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.

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 Given an unsteady flow field, one common way to compute Lagrangian Coherent Structures (LCS) is to extract extremal structures of the Finite Time Lyapunov Exponent (FTLE). Experience has shown that the resulting structures are often close to material structures (i.e., material lines or material surfaces). Moreover, it has been proven that for an integration time converging to infinity, they converge to exact material structures. However, due to the finite integration time in FTLE, they are generally not exact material structures. In this paper we introduce a modification of the FTLE method which is guaranteed to produce separating material structures as features of a scalar field. We achieve this by incorporating the complete available integration time both in forward and backward direction, and by choosing an appropriate definition for separating structures. We apply our method to two test data sets and show the differences to classical FTLE.

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.

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.

Abstract With ever increasing computing power, it is possible to process ever more complex fluid simulations. However, a gap between data set sizes and our ability to visualize them remains. This is especially true for the field of flow visualization, which deals with large, time‐dependent, multivariate simulation data sets. In this paper, geometry‐based flow visualization techniques form the focus of discussion. Geometric flow visualization methods place discrete objects in the velocity field whose characteristics reflect the underlying properties of the flow. A great amount of progress has been made in this field over the last two decades. However, a number of challenges remain, including placement, speed of computation and perception. In this survey, we review and classify geometric flow visualization literature according to the most important challenges when considering such a visualization, a central theme being the seeding algorithm upon which they are based. This paper details our investigation into these techniques with discussions on their applicability and their relative merits and drawbacks. The result is an up‐to‐date overview of the current state‐of‐the‐art that highlights both solved and unsolved problems in this rapidly evolving branch of research. It also serves as a concise introduction to the field of flow visualization research.

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.

Motivated by the growing interest in the use of ridges in scientific visualization, we analyze the two height ridge definitions by Eberly and Lindeberg. We propose a raw feature definition leading to a superset of the ridge points as obtained by these two definitions. The set of raw feature points has the correct dimensionality, and it can be narrowed down to either Eberly's or Lindeberg's ridges by using Boolean filters which we formulate. While the straight-forward computation of height ridges requires explicit eigenvalue calculation, this can be avoided by using an equivalent definition of the raw feature set, for which we give a derivation. We describe efficient algorithms for two special cases, height ridges of dimension one and of co-dimension one. As an alternative to the aforementioned filters, we propose a new criterion for filtering raw features based on the distance between contours which generally makes better decisions, as we demonstrate on a few synthetic fields, a topographical dataset, and a fluid flow simulation dataset. The same set of test data shows that it is unavoidable to use further filters to eliminate false positives. For this purpose, we use the angle between feature tangent and slope line as a quality measure and, based on this, formalize a previously published filter.

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.

Vortex breakdown bubbles are a subject which is of interest in many disciplines such as aeronautics, mixing, and combustion. Existing visualization methods are based on stream surfaces, direct volume rendering, tensor field visualization, and vector field topology. This paper presents a topological approach which is more closely oriented at the underlying theory of continuous dynamical systems. Algorithms are described for the detection of vortex rings and vortex breakdown bubbles, and for visualization of their characteristic properties such as the boundary, the chaotic dynamics, and possible islands of stability. Since some of these require very long streamlines, the effect of numerically introduced divergence has to be considered. From an existing subdivision scheme, a novel method for divergence conserving interpolation of cuboid cells is derived, and results are compared with those from standard trilinear interpolation. Also a comparison of results obtained with and without divergence cleaning is given.

This paper presents a method for filtered ridge extraction based on adaptive mesh refinement. It is applicable in situations where the underlying scalar field can be refined during ridge extraction. This requirement is met by the concept of Lagrangian coherent structures which is based on trajectories started at arbitrary sampling grids that are independent of the underlying vector field. The Lagrangian coherent structures are extracted as ridges in finite Lyapunov exponent fields computed from these grids of trajectories. The method is applied to several variants of finite Lyapunov exponents, one of which is newly introduced. High computation time due to the high number of required trajectories is a main drawback when computing Lyapunov exponents of 3-dimensional vector fields. The presented method allows a substantial speed-up by avoiding the seeding of trajectories in regions where no ridges are present or do not satisfy the prescribed filter criteria such as a minimum finite Lyapunov exponent.

Vortices are undesirable in many applications while indispensable in others. It is therefore of common interest to understand their mechanisms of creation. This paper aims at analyzing the transport of vorticity inside incompressible flow. The analysis is based on the vorticity equation and is performed along pathlines which are typically started in upstream direction from vortex regions. Different methods for the quantitative and explorative analysis of vorticity transport are presented and applied to CFD simulations of water turbines. Simulation quality is accounted for by including the errors of meshing and convergence into analysis and visualization. The obtained results are discussed and interpretations with respect to engineering questions are given.

For the rendering of vector and tensor fields, several texture-based volumetric rendering methods were presented in recent years. While they have indisputable merits, the classical vertex-based rendering of integral curves has the advantage of better zooming capabilities as it is not bound to a fixed resolution. It has been shown that lighting can improve spatial perception of lines significantly, especially if lines appear in bundles. Although OpenGL does not directly support lighting of lines, fast rendering of illuminated lines can be achieved by using basic texture mapping. This existing technique is based on a maximum principle which gives a good approximation of specular reflection. Diffuse reflection however is essentially limited to bidirectional lights at infinity. We show how the realism can be further increased by improving diffuse reflection. We present simplified expressions for the Phong/Blinn lighting of infinitesimally thin cylindrical tubes. Based on these, we propose a fast rendering technique with diffuse and specular reflection for orthographic and perspective views and for multiple local and infinite lights. The method requires commonly available programmable vertex and fragment shaders and only two-dimensional lookup textures.

The evacuation of buildings in the event of a fire requires careful planning of ventilation and evacuation routes during early architectural design stages. Different designs are evaluated by simulating smoke propagation using computational fluid dynamics (CFD). Visibility plays a decisive role in finding the nearest fire exit. This paper presents real-time volume rendering of transient smoke propagation conforming to standardized visibility distances. We visualize time dependent smoke particle concentration on unstructured tetrahedral meshes using a direct volume rendering approach. Due to the linear transfer function of the optical model commonly used in fire protection engineering, accurate pre-integration of diffuse color across tetrahedra can be carried out with a single 2D texture lookup. We reduce rounding errors during frame buffer blending by applying randomized dithering if high accuracy frame buffers are unavailable on the target platform. A simple absorption-based lighting model is evaluated in a preprocessing step using the same rendering approach. Back-illuminated exit signs are commonly used to indicate the escape route. As light emitting objects are visible further than reflective objects, the transfer function in front of illuminated exit signs must be adjusted with a deferred rendering pass.

Vorticity is the quantity used to describe the creation, transformation and extinction of vortices. It is present not only in vortices but also in shear flow. Especially in ducted flows, most of the overall vorticity is usually contained in the boundary layer. When a vortex develops from the boundary layer, this can be described by transport of vorticity. For a better understanding of a flow it is therefore of interest to examine vorticity in all of its different roles. The goal of this application study was not primarily the visualization of vortices but of vorticity distribution and its role in vortex phenomena. The underlying industrial case is a design optimization for a Pelton turbine. An important industrial objective is to improve the quality of the water jets driving the runner. Jet quality is affected mostly by vortices originating in the distributor ring. For a better understanding of this interrelation, it is crucial to not only visualize these vortices but also to analyze the mechanisms of their creation. We used various techniques for the visualization of vorticity, including field lines and modified isosurfaces. For field line based visualization, we extended the image-guided streamline placement algorithm of Turk and Banks to data-guided field line placement on three-dimensional unstructured grids.

This paper presents a signed distance transform algorithm using graphics hardware, which computes the scalar valued function of the Euclidean distance to a given manifold of co-dimension one. If the manifold is closed and orientable, the distance has a negative sign on one side of the manifold and a positive sign on the other. Triangle meshes are considered for the representation of a two-dimensional manifold and the distance function is sampled on a regular Cartesian grid. In order to achieve linear complexity in the number of grid points, to each primitive we assign a simple polyhedron enclosing its Voronoi cell. Voronoi cells are known to contain exactly all points that lay closest to its corresponding primitive. Thus, the distance to the primitive only has to be computed for grid points inside its polyhedron. Although Voronoi cells partition space, the polyhedrons enclosing these cells do overlap. In regions where these overlaps occur, the minimum of all computed distances is assigned to a grid point. In order to speed up computations, points inside each polyhedron are determined by scan conversion of grid slices using graphics hardware. For this task, a fragment program is used to perform the nonlinear interpolation and minimization of distance values.

In this case study, we explore techniques for the purpose of visualizing isolated flow structures in time-dependent data. Our primary industrial application is the visualization of the vortex rope, a rotating helical structure which builds up in the draft tube of a water turbine. The vortex rope can be characterized by high values of normalized helicity, which is a scalar field derived from the given CFD velocity data. In two related applications, the goal is to visualize the cavitation regions near the runner blades of a Kaplan turbine and a water pump, respectively. Again, the flow structure of interest can be defined by a scalar field, namely by low pressure values. We propose a particle seeding scheme based on quasi-random numbers, which minimizes visual artifacts such as clusters or patterns. By constraining the visualization to a region of interest, occlusion problems are reduced and storage efficiency is gained.

We propose an elementary operation on a pair of vector fields as a building block for defining and computing global line-type features of vector or scalar fields. While usual feature definitions often are procedural and therefore implicit, our operator allows precise mathematical definitions. It can serve as a basis for comparing feature definitions and for reuse of algorithms and implementations. Applications focus on vortex core methods.

This paper presents a novel method to extract vortical structures from 3D CFD (computational fluid dynamics) vector fields automatically. It discusses the underlying theory and some aspects of the implementation. Making use of higher-order derivatives, the method is able to locate bent vortices. In order to structure the recognition procedure, we distinguish locating the core line from calculating attributes of strength and quality. Results are presented on several flow fields from the field of turbomachinery.

Visualization of CFD data for turbomachinery design poses some special requirements which are often not addressed by standard flow visualization systems. The authors discuss the issues involved with this particular application and its requirements with respect to flow visualization. Aiming at a feature-based visualization for this task, they examine various existing techniques to locate vortices. The specific flow conditions for turbomachines demonstrate limitations of current methods. Visualization of turbomachinery flow thus raises some challenges and research topics, particularly regarding feature extraction.