We present a new method to visualize from an ensemble of flow fields the statistical properties of streamlines passing through a selected location. We use principal component analysis to transform the set of streamlines into a low-dimensional Euclidean space. In this space the streamlines are clustered into major trends, and each cluster is in turn approximated by a multivariate Gaussian distribution. This yields a probabilistic mixture model for the streamline distribution, from which confidence regions can be derived in which the streamlines are most likely to reside. This is achieved by transforming the Gaussian random distributions from the low-dimensional Euclidean space into a streamline distribution that follows the statistical model, and by visualizing confidence regions in this distribution via iso-contours. We further make use of the principal component representation to introduce a new concept of streamline-median, based on existing median concepts in multidimensional Euclidean spaces. We demonstrate the potential of our method in a number of real-world examples, and we compare our results to alternative clustering approaches for particle trajectories as well as curve boxplots.

Breast augmentation was the most commonly performed cosmetic surgery procedure in 2011 in the United States. Although aesthetically pleasing surgical results can only be achieved if the correct breast implant is selected from a large variety of different prosthesis sizes and shapes available on the market, surgeons still rely on visual assessment and other subjective approaches for operative planning because of lacking objective evaluation tools. In this paper, we present the development of a software prototype for augmentation mammaplasty simulation solely based on 3-D surface scans, from which patient-specific finite-element models are generated in a semiautomatic process. The finite-element model is used to preoperatively simulate the expected breast shapes using physical soft-tissue mechanics. Our approach uses a novel mechanism based on so-called displacement templates, which, for a specific implant shape and position, describe the respective internal body forces. Due to a highly efficient numerical solver we can provide immediate visual feedback of the simulation results, and thus, the software prototype can be integrated smoothly into the medical workflow. The clinical value of the developed 3-D computational tool for aesthetic breast augmentation surgery planning is demonstrated in patient-specific use cases.

Despite the ongoing efforts in turbulence research, the universal properties of the turbulence small-scale structure and the relationships between small- and large-scale turbulent motions are not yet fully understood. The visually guided exploration of turbulence features, including the interactive selection and simultaneous visualization of multiple features, can further progress our understanding of turbulence. Accomplishing this task for flow fields in which the full turbulence spectrum is well resolved is challenging on desktop computers. This is due to the extreme resolution of such fields, requiring memory and bandwidth capacities going beyond what is currently available. To overcome these limitations, we present a GPU system for feature-based turbulence visualization that works on a compressed flow field representation. We use a wavelet-based compression scheme including run-length and entropy encoding, which can be decoded on the GPU and embedded into brick-based volume ray-casting. This enables a drastic reduction of the data to be streamed from disk to GPU memory. Our system derives turbulence properties directly from the velocity gradient tensor, and it either renders these properties in turn or generates and renders scalar feature volumes. The quality and efficiency of the system is demonstrated in the visualization of two unsteady turbulence simulations, each comprising a spatio-temporal resolution of 10244. On a desktop computer, the system can visualize each time step in 5 seconds, and it achieves about three times this rate for the visualization of a scalar feature volume.

In this paper, we present a sample-based approach for surface coloring, which is independent of the original surface resolution and representation. To achieve this, we introduce the Orthogonal Fragment Buffer (OFB)-an extension of the Layered Depth Cube-as a high-resolution view-independent surface representation. The OFB is a data structure that stores surface samples at a nearly uniform distribution over the surface, and it is specifically designed to support efficient random read/write access to these samples. The data access operations have a complexity that is logarithmic in the depth complexity of the surface. Thus, compared to data access operations in tree data structures like octrees, data-dependent memory access patterns are greatly reduced. Due to the particular sampling strategy that is employed to generate an OFB, it also maintains sample coherence, and thus, exhibits very good spatial access locality. Therefore, OFB-based surface coloring performs significantly faster than sample-based approaches using tree structures. In addition, since in an OFB, the surface samples are internally stored in uniform 2D grids, OFB-based surface coloring can efficiently be realized on the GPU to enable interactive coloring of high-resolution surfaces. On the OFB, we introduce novel algorithms for color painting using volumetric and surface-aligned brushes, and we present new approaches for particle-based color advection along surfaces in real time. Due to the intermediate surface representation we choose, our method can be used to color polygonal surfaces as well as any other type of surface that can be sampled.

Streak surfaces are among the most important features to support 3D unsteady flow exploration, but they are also among the computationally most demanding. Furthermore, to enable a feature driven analysis of the flow, one is mainly interested in streak surfaces that show separation profiles and thus detect unstable manifolds in the flow. The computation of such separation surfaces requires to place seeding structures at the separation locations and to let the structures move correspondingly to these locations in the unsteady flow. Since only little knowledge exists about the time evolution of separating streak surfaces, at this time, an automated exploration of 3D unsteady flows using such surfaces is not feasible. Therefore, in this paper we present an interactive approach for the visual analysis of separating streak surfaces. Our method draws upon recent work on the extraction of Lagrangian coherent structures (LCS) and the real-time visualization of streak surfaces on the GPU. We propose an interactive technique for computing ridges in the finite time Lyapunov exponent (FTLE) field at each time step, and we use these ridges as seeding structures to track streak surfaces in the time-varying flow. By showing separation surfaces in combination with particle trajectories, and by letting the user interactively change seeding parameters such as particle density and position, visually guided exploration of separation profiles in 3D is provided. To the best of our knowledge, this is the first time that the reconstruction and display of semantic separable surfaces in 3D unsteady flows can be performed interactively, giving rise to new possibilities for gaining insight into complex flow phenomena.

In this paper we present techniques for the visualization of unsteady flows using streak surfaces, which allow for the first time an adaptive integration and rendering of such surfaces in real-time. The techniques consist of two main components, which are both realized on the GPU to exploit computational and bandwidth capacities for numerical particle integration and to minimize bandwidth requirements in the rendering of the surface. In the construction stage, an adaptive surface representation is generated. Surface refinement and coarsening strategies are based on local surface properties like distortion and curvature. We compare two different methods to generate a streak surface: a) by computing a patch-based surface representation that avoids any interdependence between patches, and b) by computing a particle-based surface representation including particle connectivity, and by updating this connectivity during particle refinement and coarsening. In the rendering stage, the surface is either rendered as a set of quadrilateral surface patches using high-quality point-based approaches, or a surface triangulation is built in turn from the given particle connectivity and the resulting triangle mesh is rendered. We perform a comparative study of the proposed techniques with respect to surface quality, visual quality and performance by visualizing streak surfaces in real flows using different rendering options.

Particle tracing has been established as a powerful visualization technique to show the dynamics of 3D flows. Particle tracing in 3D, however, quickly overextends the viewer due to the massive amount of visual information that is typically produced by this technique. In this paper, we present strategies to reduce this amount at the same time revealing important structures in the flow. As an importance measure, we introduce a simple, yet effective clustering approach for vector fields, and we use scalar flow quantities at different scales in combination with user-defined regions of interest. These measures are used to control the shape, the appearance, and the density of particles in such a way that the user can focus on the dynamics in important regions at the same time preserving context information. We also introduce a new focus for particle tracing, so called anchor lines. Anchor lines are used to analyze local flow features by visualizing how much particles separate over time and how long it takes until they have separated to a fixed distance. It is of particular interest if the finite time Lyapunov exponent - a scalar quantity that measures the rate of separation of infinitesimally close particles in the flow - is used to guide the placement of anchor lines. The effectiveness of our approaches for the visualization of 3D flow fields is validated using synthetic fields as well as real simulation data.

In this work we present basic methodology for interactive volume editing on GPUs, and we demonstrate the use of these methods to achieve a number of different effects. We present fast techniques to modify the appearance and structure of volumetric scalar fields given on Cartesian grids. Similar to 2D circular brushes as used in surface painting we present 3D spherical brushes for intuitive coloring of particular structures in such fields. This paint metaphor is extended to allow the user to change the data itself, and the use of this functionality for interactive structure isolation, hole filling, and artefact removal is demonstrated. Building on previous work in the field we introduce high-resolution selection volumes, which can be seen as a resolution-based focus+context metaphor. By utilizing such volumes we present a novel approach to interactive volume editing at sub-voxel accuracy. Finally, we introduce a fast technique to paste textures onto iso-surfaces in a 3D scalar field. Since the texture resolution is independent of the volume resolution, this technique allows structure-aligned textures containing appearance properties or textual information to be used for volume augmentation and annotation.

In this paper we present GPU-based techniques for the interactive visualization of large unsteady 3D flow fields on uniform grids. We propose a novel dual-core approach to asynchronously stream such fields from the CPU, thus enabling the efficient exploration of large time-resolved sequences. This approach decouples visualization from data handling, resulting in interactive frame rates. Built upon a previously published GPU particle engine for flow visualization we have developed new strategies to compute and to visualize path lines and streak lines on the GPU. To provide additional visual cues, focus+context techniques for polygonal meshes have been integrated. The proposed techniques are used in the visual analysis of the Terashake 2.1 earthquake simulation data, and they have been shown to be very effective in revealing the relevant information in this data.