Filip Sadlo

Universität Heidelberg ·  Interdisciplinary Center for Scientific Computing

We present an approach that supports the analysis of flow dynamics in the neighborhood of curved line-type features, such as vortex core lines, attachment lines, and trajectories. We achieve this with continuous deformation to the flow field to straighten such features. This provides “deformed frames of reference”, within which qualitative flow dyn...

In multiphase flows, the evolution of fluid-fluid interfaces is of interest in many applications. In addition to fluid dynamic forces governing the flow in the entire volume, surface tension determines droplet interfaces. Here, the analysis of interface kinematics can help in the investigation of interface deformation and the identification of pote...

This article presents an overview of visual analysis techniques specifically developed for high-resolution direct numerical multiphase simulations in the droplet dynamic context. Visual analysis of such data covers a large range of tasks, starting from observing physical phenomena such as energy transport or collisions for single droplets to the an...

Line integration of stream-, streak-, and pathlines is widely used and popular for visualizing single-phase flow. In multiphase flow, i.e., where the fluid consists, e.g., of a liquid and a gaseous phase, these techniques could also provide valuable insights into the internal flow of droplets and ligaments and thus into their dynamics. However, sin...

We present an approach to local extraction of 3D time‐dependent vector field topology. In this concept, Lagrangian coherent structures, which represent the separating manifolds in time‐dependent transport, correspond to generalized streak manifolds seeded along hyperbolic path surfaces (HPSs). Instead of expensive and numerically challenging direct...

We present a data-driven visual analysis approach for the in-depth exploration of large numbers of droplets. Understanding droplet dynamics in sprays is of interest across many scientific fields for both simulation scientists and engineers. In this paper, we analyze large-scale direct numerical simulation datasets of the two-phase flow of non-Newto...

In this paper, we study the visual design of hierarchical multivariate data analysis. We focus on the extension of four hierarchical univariate concepts---the sunburst chart, the icicle plot, the circular treemap, and the bubble treemap---to the multivariate domain. Our study identifies several advantageous design variants, which we discuss with re...

In this paper, we introduce uncertainty to continuous scatterplots and continuous parallel coordinates. We derive respective models, validate them with sampling-based brute-force schemes, and present acceleration strategies for their computation. At the same time, we show that our approach lends itself as well for introducing uncertainty into the d...

In this work, we present concepts for the analysis of the evolution of two-dimensional skeletons. By introducing novel persistence concepts, we are able to reduce typical temporal incoherence, and provide insight in skeleton dynamics. We exemplify our approach by means of a simulation of viscous fingering—a highly dynamic process whose analysis is...

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample—not necessarily a uniform one—of some high-dimensional manifold. In such cases, persistent homology can be successfully employed to extract features, remove noise, and c...

We develop a novel hierarchy for zero-dimensional persistence pairs, i.e., connected components, which is capable of capturing more fine-grained spatial relations between persistence pairs. Our work is motivated by a lack of spatial relationships between features in persistence diagrams, leading to a limited expressive power. We build upon a recent...

Presentation slides on VIS 2020 of paper: "Uncertainty in Continuous Scatterplots, Continuous Parallel Coordinates, and Fibers"

This paper does two main contributions to 2D time‐dependent vector field topology. First, we present a technique for robust, accurate, and efficient extraction of distinguished hyperbolic trajectories (DHT), the generative structures of 2D time‐dependent vector field topology. It is based on refinement of initial candidate curves. In contrast to pr...

In this paper, we present an integrated visual analytics approach to support the parametrization and exploration of flow visualization based on the finite‐time Lyapunov exponent. Such visualization of time‐dependent flow faces various challenges, including the choice of appropriate advection times, temporal regions of interest, and spatial resoluti...

Intersection homology is a topological invariant which detects finer information in a space than ordinary homology. Using ideas from classical simple homotopy theory, we construct local combinatorial transformations on simplicial complexes under which intersection homology remains invariant. In particular, we obtain the notions of stratified formal...

We develop a novel hierarchy for zero-dimensional persistence pairs, i.e., connected components, which is capable of capturing more fine-grained spatial relations between persistence pairs. Our work is motivated by a lack of spatial relationships between features in persistence diagrams, leading to a limited expressive power. We build upon a recent...

Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional scaling, while providing a firm theoretical ground. Many modern machine learning algorithms, however, are based on...

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional manifold. In such cases, persistent homology can be successfully employed to extract features, remove noise, a...

In this work, we present concepts for the analysis of the evolution of two-dimensional skeletons. By introducing novel persistence concepts, we are able to reduce typical temporal incoherence, and provide insight in skeleton dynamics. We exemplify our approach by means of a simulation of viscous fingering---a highly dynamic process whose analysis i...

In this paper, we generalize the parallel vectors operator due to Peikert and Roth to arbitrary dimension, i.e., to four‐dimensional fields and beyond. Whereas the original operator tested for parallelism of two (derived) 2D or 3D vector fields, we reformulate the concept in terms of linear dependency of sets of vector fields, and propose a generic...

Presentation slides on EuroVis 2019 of paper: "Visualization of Equivalence in 2D Bivariate Fields"

In this paper, we show how the equivalence property leads to the novel concept of equivalent regions in mappings from ℝⁿ to ℝⁿ. We present a technique for obtaining these regions both in the domain and the codomain of such a mapping, and determine their correspondence. This enables effective investigation of variation equivalence within mappings, a...

Techniques from computational topology, in particular persistent homol-ogy, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional scaling, while providing a firm theoretical ground. Many modern machine learning algorithms, however, are based o...

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample-not necessarily a uniform one-of some high-dimensional manifold. In such cases, persistent homology can be successfully employed to extract features, remove noise, and c...

In this paper, we present an approach to analyze 1D parameter spaces of time-dependent flow simulation ensembles. By extending the concept of the finite-time Lyapunov exponent to the ensemble domain, i.e., to the parameter that gives rise to the ensemble, we obtain a tool for quantitative analysis of parameter sensitivity both in space and time. We...

In this paper, we present an approach to the topological analysis of four-dimensional vector fields. In analogy to traditional 2D and 3D vector field topology, we provide a classification and visual representation of critical points, together with a technique for extracting their invariant manifolds. For effective exploration of the resulting four-...

Whereas the design and development of numerical solvers for field-based simulations is a highly evolved discipline, and whereas there exists a wide range of visualization techniques for the (in-situ) analysis of their numerical results, the techniques for analyzing the operation of such solvers are rather elementary. In this paper, we present a vis...

Scalar features in fluid flow are traditionally visualized with glyphs or using direct 3D representation, and their topology changes over time are often conveyed with abstract graphs. Using these techniques, however, the spatio-temporal evolution of features undergoing topological changes is difficult to analyze. In this paper, we propose a novel a...

The analysis of simulation results and the verification against experimental data is essential to develop and interpret simulation models for impact damage. We present two visualization techniques to post-process particle-based simulation data, and we highlight new aspects for the quantitative comparison with experimental data. As the underlying si...

IEEE VIS 2016 brought together researchers and practitioners to discuss the latest developments in visualization and visual analytics research and their applications. The authors describe the highlights of the 2016 event.

Modern direct gas injectors for natural-gas-powered internal combustion engines operate at ever-increasing pressures to maximize efficiency. At the operating point of current devices, real gas effects already become relevant, for example in the determination of mass flow rates. These effects have to be considered in the design process of such compo...

We present a novel and efficient technique to extract Lagrangian coherent structures in two-dimensional time-dependent vector fields. We show that this can be achieved by employing bifurcation line extraction in the space-time representation of the vector field, and generating space-time bifurcation manifolds therefrom. To show the utility and appl...

Industrial devices such as gas injectors for automotive combustion engines operate at ever-increasing pressures and already today reach regimes beyond the ideal-gas approximation. Numerical simulations are an important part of the design process for such components. In this paper, we present a case study with a computational fluid dynamics code bas...

For many years, discontinuous Galerkin (DG) methods have been proving their value as highly efficient, very well scalable high-order methods for computational fluid dynamics (CFD) calculations. However, they have so far mainly been applied in the academic environment and the step toward an application in industry is still waited for. In this articl...

We present a novel approach for handling sampling and compression in remote visualization in an integrative fashion. As adaptive sampling and compression share the same underlying concepts and criteria, the times spent for visualization and transfer can be balanced directly to optimize the image quality that can be achieved within a prescribed time...

Many concepts in computational flow visualization operate in the Lagrangian frame—they involve the integration of trajectories. A problem inherent to these approaches is the choice of an appropriate time length for the integration of these curves. While for some applications the choice of such a finite time length is straightforward, it represents...

We present a novel physically-based method to visualize stress tensor fields. By incorporating photoelasticity into traditional raycasting and extending it with reflection and refraction, taking into account polarization, we obtain the virtual counterpart to traditional experimental polariscopes. This allows us to provide photoelastic analysis of s...

We present a novel technique to visualize wave propagation in 2D scalar fields. Direct visualization of wave fronts is susceptible to visual clutter and interpretation difficulties due to space-time interference and global influence. To avoid this, we employ Huygens' principle to obtain virtual sources that provide a concise space-time representati...

Treating time as the third dimension of 2D time-dependent flow enables the application of a wide variety of visualization techniques for 3D stationary vector fields. In the resulting space-time representation, 3D streamlines represent 2D pathlines of the original field. In this paper, we investigate the application of different streamline-based vis...

In an introductory course on dynamical systems or Hamiltonian mechanics, vector field diagrams are a central tool to show a system’s qualitative behaviour in a certain domain. Because of their low sampling rates and the involved issues of vector normalization, these plots give only a coarse insight and are unable to convey the vector field behaviou...

Volumetric depth images (VDI) are a view-dependent representation that combines the high quality of images with the explorability of 3D fields. By compressing the scalar data along view rays into sets of coherent supersegments, VDIs provide an efficient representation that supports a-posteriori changes of camera parameters. In this paper, we introd...

High order methods are regarded as a primary means to significantly improve the efficiency of numerical techniques. While the particular high order methods can be very distinct, most have in common that their solution is represented by piecewise polynomials. However, since high order methods evolved only recently, most of the present visualization...

We present a technique to visualize the streamline-based mapping between the boundary of a simply-connected subregion of arbitrary 3D vector fields. While the streamlines are seeded on one part of the boundary, the remaining part serves as escape border. Hence, the seeding part of the boundary represents a map of streamline behavior, indicating if...

We present a novel scheme for progressive rendering in interactive visualization. Static settings with respect to a certain image quality or frame rate are inherently incapable of delivering both high frame rates for rapid changes and high image quality for detailed investigation. Our novel technique flexibly adapts by steering the visualization pr...

Streamsurfaces are of fundamental importance to visualization of flows. Among other features, they offer strong capabilities in revealing flow behavior (e.g., in the vicinity of vortices), and are an essential tool for the computation of 2D separatrices in vector field topology. Computing streamsurfaces is, however, typically expensive due to the d...

We present a novel and efficient method to compute volumetric soft shadows for interactive direct volume visualization to improve the perception of spatial depth. By direct control of the softness of volumetric shadows, disturbing visual patterns due to hard shadows can be avoided and users can adapt the illumination to their personal and applicati...

Visualization of pathlines is common and highly relevant for the analysis of unsteady flow. However, pathlines can intersect, leading to visual clutter and perceptual issues. This makes it intrinsically difficult to provide expressive visualizations of the entire domain by an arrangement of multiple pathlines, in contrast to well-established stream...

Finite-time and finite-size Lyapunov exponents are related concepts that have been used for the purpose of identifying transport structures in time-dependent flow. The preference for one or the other concept seems to be based more on a tradition within a scientific community than on proven advantages. In this study, we demonstrate that with the two...

Concepts from vector field topology have been successfully applied to a wide range of phenomena so far—typically to problems involving the transport of a quantity, such as in flow fields, or to problems concerning the instantaneous structure, such as in the case of electric fields. However, transport of quantities in time-dependent flows has so far...

For the rendering of multiple scattering effects in participating media, methods based on the diffusion approximation are an extremely efficient alternative to Monte Carlo path tracing. However, in sufficiently transparent regions, classical diffusion approximation suffers from non-physical radiative fluxes which leads to a poor match to correct li...

We present ambient scattering as a preintegration method for scattering on mesoscopic scales in direct volume rendering. Far-range scattering effects usually provide negligible contributions to a given location due to the exponential attenuation with increasing distance. This motivates our approach to preintegrating multiple scattering within a fin...

The winners of the 2012 IEEE Visualization Contest combined methods from molecular, flow, and scalar data visualization to reveal the characteristics and processes in the contest data. Because the simulated material didn't behave according to theory from textbooks, one challenge was to find meaningful visualizations to facilitate exploratory analys...

View-dependent image-based rendering techniques have become increasingly popular as they combine the high quality of images with the explorability of interactive techniques. However, in the context of volume rendering, previous approaches suffer from various shortcomings, including the limitation to surfaces, expensive generation, and insufficient...

This paper presents an approach for the fast generation of meshes from Layered Depth Images (LDI), a representation that is independent of the underlying data structure and widely used in image-based rendering. LDIs can be quickly generated from high-quality, yet computationally expensive isosurface raycasters that are available for a wide range of...

It is difficult to create appropriate bar charts for data that cover large value ranges. The usual approach for these cases employs a logarithmic scale, which, however, suffers from issues inherent to its non-linear mapping: for example, a quantitative comparison of different values is difficult. We present a new approach for bar charts that combin...

Piecewise linear interface calculation (PLIC) is one of the most widely employed reconstruction schemes for the simulation of multiphase flow. In this visualization paper we focus on the reconstruction from the simulation point of view, i.e., we present a framework for the analysis of this reconstruction scheme together with its implications on the...

Flow fields are often investigated by adopting a Lagrangian view, for example, by particle tracing of integral curves such as streamlines and path lines or by computing delocalized quantities. For visual exploration, mouse interaction is predominantly used to define starting points for time-dependent Lagrangian methods. This paper focuses on the un...

Stretching and compression in tangent directions of Lagrangian coherent structures (LCS) are of particular interest in the vicinity of hyperbolic trajectories and play a key role in turbulence and mixing. Since integration of hyperbolic trajectories is difficult, we propose to visualize them in 2D time-dependent vector fields by space-time intersec...

This paper presents a visualization approach for detecting and exploring similarity in the temporal variation of field data. We provide an interactive technique for extracting correlations from similarity matrices which capture temporal similarity of univariate functions. We make use of the concept to extract periodic and quasiperiodic behavior at...

Lagrangian coherent structures (LCS) can be extracted from time-dependent vector fields by means of ridges in the finite-time Lyapunov exponent (FTLE). While the LCS approach has proven successful in many areas and applications for the analysis of time-dependent topology, it is to some extent still an open problem how the finite time scope is appro...

Computational dye advection helps engineers understand fluid dynamics simulations by providing interactive tools that mimic physical experiments.

High performance computing still typically disregards heterogeneous environments and focuses on homogeneous clusters. While providing advantages and easing development, this fails to address the recent change toward heterogeneous computing infrastructure. With DIANA we presented an abstraction layer for unified access to local compute hardware incl...

Magnetic fields exhibit higher-order, nonlinear singularities in the form of point-dipole singularities. In addition, due to absence of divergence, they feature only a subset of invariant structures from traditional vector field topology. For magnetic fields of sets of point dipoles—widely present in physics and often used as an approximation—we pr...

Advection has been the standard transport mechanism in flow visualization. Diffusion, in contrast, has not been considered important in visual flow field analysis so far, although it is inherent to many physical processes. We present a novel technique that allows for interactive 3D visualization of both advection and diffusion in unsteady fluid flo...

It was shown recently how the 2D vector field topology concept, directly applicable to stationary vector fields only, can be generalized to time-dependent vector fields by replacing the role of stream lines by streak lines [1]. The present paper extends this concept to 3D vector fields. In traditional 3D vector field topology separatrices can be ob...

Lagrangian coherent structures (LCS), apparent as ridges in the finite-time Lyapunov exponent (FTLE) field, represent a time-dependent alternative to the concept of separatrices in vector field topology. Traditionally, LCS are analyzed and visualized in terms of their geometric shape only, neglecting stretching and compression in tangent directions...

We present a framework for different approaches to finite-time Lyapunov exponent (FTLE) computation for 2D vector fields, based on the advection of seeding circles. On the one hand it unifies the popular flow map approach with techniques based on the evaluation of distinguished trajectories, such as renormalization. On the other hand it allows for...

Solar dynamics data, particularly those from the Solar Dynamics Observatory, are now available in a sheer volume that is hard to investigate with traditional visualization tools, which mainly display 2D images. While the challenge of data access and browsing has been solved by web-based interfaces and efforts like the Helioviewer project, the appro...

Lagrangian coherent structures play an important role in the analysis of unsteady vector fields because they represent the time-dependent analog to vector field topology. Nowadays, they are often obtained as ridges in the finitetime Lyapunov exponent of the vector field. However, one drawback of this quantity is its very high computational cost because...

This paper presents an acceleration scheme for the numerical computation of sets of trajectories in vector fields or iterated solutions in maps, possibly with simultaneous evaluation of quantities along the curves such as integrals or extrema. It addresses cases with a dense evaluation on the domain, where straightforward approaches are subject to...

This paper generalizes the concept of Lagrangian coherent structures, which is known for its potential to visualize coherent regions in vector fields and to distinguish them from each other. In particular, we extend the concept of the flow map to generic mappings of coordinates. As the major application of this generalization, we present a semiglob...

The parallel vectors (PV) operator is a feature extraction approach for defining line-type features such as creases (ridges and valleys) in scalar fields, as well as separation, attachment, and vortex core lines in vector fields. In this work, we extend PV feature extraction to higher-order data represented by piecewise analytical functions defined...

This paper presents an approach to a time-dependent variant of the concept of vector field topology for 2-D vector fields. Vector field topology is defined for steady vector fields and aims at discriminating the domain of a vector field into regions of qualitatively different behaviour. The presented approach represents a generalization for saddle-...

Direct visualization of higher-order data avoids the error and overhead introduced by the widely used resampling approach. Here, we give an overview of problems and solution strategies in the context of our research on higher order visualization and exemplify them using volume rendering and extraction of isosurfaces and line-type features. We also...

The parallel vectors (PV) operator is a feature extraction approach for defining line-type features such as creases (ridges and valleys) in scalar fields, as well as separation, attachment, and vortex core lines in vector fields. In this work, we extend PV feature extraction to higher-order data represented by piecewise analytical functions defined...

Tilt-shift camera lenses are a powerful artistic tool to achieve effects like selective focus with very shallow depth of field. Typically they are used by professional photographers only, which is due to the high cost and weight, and the intricate, non-intuitive handling. We introduce the auto-tilt mechanism which is as easy to use as the standard...

Direct visualization of higher-order data provides manifold advantages over the traditional approach, which is based on resampling and subsequent visualization by interpolation-based techniques. Most important, it avoids excessive computation and consumption of memory, and prevents artifacts by pixel-accurate visualization at interactive rates. Thi...

We present an exemplary steering system that performs 2D flow simulation and visualization on graphics processing units (GPUs). The topology of a vector field provides the overall structure and therefore lends itself for steering purposes. We build on the concept of Lagrangian coherent structures present as ridges in the finite-time Lyapunov expone...

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 for unsteadiness which 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 in...

When vector field topology is used for the visualization of a 3D vector field, various types of topological features have uniquely defined stream surfaces associated with them. Compared to arbitrary stream surfaces, such topology-induced stream surfaces are usually of simpler geometric shape and at the same time more expressive. We present a stream...

A pattern often found in regions of recirculating flow is the vortex ring. Smoke rings and vortex breakdown bubbles are two familiar instances of this pattern. A vortex ring requires at least two critical points, and in fact this minimum number is observed in many synthetic or real-world examples. Based on this observation, we propose a visualizati...

Our algorithm applied to the Lorenz dynamical system. Stable manifold of the critical point at the origin, colored by geodesic distance (left), unstable manifold of a spiral saddle critical point, colored by node index (middle), and 2D manifolds of all three critical points (right). Abstract When vector field topology is used for the visualization...

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 p...

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 narro...

In this paper we discuss generalizations of instan- taneous, local vortex criteria. We incorporate in- formation on spatial context and temporal devel- opment into the detection process. The presented method is generic in so far that it can extend any given Eulerian criterion to take the Lagrangian ap- proach into account. Furthermore, we present a...

This chapter provides a fully automated and robust 3D photography system optimized for the generation of high-quality renderings of objects. The basic premise of the scanning approach is to use large amounts of radiance and opacity information to produce accurate renderings of the object instead of relying on accurate geometry. The chapter gives a...

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 in...

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 und...

Bubbles and foam are important fluid phenomena on scales that we encounter in our lives every day. While different techniques to handle these effects were developed in the past years, they require a full 3D fluid solver with free surfaces and surface tension. We present a shallow water based particle model that is coupled with a smoothed particle h...