearing in wall-bounded turbulent flows. While VLSM in non-reacting, cold flows have been found to be important and noticeably impact turbulence statistics, the possible influence of VLSM on turbulent premixed flames has not been considered up to now to the best of our knowledge. The present study investigates the interaction of a turbulent flame with VLSM in a channel flow using direct numerical simulations (DNS). Detailed chemical kinetics have been used to compute a H2 flame. The turbulent channel flow corresponds to Reτ= 280, while the premixed flame is associated to a Damköhler number Da = 0.167. First, VLSM have been identified for the non-reacting flow by proper orthogonal decomposition (POD). Interestingly, the propagation of the turbulent flame is found to have a negligible effect on the VLSM, highlighting their resilience. At the same time, the VLSM do not modulate strongly the flame structure, while it is noticeably affected by small-scale vortices. This decoupling might be explained by the very different length scales of both processes, the VLSM covering the full channel length, while the turbulent flame is characterized by small-scale structures. In the same manner, the characteristic time scales also differ widely, the flame time scale being much faster than the characteristic time of the VLSM. The flame curvature is positively correlated with the fluctuating streamwise velocity when the flame is still far from the wall. When approaching the wall, flame quenching takes place in a complex process. Overall, it appears for the present conditions that VLSM do not impact directly the turbulent flame propagation, but there is still an indirect impact through the modifications of the turbulence statistics.

To identify and characterize very-large-scale motions (VLSM) in turbulent channel flows, direct numerical simulations are performed at Re tau = 906 and 3216. The turbulence structure is then analyzed by proper orthogonal decomposition (POD) and multiscale POD (mPOD). Unlike POD, mPOD is able to distinguish the most energetic modes at selected scales (or frequencies) by imposing spectral cutoffs to separate VLSM, large-scale motions (LSM), and small-scale motions. The VLSM can be clearly visualized from the most energetic spatial modes of the mPOD analysis at both Reynolds numbers. The mPOD results identify a new energetic mode that is aligned in the streamwise direction with a characteristic length covering the whole domain length. This new mode (called eVLSM mode) contains substantial energy, making it an important component of the VLSM in the flow field. The other energetic modes typically appear in pairs with specific streamwise phase shifts. The large-scale structures (apart from eVLSM) are inclined to the streamwise direction and appear to be responsible for the typical meandering behavior or even for the breakup of VLSM.

Sparse trajectory data consist of a low number of trajectories such that the reconstruction of an underlying velocity field is not possible. Recently, approaches have been introduced to analyze flow behavior based on a single trajectory only: trajectory stretching exponent (TSE) to detect hyperbolic (stretching) behavior, and trajectory angular velocity (TRA) to detect elliptic (rotation) behavior. In this paper, we analyze these approaches and in particular show that they are – contrary to what is claimed in the literature – not objective in the extended phase space. Furthermore, we introduce the first objective measure of rotation behavior that is based on only few trajectories: at least 3 in 2D, and at least 4 in 3D. For this measure – called trajectory vorticity (TRV) – we show that it is objective and that it can be introduced in two independent ways: by approaches for unsteadiness minimization and by considering the relative spin tensor. We apply TRV to a number of constructed and real trajectory data sets, including drifting buoys in the Atlantic, midge swarm tracking data, and a simulated vortex street.

The model of a Double Gyre flow by Shadden et al. is a standard benchmark data set for the computation of hyperbolic Lagrangian Coherent Structures (LCS) in flow data. While structurally extremely simple, it generates hyperbolic LCS of arbitrary complexity. Unfortunately, the Double Gyre does not come with a well‐defined ground truth: the location of hyperbolic LCS boundaries can only be approximated by numerical methods that usually involve the gradient of the flow map. We present a new benchmark data set that is a small but carefully designed modification of the Double Gyre , which comes with ground truth closed‐form hyperbolic trajectories. This allows for computing hyperbolic LCS boundaries by a simple particle integration without the consideration of the flow map gradient. We use these hyperbolic LCS as a ground truth solution for testing an existing numerical approach for extracting hyperbolic trajectories. In addition, we are able to construct hyperbolic LCS curves that are significantly longer than in existing numerical methods.

This special section of the IEEE Transactions on Visualization and Computer Graphics (IEEE TVCG) presents the five most highly rated papers from the 2021 IEEE Pacific Visualization Symposium (IEEE PacificVis). This year, IEEE PacificVis was scheduled to be hosted by Tianjin University and held in Tianjin, China, from April 19 to 22, 2021. IEEE PacificVis, sponsored by the IEEE Visualization and Graphics Technical Committee (VGTC), aims to foster greater exchange between visualization researchers and practitioners, especially in the Asia-Pacific region. This forum has grown to be a truly international event, attracting submissions and attendees from many countries in the Asia-Pacific and Europe, America, and beyond. Thus, IEEE PacificVis is serving the additional purposes of sharing the latest advances in visualization with researchers and practitioners in the region and introducing research developments in the region to the broader international visualization research community.

Reference frame optimization is a generic framework to calculate a spatially-varying observer field that views an unsteady fluid flow in a reference frame that is as-steady-as-possible. In this paper, we show that the optimized vector field is objective, i.e., it is independent of the initial Euclidean transformation of the observer. To check objectivity, the optimized velocity vectors and the coordinates in which they are defined must both be connected by an Euclidean transformation. In this paper we show that a recent publication [1] applied this definition incorrectly, falsely concluding that reference frame optimizations are not objective. Further, we prove the objectivity of the variational formulation of the reference frame optimization proposed in [1], and discuss how the variational formulation relates to recent local and global optimization approaches to unsteadiness minimization.

In Flow Visualization, the consideration of flow maps instead of velocity fields has recently moved into the focus of research. We present an approach to transforming standard techniques in vector field processing – like smoothing, modeling, deformation – to flow maps. This requires a solution to the fundamental problem that – contrary to vector fields – a specific modification of the flow map is, in general, not a flow map anymore. We introduce a concept that enables the modification of discrete sampling of a flow map while enforcing the flow map properties. Based on this, we present approaches for flow map deformation that are applied to a 2D time-dependent flow field.