IEEE VIS Publication Dataset

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Vis
2004
Quick-VDR: interactive view-dependent rendering of massive models
10.1109/VISUAL.2004.86
1. 138
C
We present a novel approach for interactive view-dependent rendering of massive models. Our algorithm combines view-dependent simplification, occlusion culling, and out-of-core rendering. We represent the model as a clustered hierarchy of progressive meshes (CHPM). We use the cluster hierarchy for coarse-grained selective refinement and progressive meshes for fine-grained local refinement. We present an out-of-core algorithm for computation of a CHPM that includes cluster decomposition, hierarchy generation, and simplification. We make use of novel cluster dependencies in preprocess to generate crack-free, drastic simplifications at runtime. The clusters are used for occlusion culling and out-of-core rendering. We add a frame of latency to the rendering pipeline to fetch newly visible clusters from the disk and to avoid stalls. The CHPM reduces the refinement cost for view-dependent rendering by more than an order of magnitude as compared to a vertex hierarchy. We have implemented our algorithm on a desktop PC. We can render massive CAD, isosurface, and scanned models, consisting of tens or a few hundreds of millions of triangles at 10-35 frames per second with little loss in image quality.
Yoon, S.-E.;Salomon, B.;Gayle, R.;Manocha, D.
Dept. of Comput. Sci., North Carolina Univ., Chapel Hill, NC, USA|c|;;;
10.1109/VISUAL.2002.1183760;10.1109/VISUAL.2003.1250366;10.1109/VISUAL.2001.964503;10.1109/VISUAL.2002.1183796;10.1109/VISUAL.1998.745282;10.1109/VISUAL.2001.964534;10.1109/VISUAL.2003.1250368;10.1109/VISUAL.2001.964502
Interactive display, view-dependent rendering, occlusion culling, external-memory algorithm, levels-of-detail
Vis
2004
Radial hermite operators for scattered point cloud data with normal vectors and applications to implicitizing polygon mesh surfaces for generalized CSG operations and smoothing
10.1109/VISUAL.2004.87
2. 210
C
We describe a new technique for fitting scattered point cloud data. Given a scattered point cloud of 3D data points and associated normal vectors, our new method produces an implicit volume model whose zero level isosurface interpolates the given points and associated normal vectors. We concentrate on certain application of these new volume modeling techniques. We take existing polygon mesh surfaces and use the present methods to construct implicit volume models for these surfaces. Implicit models allow for the application of Boolean operations on these surfaces through the techniques of constructive solid geometry. Also, standard wavelet and filter operators can be applied to the implicit volume model leading to effective smoothing and filtering algorithms, which are simple to implement.
Nielson, G.M.
Arizona State Univ., AZ, USA|c|
10.1109/VISUAL.2002.1183766;10.1109/VISUAL.2003.1250358;10.1109/VISUAL.2004.28;10.1109/VISUAL.2002.1183782;10.1109/VISUAL.1996.567602;10.1109/VISUAL.2002.1183808;10.1109/VISUAL.2003.1250398;10.1109/VISUAL.2003.1250359
Surface reconstruction, point clouds, isosurfaces, polygon mesh
Vis
2004
Real-time motion estimation and visualization on graphics cards
10.1109/VISUAL.2004.88
5. 552
C
We present a tool for real-time visualization of motion features in 2D image sequences. The motion is estimated through an eigenvector analysis of the spatio-temporal structure tensor at every pixel location. This approach is computationally demanding but allows reliable velocity estimates as well as quality indicators for the obtained results. We use a 2D color map and a region of interest selector for the visualization of the velocities. On the selected velocities we apply a hierarchical smoothing scheme which allows the choice of the desired scale of the motion field. We demonstrate several examples of test sequences in which some persons are moving with different velocities than others. These persons are visually marked in the real-time display of the image sequence. The tool is also applied to angiography sequences to emphasize the blood flow and its distribution. An efficient processing of the data streams is achieved by mapping the operations onto the stream architecture of standard graphics cards. The card receives the images and performs both the motion estimation and visualization, taking advantage of the parallelism in the graphics processor and the superior memory bandwidth. The integration of data processing and visualization also saves on unnecessary data transfers and thus allows the real-time analysis of 320×240 images. We expect that on the newest generation of graphics hardware our tool could run in real time for the standard VGA format.
Strzodka, R.;Garbe, C.
Caesar Res. Center, Bonn, Germany|c|;
10.1109/VISUAL.1999.809934;10.1109/VISUAL.2003.1250361;10.1109/VISUAL.2003.1250401;10.1109/VISUAL.2003.1250357
motion estimation, motion visualization, structure tensor, eigenvector analysis, real-time processing, graphics hardware
Vis
2004
Real-Time Volume Rendering of Four Channel Data Sets
10.1109/VISUAL.2004.89
3. 34
M
We present a novel method to encode four data channels in a volumetric data set, and render it at interactive frame rates with maximum intensity projection (MIP) using textured polygons. The first three channels are stored in the volume texture’s red, green, and blue components. The fourth channel is stored in the alpha channel. To achieve real-time rendering speed we are using a pixel shader.
Schulze, J.P.;Rice, A.
Brown University|c|;
Vis
2004
Rendering implicit flow volumes
10.1109/VISUAL.2004.90
9. 106
C
Traditional flow volumes construct an explicit geometrical or parametrical representation from the vector field. The geometry is updated interactively and then rendered using an unstructured volume rendering technique. Unless a detailed refinement of the flow volume is specified for the interior, information inside the underlying flow volume is lost in the linear interpolation. These disadvantages can be avoided and/or alleviated using an implicit flow model. An implicit flow is a scalar field constructed such that any point in the field is associated with a termination surface using an advection operator on the flow. We present two techniques, a slice-based three-dimensional texture mapping and an interval volume segmentation coupled with a tetrahedron projection-based renderer, to render implicit stream flows. In the first method, the implicit flow representation is loaded as a 3D texture and manipulated using a dynamic texture operation that allows the flow to be investigated interactively. In our second method, a geometric flow volume is extracted from the implicit flow using a high dimensional isocontouring or interval volume routine. This provides a very detailed flow volume or set of flow volumes that can easily change topology, while retaining accurate characteristics within the flow volume. The advantages and disadvantages of these two techniques are compared with traditional explicit flow volumes.
Xue, D.;Zhang, C.;Crawfis, R.
Dept. of Comput. Sci. & Eng., Ohio State Univ., Columbus, OH, USA|c|;;
10.1109/VISUAL.2001.964519;10.1109/VISUAL.1993.398846;10.1109/VISUAL.2000.885688;10.1109/VISUAL.1991.175789;10.1109/VISUAL.2003.1250364;10.1109/VISUAL.1992.235211;10.1109/VISUAL.1996.567777;10.1109/VISUAL.2000.885704;10.1109/VISUAL.1999.809909;10.1109/VISUAL.2003.1250376;10.1109/VISUAL.2003.1250377;10.1109/VISUAL.1993.398875;10.1109/VISUAL.2003.1250378;10.1109/VISUAL.1999.809892
interval volume rendering, implicit stream flow, flow visualization, graphics hardware
Vis
2004
Rendering planar cuts through quadratic and cubic finite elements
10.1109/VISUAL.2004.91
4. 416
C
Coloring higher order scientific data is problematic using standard linear methods as found in OpenGL. The visual results are inaccurate when there is a large scalar gradient over an element or when the scalar field is nonlinear. In addition to shading nonlinear data, last and accurate rendering of planar cuts through parametric elements can be implemented using programmable shaders on current graphics hardware. The intersection of a planar cut with geometrically curved volume elements can be rendered using a combination of selective refinement and programmable shaders. This hybrid algorithm also handles curved 2D planar triangles.
Brasher, M.;Haimes, R.
Aerosp. Computational Design Lab., MIT, MA, USA|c|;
Higher Order Elements, Programmable Shaders, Cut-planes
Vis
2004
Rough interface reconstruction using the level set method
10.1109/VISUAL.2004.94
2. 258
C
We present a new level set method for reconstructing interfaces from point aggregations. Although level-set-based methods are advantageous because they can handle complicated topologies and noisy data, most tend to smooth the inherent roughness of the original data. Our objective is to enhance the quality of a reconstructed surface by preserving certain roughness-related characteristics of the original dataset. Our formulation employs the total variation of the surface as a roughness measure. The algorithm consists of two steps: a roughness-capturing flow and a roughness-preserving flow. The roughness capturing step attempts to construct a surface for which the original roughness is captured - distance flow is well suited for roughness capturing. Surface reconstruction is enhanced by using a total variation preserving (TVP) scheme for the roughness-preserving flow. The shock filter formulation of Osher and Rudin is exploited to achieve this goal. In practice, we have found that better results arc obtained by balancing the TVP term with a smoothing term based on curvature. The algorithm is applied to both fractal surface growth simulations and scanned data sets to demonstrate the efficacy of our approach.
Kim, Y.;Machiraju, R.;Thompson, D.
Ohio State Univ., Columbus, OH, USA|c|;;
point sampled data, surface reconstruction, level set method, shock filter, total variation preserving, rough surface
Vis
2004
Scout: a hardware-accelerated system for quantitatively driven visualization and analysis
10.1109/VISUAL.2004.95
1. 178
C
Quantitative techniques for visualization are critical to the successful analysis of both acquired and simulated scientific data. Many visualization techniques rely on indirect mappings, such as transfer functions, to produce the final imagery. In many situations, it is preferable and more powerful to express these mappings as mathematical expressions, or queries, that can then be directly applied to the data. We present a hardware-accelerated system that provides such capabilities and exploits current graphics hardware for portions of the computational tasks that would otherwise be executed on the CPU. In our approach, the direct programming of the graphics processor using a concise data parallel language, gives scientists the capability to efficiently explore and visualize data sets.
McCormick, P.;Inman, J.;Ahrens, J.;Hansen, C.;Roth, G.
Advanced Comput. Lab., Los Alamos Nat. Lab., NM, USA|c|;;;;
10.1109/VISUAL.1995.480821;10.1109/VISUAL.1999.809864;10.1109/VISUAL.2001.964519;10.1109/VISUAL.2003.1250357
Visualization systems, hardware acceleration, multi-variate visualization, volume rendering
Vis
2004
Self-illustrating phenomena
10.1109/VISUAL.2004.12
x.
M
Summary form only given. A self-illustrating phenomenon is an image which exposes the science behind it. Some famous examples are pictures of iron filings aligned along magnetic lines of force, sand particles collecting at the stationary points of the standing waves of a violin, stress in a mechanical part revealed through birefringence, and particle tracks in a bubble chamber. Such images brilliantly combine experimental design, analysis, and visualization. Quoting J. Tukey, "the general purposes of conducting experiments and analyzing data match, point by point". We argue in this talk that computer tools for visual analysis should normally be conceived of as aids in constructing computational visual experiments; and that the resulting visualizations be consciously designed to help validate or invalidate the hypothesis being tested by the experiment.
Hanrahan, P.
Comput. Sci. & Electr. Eng., Stanford Univ., CA, USA|c|
Vis
2004
Simplifying flexible isosurfaces using local geometric measures
10.1109/VISUAL.2004.96
4. 504
C
The contour tree, an abstraction of a scalar field that encodes the nesting relationships of isosurfaces, can be used to accelerate isosurface extraction, to identify important isovalues for volume-rendering transfer functions, and to guide exploratory visualization through a flexible isosurface interface. Many real-world data sets produce unmanageably large contour trees which require meaningful simplification. We define local geometric measures for individual contours, such as surface area and contained volume, and provide an algorithm to compute these measures in a contour tree. We then use these geometric measures to simplify the contour trees, suppressing minor topological features of the data. We combine this with a flexible isosurface interface to allow users to explore individual contours of a dataset interactively.
Carr, H.;Snoeyink, J.;van de Panne, M.
Dept. of Comput. Sci., British Columbia Univ., Vancouver, BC, Canada|c|;;
10.1109/VISUAL.2001.964499;10.1109/VISUAL.2002.1183774
Isosurfaces, contourtrees, topological simplification
Vis
2004
STEPS - an application for simulation of transsphenoidal endonasal pituitary surgery
10.1109/VISUAL.2004.98
5. 520
C
Endonasal transsphenoidal pituitary surgery is a minimally invasive endoscopic procedure, applied to remove various kinds of pituitary tumors. To reduce the risk associated with this treatment, the surgeon must be skilled and well-prepared. Virtual endoscopy can be beneficial as a tool for training, preoperative planning and intraoperative support. This work introduces STEPS, a virtual endoscopy system designed to aid surgeons in getting acquainted with the endoscopic view, the handling of instruments, the transsphenoidal approach and challenges associated with the procedure. STEPS also assists experienced surgeons in planning a real endoscopic intervention by getting familiar with the individual patient anatomy, identifying landmarks, planning the approach and deciding upon the ideal target position of the actual surgical activity. Besides interactive visualization using two different first-hit ray casting techniques, the application provides navigation and perception aids and the possibility to simulate the procedure, including haptic feedback and simulation of surgical instruments.
Neubauer, A.;Mroz, L.;Wolfsberger, S.;Wegenkittl, R.;Forster, M.-T.;Buhler, K.
VRVis Res. Center, Vienna, Austria|c|;;;;;
10.1109/VISUAL.2000.885732;10.1109/VISUAL.2000.885702;10.1109/VISUAL.2000.885673
virtual endoscopy, ray casting, iso-surfacing, pituitary surgery
Vis
2004
Stream line and path line oriented topology for 2D time-dependent vector fields
10.1109/VISUAL.2004.99
3. 328
C
Topological methods aim at the segmentation of a vector field into areas of different flow behavior. For 2D time-dependent vector fields, two such segmentations are possible: either concerning the behavior of stream lines, or of path lines. While stream line oriented topology is well established, we introduce path line oriented topology as a new visualization approach in this paper. As a contribution to stream line oriented topology we introduce new methods to detect global bifurcations like saddle connections and cyclic fold bifurcations. To get the path line oriented topology we segment the vector field into areas of attracting, repelling and saddle-like behavior of the path lines. We compare both kinds of topologies and apply them to a number of data sets.
Theisel, H.;Weinkauf, T.;Hege, H.-C.;Seidel, H.-P.
Max-Planck-Inst. fur Inf., Saarbrucken, Germany|c|;;;
10.1109/VISUAL.1999.809907;10.1109/VISUAL.2000.885714;10.1109/VISUAL.1993.398849;10.1109/VISUAL.1991.175773;10.1109/VISUAL.1996.567777;10.1109/VISUAL.2000.885716;10.1109/VISUAL.2001.964507;10.1109/VISUAL.2003.1250376
flow visualization, vector field topology, bifurcations, stream lines, path lines
Vis
2004
Surface reconstruction of noisy and defective data sets
10.1109/VISUAL.2004.101
2. 266
C
We present a novel surface reconstruction algorithm that can recover high-quality surfaces from noisy and defective data sets without any normal or orientation information. A set of new techniques is introduced to afford extra noise tolerability, robust orientation alignment, reliable outlier removal, and satisfactory feature recovery. In our algorithm, sample points are first organized by an octree. The points are then clustered into a set of monolithically singly-oriented groups. The inside/outside orientation of each group is determined through a robust voting algorithm. We locally fit an implicit quadric surface in each octree cell. The locally fitted implicit surfaces are then blended to produce a signed distance field using the modified Shepard's method. We develop sophisticated iterative fitting algorithms to afford improved noise tolerance both in topology recognition and geometry accuracy. Furthermore, this iterative fitting algorithm, coupled with a local model selection scheme, provides a reliable sharp feature recovery mechanism even in the presence of bad input.
Xie, H.;McDonnell, K.T.;Hong Qin
Dept. of Comput. Sci., State Univ. of New York, Stony Brook, NY, USA|c|;;
10.1109/VISUAL.2003.1250359
Computer Graphics, Surface Reconstruction, Surface Representation, MPU implicits, Modified Shepard's Method
Vis
2004
TetSplat: real-time rendering and volume clipping of large unstructured tetrahedral meshes
10.1109/VISUAL.2004.102
4. 440
C
We present a novel approach to interactive visualization and exploration of large unstructured tetrahedral meshes. These massive 3D meshes are used in mission-critical CFD and structural mechanics simulations, and typically sample multiple field values on several millions of unstructured grid points. Our method relies on the preprocessing of the tetrahedral mesh to partition it into nonconvex boundaries and internal fragments that are subsequently encoded into compressed multiresolution data representations. These compact hierarchical data structures are then adaptively rendered and probed in real-time on a commodity PC. Our point-based rendering algorithm, which is inspired by QSplat, employs a simple but highly efficient splatting technique that guarantees interactive frame-rates regardless of the size of the input mesh and the available rendering hardware. It furthermore allows for real-time probing of the volumetric data-set through constructive solid geometry operations as well as interactive editing of color transfer functions for an arbitrary number of field values. Thus, the presented visualization technique allows end-users for the first time to interactively render and explore very large unstructured tetrahedral meshes on relatively inexpensive hardware.
Museth, K.;Lombeyda, S.
Linkoping Inst. of Technol., Sweden|c|;
10.1109/VISUAL.2000.885703;10.1109/VISUAL.1998.745329;10.1109/VISUAL.2000.885680;10.1109/VISUAL.1997.663869
Large volumetric data, tetrahedral meshes, real-time visualization, point-based rendering, constructive solid geometry
Vis
2004
TexMol: interactive visual exploration of large flexible multi-component molecular complexes
10.1109/VISUAL.2004.103
2. 250
C
While molecular visualization software has advanced over the years, today, most tools still operate on individual molecular structures with limited facility to manipulate large multicomponent complexes. We approach this problem by extending 3D image-based rendering via programmable graphics units, resulting in an order of magnitude speedup over traditional triangle-based rendering. By incorporating a biochemically sensitive level-of-detail hierarchy into our molecular representation, we communicate appropriate volume occupancy and shape while dramatically reducing the visual clutter that normally inhibits higher-level spatial comprehension. Our hierarchical, image based rendering also allows dynamically computed physical properties data (e.g. electrostatics potential) to be mapped onto the molecular surface, tying molecular structure to molecular function. Finally, we present another approach to interactive molecular exploration using volumetric and structural rendering in tandem to discover molecular properties that neither rendering mode alone could reveal. These visualization techniques are realized in a high-performance, interactive molecular exploration tool we call TexMol, short for Texture Molecular viewer.
Bajaj, C.L.;Djeu, P.;Siddavanahalli, V.;Thane, A.
Center for Computational Visualization, Texas Univ., Austin, TX, USA|c|;;;
10.1109/VISUAL.1993.398882;10.1109/VISUAL.1998.745320
molecular visualization, image-based rendering, texture-based rendering, imposter rendering, volume rendering, programmable graphics hardware, level-of-detail, hierarchy, multiresolution, synchronous view, computer graphics
Vis
2004
The human visual system: how is its design related to the physics of the natural environment?
10.1109/VISUAL.2004.61
x.
M
Summary form only given. The human visual system is the result of evolution by natural selection and hence its design must incorporate detailed knowledge of the physical properties of the natural environment. This is an obvious statement, but the scientific community has been slow to take it seriously. Only recently has there been an increased effort to directly measure the statistical properties of natural scenes and compare them to the design and performance of the human visual system. This work describes some recent studies of the chromatic and geometrical properties of natural materials and natural images, as well as some perceptual and physiological studies designed to test how those physical properties are related to human perceptual mechanisms.
Geisler, W.S.
Dept. of Psychol., Texas Univ., Austin, TX, USA|c|
Vis
2004
The VesselGlyph: focus & context visualization in CT-angiography
10.1109/VISUAL.2004.104
3. 392
C
Accurate and reliable visualization of blood vessels is still a challenging problem, notably in the presence of morphologic changes resulting from atherosclerotic diseases. We take advantage of partially segmented data with approximately identified vessel centerlines to comprehensively visualize the diseased peripheral arterial tree. We introduce the VesselGlyph as an abstract notation for novel focus & context visualization techniques of tubular structures such as contrast-medium enhanced arteries in CT-angiography (CTA). The proposed techniques combine direct volume rendering (DVR) and curved planar reformation (CPR) within a single image. The VesselGlyph consists of several regions where different rendering methods are used. The region type, the used visualization method and the region parameters depend on the distance from the vessel centerline and on viewing parameters as well. By selecting proper rendering techniques for different regions, vessels are depicted in a naturally looking and undistorted anatomic context. This may facilitate the diagnosis and treatment planning of patients with peripheral arterial occlusive disease. In this paper we furthermore present a way of how to implement the proposed techniques in software and by means of modern 3D graphics accelerators.
Straka, M.;Cervenansky, M.;La Cruz, A.;Kochl, A.;Sramek, M.;Groller, E.;Fleischmann, D.
Comm. for Sci. Visualization, Austrian Acad. of Sci., Austria|c|;;;;;;
10.1109/VISUAL.2001.964538;10.1109/VISUAL.2002.1183754;10.1109/VISUAL.2001.964555
focus & context technique, direct volume rendering, curved planar reformation, vessel visualization
Vis
2004
Topological lines in 3D tensor fields
10.1109/VISUAL.2004.105
3. 320
C
Visualization of 3D tensor fields continues to be a major challenge in terms of providing intuitive and uncluttered images that allow the users to better understand their data. The primary focus of this paper is on finding a formulation that lends itself to a stable numerical algorithm for extracting stable and persistent topological features from 2nd order real symmetric 3D tensors. While features in 2D tensors can be identified as either wedge or trisector points, in 3D, the corresponding stable features are lines, not just points. These topological feature lines provide a compact representation of the 3D tensor field and are essential in helping scientists and engineers understand their complex nature. Existing techniques work by finding degenerate points and are not numerically stable, and worse, produce both false positive and false negative feature points. This work seeks to address this problem with a robust algorithm that can extract these features in a numerically stable, accurate, and complete manner.
Zheng, X.;Pang, A.
Dept. of Comput. Sci., California Univ., Santa Cruz, CA, USA|c|;
10.1109/VISUAL.1998.745316;10.1109/VISUAL.1999.809894;10.1109/VISUAL.1993.398849;10.1109/VISUAL.2003.1250379;10.1109/VISUAL.2002.1183798;10.1109/VISUAL.1994.346326;10.1109/VISUAL.1999.809905;10.1109/VISUAL.1998.745294;10.1109/VISUAL.1999.809886
hyperstreamlines, real symmetric tensors, degenerate tensors, tensor topology, topological lines
Vis
2004
Topology visualization of the optical power flow through a novel C-shaped nano-aperture
10.1109/VISUAL.2004.106
3. 344
C
An ideal visualization tool that has not been used before in studying the optical behavior of near-field apertures is three-dimensional vector field topology. The global view of the vector field structure is deduced by locating singularities (critical points) within the field and augmenting these points with nearby streamlines. We have used for the first time, to the best of our knowledge, three-dimensional topology to analyze the topological differences between a resonant C-shaped nano-aperture and various nonresonant conventional apertures. The topological differences between these apertures are related to the superiority in power throughput of the C-aperture versus conventional round and square sub-wavelength apertures. We demonstrate how topological visualization techniques provide significant insight into the energy enhancement mechanism of the C aperture, and also shed light on critical issues related to the interaction between multiple apertures located in close proximity to each other, which gives rise to cross-talk, for example as a function of distance. Topological techniques allow us to develop design rules for the geometry of these apertures and their desired spot sizes and brightness. The performance of various sub-wavelength apertures can also be compared quantitatively based on their topology. Since topological methods are generically applicable to tensor and vector fields, our approach can be readily extended to provide insight into the broader category of finite-difference-time-domain nano-photonics and nano-science problems.
Sun, L.;Batra, R.;Xiaolei Shi;Hesselink, L.
Dept. of Phys., Stanford Univ., CA, USA|c|;;;
10.1109/VISUAL.1999.809874
energy flow topology, Finite-Difference-Time-Domain (fdtd), C-aperture, vector field visualization
Vis
2004
Tracking of vector field singularities in unstructured 3D time-dependent datasets
10.1109/VISUAL.2004.107
3. 336
C
We present an approach for monitoring the positions of vector field singularities and related structural changes in time-dependent datasets. The concept of singularity index is discussed and extended from the well-understood planar case to the more intricate three-dimensional setting. Assuming a tetrahedral grid with linear interpolation in space and time, vector field singularities obey rules imposed by fundamental invariants (Poincare index), which we use as a basis for an efficient tracking algorithm. We apply the presented algorithm to CFD datasets to illustrate its purpose. We examine structures that exhibit topological variations with time and describe some of the insight gained with our method. Examples are given that show a correlation in the evolution of physical quantities that play a role in vortex breakdown.
Garth, C.;Tricoche, X.;Scheuermann, G.
Dept. of Comput. Sci., Kaiserslautern Univ., Germany|c|;;
10.1109/VISUAL.2003.1250376;10.1109/VISUAL.2002.1183786;10.1109/VISUAL.1991.175773;10.1109/VISUAL.1997.663910
flow visualization, topology tracking, time-dependent datasets, vortex breakdown