Flow Visualization-STAR: Dense and Texture-Based Techniques · The State of the Art in Flow...

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Volume 22 (2003), Number 2, yet unknown pages The State of the Art in Flow Visualization: Dense and Texture-Based Techniques Robert S. Laramee, 1 Helwig Hauser, 1 Helmut Doleisch, 1 Benjamin Vrolijk, 2 Frits H. Post, 2 and Daniel Weiskopf 3 1 {Laramee, Hauser, Doleisch}@VRVis.at,VRVis Research Center, Austria, http://www.VRVis.at 2 {B.Vrolijk, F.H.Post}@ewi.tudelft.nl,Delft University of Technology, Netherlands, http://visualisation.tudelft.nl 3 [email protected], VIS, University of Stuttgart, Germany, http://www.vis.uni-stuttgart.de Abstract Flow visualization has been a very attractive component of scientific visualization research for a long time. Usu- ally very large multivariate datasets require processing. These datasets often consist of a large number of sample locations and several time steps. The steadily increasing performance of computers has recently become a driv- ing factor for a reemergence in flow visualization research, especially in texture-based techniques. In this paper, dense, texture-based flow visualization techniques are discussed. This class of techniques attempts to provide a complete, dense representation of the flow field withhigh spatio-temporal coherency. An attempt of categorizing closely related solutions is incorporated and presented. Fundamentals are shortly addressed as well as advantages and disadvantages of the methods. Categories and Subject Descriptors (according to ACM CCS): I.3 [Computer Graphics]: visualization, flow visual- ization, computational flow visualization 1. Introduction Flow visualization (FlowVis) is one of the classic subfields of visualization, covering a rich variety of applications, from the automotive industry, aerodynamics, turbomachinery de- sign, to weather simulation, meteorology, climate modeling, ground water flow, and medical visualization. Consequently, the spectrum of FlowVis solutions is very rich, spanning multiple technical challenges: 2D vs. 3D solutions and tech- niques for steady or time-dependent data. Bringing many of those solutions in linear order (as neces- sary for a text like this) is neither easy nor intuitive. Several options of subdividing this broad field of literature are pos- sible. Hesselink et al., for example, addressed the problem of how to categorize techniques in their 1994 overview of research issues 24 and consider dimensionality as a means to classify the literature. In the following, several aspects are discussed on an abstract level before literature is addressed directly. 1.1. Classification According to the different needs of the users, there are dif- ferent approaches to flow visualization (cf. Figure 1): Direct flow visualization: This category of techniques uses a translation that is as direct as possible for repre- senting flow data in the resulting visualization. The result is an overall picture of the flow. Common approaches are drawing arrows (Figure 2, left) or color coding velocity. Intuitive pictures can be provided, especially in the case of two dimensions. Solutions of this kind allow immedi- ate investigation of the flow data. Dense, texture-based flow visualization: Similar to di- rect flow visualization, a texture is computed that is used to generate a dense representation of the flow (Figure 2, middle). A notion of where the flow moves is incorpo- rated through co-related texture values along the vector field. In most cases this effect is achieved through filter- ing of texture values according to the local flow vector. Texture-based methods offer a dense representation of the flow with complete coverage of the vector field. Geometric flow visualization: For a better communica- tion of the long-term behavior induced by flow dynamics, integration-based approaches first integrate the flow data and use geometric objects as a basis for flow visualization. The resulting integral objects have a geometry that reflects submitted to COMPUTER GRAPHICS Forum (3/2004).

Transcript of Flow Visualization-STAR: Dense and Texture-Based Techniques · The State of the Art in Flow...

Page 1: Flow Visualization-STAR: Dense and Texture-Based Techniques · The State of the Art in Flow Visualization: Dense and Texture-Based Techniques Robert S. Laramee,1 Helwig Hauser,1 Helmut

Volume 22 (2003), Number 2, yet unknown pages

The State of the Art in Flow Visualization:Dense and Texture-Based Techniques

Robert S. Laramee,1 Helwig Hauser,1 Helmut Doleisch,1 Benjamin Vrolijk,2 Frits H. Post,2 and Daniel Weiskopf3

1Laramee, Hauser, [email protected], VRVis Research Center, Austria, http://www.VRVis.at2B.Vrolijk, [email protected], Delft University of Technology, Netherlands, http://visualisation.tudelft.nl

[email protected], VIS, University of Stuttgart, Germany, http://www.vis.uni-stuttgart.de

AbstractFlow visualization has been a very attractive component of scientific visualization research for a long time. Usu-ally very large multivariate datasets require processing. These datasets often consist of a large number of samplelocations and several time steps. The steadily increasing performance of computers has recently become a driv-ing factor for a reemergence in flow visualization research, especially in texture-based techniques. In this paper,dense, texture-based flow visualization techniques are discussed. This class of techniques attempts to provide acomplete, dense representation of the flow field with high spatio-temporal coherency. An attempt of categorizingclosely related solutions is incorporated and presented. Fundamentals are shortly addressed as well as advantagesand disadvantages of the methods.

Categories and Subject Descriptors (according to ACM CCS): I.3 [Computer Graphics]: visualization, flow visual-ization, computational flow visualization

1. Introduction

Flow visualization (FlowVis) is one of the classic subfieldsof visualization, covering a rich variety of applications, fromthe automotive industry, aerodynamics, turbomachinery de-sign, to weather simulation, meteorology, climate modeling,ground water flow, and medical visualization. Consequently,the spectrum of FlowVis solutions is very rich, spanningmultiple technical challenges: 2D vs. 3D solutions and tech-niques for steady or time-dependent data.

Bringing many of those solutions in linear order (as neces-sary for a text like this) is neither easy nor intuitive. Severaloptions of subdividing this broad field of literature are pos-sible. Hesselink et al., for example, addressed the problemof how to categorize techniques in their 1994 overview ofresearch issues 24 and consider dimensionality as a means toclassify the literature. In the following, several aspects arediscussed on an abstract level before literature is addresseddirectly.

1.1. Classification

According to the different needs of the users, there are dif-ferent approaches to flow visualization (cf. Figure 1):

Direct flow visualization: This category of techniquesuses a translation that is as direct as possible for repre-senting flow data in the resulting visualization. The resultis an overall picture of the flow. Common approaches aredrawing arrows (Figure 2, left) or color coding velocity.Intuitive pictures can be provided, especially in the caseof two dimensions. Solutions of this kind allow immedi-ate investigation of the flow data.

Dense, texture-based flow visualization: Similar to di-rect flow visualization, a texture is computed that is usedto generate a dense representation of the flow (Figure 2,middle). A notion of where the flow moves is incorpo-rated through co-related texture values along the vectorfield. In most cases this effect is achieved through filter-ing of texture values according to the local flow vector.Texture-based methods offer a dense representation of theflow with complete coverage of the vector field.

Geometric flow visualization: For a better communica-tion of the long-term behavior induced by flow dynamics,integration-based approaches first integrate the flow dataand use geometric objects as a basis for flow visualization.The resulting integral objects have a geometry that reflects

submitted to COMPUTER GRAPHICS Forum (3/2004).

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data acquisition

directvisualization

geometryextraction

visualization

featureextraction

geometryextraction

visualization

user perception

dense

visualizationtexture−based

Figure 1: Classification of flow visualization tech-niques – (left) direct, (middle-left) texture-based, (middle-right) based on geometric objects, and (right) feature-based.

the properties of the flow. Examples include streamlines(Figure 2, right) , streaklines, and pathlines. These ge-ometric objects are based on integration as opposed toother geometric objects, like isosurfaces, that may also beuseful for visualization. A description of geometric tech-niques is presented by Post et al. 55

Feature-based flow visualization: Another approachmakes use of an abstraction and/or extraction step whichis performed before visualization. Special features are ex-tracted from the original dataset, such as important phe-nomena or topological information of the flow. Visualiza-tion is then based on these flow features (instead of theentire dataset), allowing for compact and efficient flowvisualization, even of very large and/or time-dependentdatasets. This can also be thought of as visualization ofderived data. Post et al. 56 cover feature-based flow visu-alization in detail.

Figure 1 illustrates a classification of the aforementionedclasses and Figure 2 shows three typical examples. Note thatthere are different amounts of computation associated witheach category. In general, direct flow visualization tech-niques require less computation than the other three cate-gories, whereas feature-based techniques require the mostcomputation. This overview focuses on the body of researchrelated to dense, texture-based techniques.

1.2. Spatial, Temporal, and Data Dimensionality

Solutions in flow visualization differ with respect to the di-mensionality of the flow data. Useful techniques for 2D flowdata, like color coding or arrow plots, sometimes lack simi-lar advantages in 3D. Here, the spatial dimensionality of theflow data is indicated as either 2D, 2.5D, or 3D. In our clas-sification the dimensionality of the results from each tech-nique is marked with a corresponding label indicating di-mensionality (see Figure 4).

By 2.5D we mean flow visualization restricted to surfacesin 3D. We draw attention to the notion that in many cases

like CFD, the simulation sets all velocities on a surface tozero. One way to approach this is to extrapolate the vectorfield just inside the surface to the boundary. In any case,the vector component normal to the surface is usually lostin the visualization. Furthermore another vector field can becalculated on a surface, such as skin friction.

In addition to spatial dimension, temporal dimension (di-mensionality with respect to time) is of great importance.Firstly, velocity incorporates a notion of time – flows are of-ten interpreted as differential data with respect to time (cf.Equation 1), i.e., when integrating the data, instantaneouspaths such as streamlines may be obtained (cf. Equation 3).We can call this steady velocity time. Additionally, the flowdata can change over time resulting in time-dependent (orunsteady) flow. We can refer to this as unsteady velocitytime. In this case, both steady velocity time for integrationand unsteady velocity time for simulation are represented.The visualization must carefully distinguish between both.Performing integration in the case of unsteady data resultsin pathlines or streaklines as opposed to streamlines.

The distinction between steady and unsteady velocitytime is important, when animation is used in the visualiza-tion. Then, even a third temporal dimension, i.e., animationtime, may affect the visualization Animation time is simplyan arbitrary time added to the visualization after the origi-nal data is acquired, like the motion of color controlled by acolor-table 31. Special attention is required for correct inter-pretation of animation time.

In many cases, further data dimensions, i.e., attributes,are supplied with the data, such as temperature, pressure,or vorticity in addition to spatial and temporal dimensions.The dimension of the data values is also associated with theterms multivariate and multi-field data. Flow visualizationmay also take these values into account, e.g., by using coloror isosurface extraction.

Although we do not have space to focus on experimen-tal flow visualization, it is interesting to recognize that manycomputational solutions more or less mimic the visual ap-pearance of well-accepted techniques in experimental visu-alization (cf. particle traces, dye injection, or Schlieren tech-niques 77).

1.3. Data Sources

Computational flow visualization, in general, deals with datathat exhibits temporal dynamics like the results from (a) flowsimulation (e.g., the simulation of fluid flow through a tur-bine), (b) flow measurements (possibly acquired throughlaser-based technology), or (c) analytic models of flows(e.g., dynamical systems 1, given as set of differential equa-tions).

We focus on visualization of data from computationalflow simulation, i.e., flow data given as a set of samples ona grid. In many cases, the velocity information in a flowdataset (encoded as a set of velocity vectors) represents the

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Figure 2: An example of circular flow at the surface of a ring to help illustrate our flow visualization classification: (left) directvisualization by the use of arrow glyphs, (middle) texture-based by the use of LIC, and (right) visualization based on geometricobjects, here streamlines.

focus. Therefore, flow visualization is strongly related tovector field visualization, which may also deal with vectorfields other than velocity vector fields.

The relation of computational and experimental visualiza-tion is worthy of mention. Experimental flow visualization,as in a wind tunnel, is also used to validate computationalflow simulation. In such a case the computational visualiza-tion needs to be set up in a way such that results can be easilycompared.

2. Fundamentals

Before outlining some of the most important texture-basedtechniques, a short overview of common mathematics aswell as some general concepts with regard to the compu-tation of results are presented.

Flow simulations are often solutions to systems of PDEs,such as the Navier Stokes, Euler, or Advection-Diffusionequations 83. In general, discretized solution methods areused. Noteworthy are finite volume (FV) and finite element(FE) analysis, which subdivide the domain into small ele-ments like hexahedral or tetrahedral cells. A solution is de-fined on the computation grid in physical space: unstruc-tured for FE and structured curvilinear for FV solutions. Inthe discussion that follows, we assume that vector data aredefined on the grid nodes (cell vertices).

2.1. Reconstruction of Flow Data

An inherent characteristic of flow data is that derivative in-formation is given with respect to time, which is laid outwith respect to an n-dimensional spatial domain Ω

Rn,e.g., n 3 for representing 3D fluid flow. Temporal deriva-tives v of nD locations p within the flow domain Ω are n-dimensional vectors:

v dp d t p Ω Rn v Rn t R (1)

A general formulation of (possibly unsteady) flow data v is

v p t : Ω Π Rn (2)

where p Ω Rn represents the spatial reference of the flow

data and t Π R represents the system time. For steady

flow data, the simpler case of v p : Ω Rn is given (v notdependent on t).

In results from nD flow simulation, such as from automo-tive applications or airplane design, vector data v is usuallynot given in analytic form, but requires reconstruction fromthe discrete simulation output. The numerical methods usedfor the flow simulation, such as finite element methods, out-put simulation values usually on large-sized grids of manysample vectors vi, which discretely represent the solution ofthe simulation process. Furthermore, it is assumed that theflow simulation is based on a continuous model of the flowallowing continuous reconstruction of the flow data v. Oneoption is to apply a reconstruction filter h : Rn R to com-pute v p ∑i h p pi vi. For practical reasons, filter husually has only local extent. Efficient procedures for find-ing flow samples vi, which are nearest to the query point p,are needed to do proper reconstruction.

2.2. Grids

In flow simulation, the vector samples vi usually are laid outacross the flow domain with respect to a certain type of grid.Grid types range from simple rectilinear or Cartesian gridsto curvilinear grids to complex unstructured grids (cf. Fig-ure 3). Typically, simulation grids exhibit large variationsin cell sizes. This variety of cell sizes stems from the in-fluence of grid generation onto the flow simulation process.The quality of the grid model and its implementation impactthe quality of the simulation results.

Although the principal theory of reconstruction from dis-crete samples does not exhibit many differences with respect

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(b) Curvilinear (c) Unstructured(a) Cartesian

Figure 3: Grids involved in flow simulation – rectilinear (a)vs. curvilinear (b) vs. unstructured grids (c). Issues are im-plicit (a) vs. explicit locations (b, c), implicit (a, b) vs. ex-plicit neighborhood (c).

to grid cell types, the practical handling does. While neigh-bor searching might be trivial in a rectilinear grid, it usuallyis not in a tetrahedral grid. Similar differences hold for theproblems of point location and vector reconstruction. In thefollowing we shortly describe some fundamental operationswhich form the basis for visualization computations on sim-ulation grids.

Starting with point location, i.e., the problem of findingthe grid cell in which a given nD-point lies, usually twocases are distinguished. For general point location, specialdata structures can be used that subdivide the spatial do-main to speed up the search. For iterative point location,often needed during integral curve computation, algorithmsare used that efficiently exploit spatial coherence during thesearch. One kind of such algorithms starts with an initialguess for the target cell, checks for point-containment andrefines accordingly afterward. This process is iterated untilthe target cell is found. More details can be found in textbooks about flow visualization fundamentals 53 68.

Beside point location, flow reconstruction, or interpola-tion, within a cell of the dataset is a crucial issue. Often,once the cell containing the query location is found, onlythe sample vectors at the cell’s vertices are considered forreconstruction. The approach used most often is first-orderreconstruction by performing linear interpolation within thecell. For example, trilinear flow reconstruction may be usedwithin a 3D hexahedral cell.

After point location and flow reconstruction, visualizationbegins: vectors can be represented with glyphs, virtual parti-cles can be injected and traced across the flow domain. Nev-ertheless, the computation of derived data may be necessaryto do more sophisticated flow visualization. Usually, the firststep is to request second-order gradient information for arbi-trary points in the flow domain, i.e., v p, which gives infor-mation about local properties of the flow (at point p) such asflow convergence and divergence, or flow rotation and shear.For feature extraction, flow vorticity ω v can be ofhigh interest. Further details about local flow properties canbe found in previous work 45 54.

2.3. Integration

Recalling that flow data in most cases is derivative informa-tion with respect to time, the idea of integrating flow dataover time is natural to provide an intuitive notion of evolu-tion induced by the flow. One example is visualization by theuse of particle advection. A respective particle path p t –here through unsteady flow – can be defined by

p t p0 t

τ 0v p τ τ dτ (3)

where p0 represents the location of the particle path at seedtime 0. Note that Equations 1 and 3 are complimentary toeach other. For other types of integral curves, such as streak-lines see previous work 36 68.

In addition to the theoretical specification of integralcurves, it is important to note that respective integral equa-tions like Equation 3 usually cannot be resolved for thecurve function analytically, and thereby numerical integra-tion methods are employed. The most simple approach isto use a first-order Euler method to compute an approxima-tion pE t – one iteration of the curve integration is specifiedby

pE t ∆ t p t ∆ t v p t t (4)

where ∆ t usually is a very small step in time and p t de-notes the location to start this Euler step from. A more ac-curate but also more costly technique is the second-orderRunge-Kutta method, 57 which uses the Euler approxima-tion pE as a look-ahead to compute a better approxima-tion pRK2 t of the integral curve:

pRK2 t ∆ t p t ∆ t v p t t v pE t ∆ t t 2 (5)

Higher-order methods like the often used fourth-orderRunge-Kutta integrator utilize more such steps to better ap-proximate the local behavior of the integral curve. Also,adaptive step sizes are used to compute smaller steps in re-gions of high curvature. Related approaches may also in-volve implicit integration schemes 78.

3. Dense and Texture-Based Flow Visualization

Dense, texture-based techniques in flow visualization gener-ally provide full spatial coverage of the vector field. In ourclassification we group these methods into the following cat-egories based on their respective primitive: the fundamentalobject upon which the algorithm is based. Our classificationsubdivides the techniques based on their similarity. Spot Noise techniques: These methods (Section 3.1) are

based on a technique introduced by Van Wijk 79. In thiscategory, the basic primitive on which the algorithms op-erate is the so-called spot: an ellipse or other shape that iswarped and distributed in order to reflect the characteris-tics of a vector field.

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LIC techniques: The methods in this category (Sec-tion 3.2) are derived from an algorithm introduced byCabral and Leedom 8, namely, Line Integral Convolution(LIC). The basic primitive here is a noise texture: theproperties of texture are convolved, or smeared, using akernel filter in the direction of the underlying vector field. Texture advection and GPU-based techniques: The prim-itive in this case (Section 3.3) is a moving texel 50. Indi-vidual texels, or groups of texels are advected in the di-rection of the vector field. Many of the techniques in thiscategory utilize more computation on the GPU (Graph-ics Processing Unit) – rather than the CPU – in order torealize performance gains. Related techniques: Most of the dense, texture-basedflow visualization research falls into one of the previouscategories. Related research that does not fit cleanly intoone of the previous classifications is discussed in Sec-tion 3.4.

We have included a section of meta-research papers in Sec-tion 4 after the individual research techniques. These pa-pers attempt to provide an alternative, higher-level frame-work that incorporates many of the techniques discussedhere. They are, in general, more narrow in scope than thisreview.

3.1. Spot Noise

Spot noise, introduced by Van Wijk 79, was one of the firstdense, texture-based techniques for vector field visualiza-tion. Spot noise generates a texture by distributing a set ofintensity functions, or spots, over the domain. Each spot rep-resents a particle warped over a small step in time and resultsin a streak in the direction of the local flow from where theparticle is seeded. A spot noise texture is defined by: 79

f x ∑aih x xi v xi (6)

in which h is called the intensity function, ai is a scalingfactor, and xi is a random position. A spot is a functionwith a value of unity for the spot, e.g., a ellipse and its inte-rior, and zero everywhere else. The sigma translates into theblending of each instance of the intensity function at randompositions.

The hierarchy shown in Figure 4 illustrates the relation-ship amongst spot noise related methods. Follow-up re-search that builds upon a previous technique is shown as achild in the hierarchy. Children that share a common par-ent are presented in chronological order of appearance whenreading from left to right. Each node in the hierarchy is la-beled and the corresponding description can be matched inthe text of this article. The dimensionality of the flow dataused to generate the results is indicated for convenience. Thetime dimension label is given a different shape to distinguishit from the spatial dimensions. We believe the spot noise hi-erarchy (Figure 4) and the LIC hierarchy (Figure 7) will bevaluable assets in helping the reader navigate the related re-

Spot Noise

EnhancedSpot Noise

ExperimentalFlow Simulation

Parallel UnsteadySpot Noise Spot Noise

2D

2.5D

3D

LEGEND

Unsteady

Figure 4: The Spot Noise hierarchy of related research.Children in the hierarchy build upon the work of their par-ent.

Figure 5: A snapshot of the unsteady spot noise algo-rithm 16. Image courtesy of De Leeuw and Van Liere.

search literature. In what follows, we visit each node in thehierarchy in depth-first-search order.

Experimental Flow Simulation – Spot noise has been usedto simulate the results from the field of experimental flowvisualization 14. First the parameters of the spot noise tech-nique are tuned in order to simulate the smearing of oil on asurface. A post-processing step is then added to enhance thevisualization result such that it looks closer to the smearingof real oil from experimental flow visualization.

Enhanced Spot Noise – One limitation of the original spotnoise algorithm was the inability to represent high, local ve-locity gradients especially with high speeds. Enhanced spotnoise 12 by De Leeuw and Van Wijk addresses these chal-lenges through the use of bent spot primitives.

Parallel and Unsteady Spot Noise – In order to acceleratethe performance of enhanced spot noise towards interactiveframe rates, a parallel implementation of the algorithm wasintroduced by De Leeuw 13. The parallel implementationwas applied to the steering of a smog prediction simulationand searching a very large data set resulting from a numeri-cal simulation of turbulence.

The first application of spot noise to unsteady flow is pre-sented by De Leeuw and Van Liere 16 (Figure 5). The motion

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Figure 6: Visualization of flow past a box using (left) spot noise and (right) LIC. Simulation data courtesy of AVL(www.avl.com).

of spots is modeled after particles in unsteady flow. In orderto visualize unsteady flow, the distribution of spots with re-spect to the temporal domain is discussed. Unsteady spotnoise also introduces support for zooming views of the vec-tor field. Spot noise with zooming is also utilized by DeLeeuw and Van Liere when visualizing topological featuresof 2D flow 10.

Spot Noise Related Literature – A combination of bothtexture-based FlowVis on 2D slices and 3D arrows for 3Dflow visualization is employed by Telea and Van Wijk 74.Arrows denote the main characteristics of the 3D flow afterclustering and a 2D slice with spot noise visualization servesas context. The focus of this work is on vector field cluster-ing.

Löffelmann et al 44 use anisotropic spot noise createdfrom a grid-shaped spot to visualize streamlines and time-lines concurrently on stream surfaces. Another interestingapplication of spot noise is its use for the depiction of dis-crete maps (non-continuous flow) 43.

flow 15 and in combination with the visualization of flowtopology 10 11. We refer the reader to Post et al. 55 56 formore on the subject of flow topology.

Spot Noise vs. LIC – A visual comparison of LIC (the fo-cus of the next section) and spot noise is shown in Figure 6.Spot noise is capable of reflecting velocity magnitude withinthe amount of smearing in the texture, thus freeing up huefor the visualization of another attribute such as pressure,temperature, etc. On the other hand, LIC is more suited forthe visualization of critical points which is a key element

in conveying the flow topology. The vector magnitudes arenormalized thus retaining lower spatial frequency texture inareas of low velocity magnitude. De Leeuw and Van Lierealso compare spot noise to LIC 17. They report that LIC isbetter at showing direction than spot noise, but it does notencode velocity magnitude. By flow direction, we refer tothe path along which a massless particle follows when in-jected into the flow.

3.2. Line Integral Convolution

Line integral convolution (LIC), first introduced by Cabraland Leedom 8, has spawned a large collection of research asindicated in Figure 7. The original LIC method takes as in-put a vector field on a 2D, Cartesian grid and a white noisetexture of the same size. Texels are convolved (or correlated)along the path of streamlines using a filter kernel in order tocreate a dense visualization of the flow field. More specif-ically, given a streamline σ, LIC consists of calculating theintensity I for a pixel located at x0 σ s0 by: 70

I x0 s0 L 2

s0 ! L 2k s " s0 T σ s ds (7)

where T stands for an input noise texture, k denotes the filterkernel, s is an arc length used to parameterize the stream-line curve, and L represents the filter kernel length. See Fig-ure 2 (middle) for a result. LIC was one of the first dense,texture-based algorithms able to accurately reflect velocityfields with high local curvature.

The research in LIC-based flow visualization described

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ParallelFast LIC

Fast LIC onSurfaces

VolumeLIC

EnhancedFast LIC

LIC withNormal

DyeInjection

Multi−Frequency

LIC

MultivariateLIC

OLIC

FROLIC

LIC onSurfaces

3D LIC GeometricLIC

CurvilinearLIC

UnsteadyLIC

Fast LIC

DLIC

LIC

AUFLIC

UFLIC

2D

2.5D

3D

Unsteady

LEGEND

Figure 7: The LIC hierarchy of related research. Node labels correspond to paragraphs in the text, which then lead to specificentries in the bibliography.

here extends LIC in several directions: (1) adding flow orien-tation cues, (2) showing local velocity magnitude, (3) addingsupport for non-rectilinear grids, (4) animating the result-ing textures such that the animation shows the upstream anddownstream flow direction, (4) allowing real-time and inter-active exploration, (5) extending LIC to 3D, and (6) extend-ing LIC to unsteady vector fields. In the following, we visitthe LIC hierarchy of Figure 7 in depth-first-search order.

Curvilinear Grids and Unsteady LIC – Forssell 20 wasearly to extend LIC to surfaces represented by curvilineargrids. The original LIC method portrays a vector field withuniform velocity magnitude. Forssell introduces a techniquefor displaying vector magnitude. She also describes one ap-proach to animate the resulting LIC textures. Forssell andCohen extend this work to visualize unsteady flow 21. Theirapproach modifies the convolution such that the filter ker-nel operates on streaklines rather than streamlines. In otherwords, they modify the LIC algorithm to trace a path thatincorporates multiple time steps.

Fast LIC – Many algorithms are built on fast LIC intro-duced by Stalling and Hege 70. Fast LIC is approximatelyone order of magnitude faster than the original. The speedupis achieved through two key observations: (1) fast LIC min-imizes the computation of redundant streamlines present inthe original method and (2) fast LIC exploits similar con-volution integrals along a single streamline and thus re-uses parts of the convolution computation from neighboringstreamline texels. They also introduce support for filteredimages at arbitrary resolution.

Parallel Fast LIC – Amongst the first parallel implementa-tions of fast LIC is that of Zöckler et al. 90. The proposed al-gorithm computes animation sequences on a massively par-allel distributed memory computer. Parallelization is per-formed in image space rather than in time in order to takeadvantage of the strong temporal coherence between frames.Luckily, as we shall see later, flow visualization research inthis area has evolved far enough such that expensive paral-lel processing hardware is not always necessary to achieve

interactive visualization 28 29 38 80. However, for 3D and un-steady flow there is still need for parallelization. For the sakeof completeness, we also mention the work of Cabral andLeedom on parallelization of LIC 7 although this is a paral-lel processing version of the original LIC algorithm, not fastLIC.

Fast LIC on Surfaces – Battke et al. 2 extend fast LIC tosurfaces represented by arbitrary grids in 3D. The approachby Forssell and Cohen 21 was limited to surfaces representedby curvilinear grids. The method works by tessellating agiven surface representation with triangles. The triangles arepacked (or tiled) into texture memory and a local LIC textureis computed for each triangle. The results presented hereare limited to relatively small simple surface representationscomposed of equilateral triangles (1,600–4,000 triangles).

Volume LIC – Interrante and Grosch 25 26 visualize true 3Dflow using the fast LIC algorithm as a starting point. Clearly,there are perceptual challenges related to 3D flow visualiza-tion such as occlusion, depth perception, and visual com-plexity. Volume LIC introduces the use of halos in orderto enhance depth perception such that the user has a bet-ter chance at perceiving the 3D space covered in the visual-ization (Figure 8). Areas of higher velocity magnitude aremapped to higher texture opacity. It is interesting to notethat with the introduction of halos, we are then able to iden-tify distinct entities in the 3D field, a property generally notpresent in other LIC techniques. Thus the 3D LIC takes astep in the direction of being a geometric flow visualizationtechnique where discrete integral objects such as streamlinescan be distinguished. Without introducing some notion ofsparseness into the visualization, the results would not bevery useful. However, with the introduction of sparseness, atrade-off is made between flow field coverage and reducingocclusion.

Enhanced Fast LIC and LIC with Normal – Two use-ful extensions to the fast LIC algorithm are introduced byHege and Stalling 22 and Scheuermann et al. 64 Hege and

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Figure 8: A result from the Volume LIC method 25 26. Imagecourtesy of Interrante and Grosch.

Stalling 22 experiment with higher order filter kernels in or-der to enhance the quality of the resulting LIC textures.

In the case of slices, vector components orthogonal to theslice are removed when using texture-based and geometricmethods for visualization results. Scheuermann et al. 64 ad-dress this missing orthogonal vector field component by ex-tending fast LIC to incorporate a normal component into thevisualization.

DLIC – Sundquist 71 presents an extension to fast LIC,DLIC (Dynamic LIC), in order to visualize time-dependentelectromagnetic fields. According to Sundquist, the motionof the field is not necessarily along the direction of the fielditself in the case of electromagnetic fields. The algorithmproposed here handles the case of when the vector field andthe direction of the motion of the field lines are indepen-dent. Conceptually, there are two vector fields used in thisapproach: (1) the electromagnetic field itself and (2) the vec-tor field that describes the evolution of streamlines as a func-tion of time.

Multivariate LIC – Urness et al. 76 present an extension tofast LIC that incorporates a new coloring scheme that can beused to incorporate multiple 2D scalar and vector attributes.Color weaving (see Figure 9) assigns a specific attribute rep-resented by a color to an individual streamline thread in thevisualization. The streamline patterns may interweave andthus so may the color patterns. Using multiple colors allowsvisualization of more than one variate in the result. Theirsecond contribution is called texture stitching: an extensionto the idea presented by Kiu and Banks 34, namely multi-frequency LIC. However, in the case of Urness et al. 76 themulti-frequency noise textures are used to highlight regionsof interest as opposed to velocity magnitude as by Kiu andBanks 34.

Dye Injection – Shen et al. address the problem of direc-tional cues in LIC by incorporating animation and introduc-ing dye advection into the computation 66. The simulation

Figure 9: A composite “color woven” LIC image of 2Dflow that highlights areas of significant positive vorticity(red), negative vorticity (blue), strongly negative Reynoldsshear stress (green), and high swirl strength (orange andmagenta). Image courtesy of Urness et al. 76.

of dye may be used to highlight features of the flow. In ad-dition, they incorporate volume rendering methods that mapa LIC texture onto a 3D surface. Thus the user is able to vi-sualize the dye throughout the volume. We point out that themodeling of dye transport is not always physically correctsince dye is dispersed not only by advection, but also by dif-fusion. Note that dye advection techniques can be classifieddifferently. Dye injection can result in discrete geometricobjects used to visualize the flow, and thus, could be classi-fied as a group of geometric visualization techniques. Dyeinjection is also implemented by some of the texture advec-tion and GPU-based techniques described in Section 3.3.

Again, in Shen et al. we see the notion of a sparser visu-alization in order to see into the 3D flow. The resulting 3Dvisualization approaches that of a geometric technique suchas the use of streamsurfaces. And just as with the other geo-metric techniques, the notion of where to place or inject thedye into the flow becomes important. Figure 10 illustratesthe use of dye injection.

Multi-Frequency LIC – Kiu and Banks propose to use amulti-frequency noise for LIC 34. The spatial frequency ofthe noise is a function of the magnitude of the local velocity.Long, fat streaks indicate regions of the flow with highervelocity magnitude.

One problem with many curvilinear grid LIC algorithmsis that the resulting LIC textures may be distorted after beingmapped onto the geometric surfaces, since a curvilinear gridusually consists of cells of different sizes. Mao et al. propose

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Figure 10: Dye injection is used to highlight areas of theflow in combination on the boundary surface of an intakeport and combustion chamber.

a solution to the problem by using multi-granularity noise asthe input image for LIC 46.

OLIC and FROLIC – Wegenkittl et al. address the prob-lem of direction of flow in still images with their OLIC (Ori-ented LIC) approach 85. By orientation, they mean the up-stream and downstream directions of the flow, not visible inthe original LIC implementation. Conceptually, the OLICalgorithm makes use of a sparse texture consisting of manyseparated spots that are smeared in the direction of the lo-cal vector field through integration. A fast version of OLIC,called FROLIC (Fast Rendering of OLIC), is achieved byWegenkittl and Gröller 84 via a trade-off of accuracy fortime. FROLIC approximates the simulated droplet trace re-sulting from OLIC with a sequence of disks of varying inten-sity, with disk intensity increasing towards the downstreamdirection.

Animated FROLIC 4 achieves animation of the result viaa color-table and is based on the observation that only thecolors of the FROLIC disks need to be changed. Each pixelis assigned a color-table index that points to a specific entryin the color-table. Color-table animation then changes theentries of the color-table itself rather than the pixels of thecorresponding image.

LIC on Surfaces – Mao et al.47 extend the original LICmethod by applying it to surfaces represented by arbitrarygrids in 3D. Former LIC methods targeted at surfaces wererestricted to structured grids 20 21 66. Also, mapping a com-puted 2D LIC texture to a curvilinear grid may introducedistortions in the texture. Mao el al. propose solutions toovercome these limitations. The principle behind their algo-rithm relies on solid texturing 52. The convolution of a 3D

white noise image, with filter kernels defined along the localstreamlines, is performed only at visible ray-surface inter-sections.

This idea has an advantage over that of Battke et al. 2 inthat it avoids what can be a timely and complex assemblyof triangles into texture space. However, ray-tracing is alsocostly. The method here is view-point dependent and re-quired relatively lengthy processing time for an unstructuredmesh composed of 10,000 triangles.

A significant body of research is dedicated to the exten-sion of LIC onto boundary surfaces. Teitzel et al. 73 presentan approach that works on both 2D unstructured grids anddirectly on triangulated grids in 3D space. This topic itselfis the subject of a survey by Stalling 69.

UFLIC – Shen and Kao 67 extend the original LIC algo-rithm to handle unsteady flows. Their extension, calledUFLIC (Unsteady Flow LIC), handles the case of unsteadyflow fields by introducing a new convolution filter that bet-ter models the nature of unsteady flow. The convolution isdone along pathlines (as opposed to streamlines). They im-prove upon the shortcomings of the previous unsteady LICattempt presented by Forssell and Cohen 21. According toShen and Kao, Forssell and Cohen’s approach has multiplelimitations including: (1) lack of clarity with respect to spa-tial coherence, (2) deriving current flow values from futureflow values, (3) unclear exposition with respect to temporalcoherence, and (4) lack of accurate time stepping. All ofthese problems are addressed by UFLIC. Shen and Kao alsoapply UFLIC to the visualization of time-dependent flow toparameterized surfaces. UFLIC is also extended using a par-allel implementation by Shen and Kao 65.

AUFLIC – AUFLIC (Accelerated UFLIC) is an extensionto UFLIC that enhances performance times 41. The princi-ple behind AUFLIC is to save, re-use, and update pathlinesin a vector field seeding strategy. AUFLIC requires approxi-mately one half of the time required by UFLIC and generatessimilar results.

3D LIC – Rezk-Salama et al. 59 propose rendering methodsto effectively display the results of 3D LIC computations.They utilize texture-based volume rendering in an effort toprovide exploration of 3D LIC textures at interactive framerates. Like Interrante 26, they address the perceptual prob-lems posed by dense, 3D visualization. They approach thesechallenges through the use of transfer functions and clippingplanes, as in Figure 11. Transfer functions allow the user tosee through portions of the LIC textures deemed uninterest-ing by the user. In addition to conventional clipping planes,Rezk-Salama et al. also use clipping with arbitrary closed-surface geometries.

The use of transfer functions and geometric clipping ob-jects are interesting choices for dealing with the perceptualproblems associated with 3D. In some sense, these can becompared with the seeding problem of the geometric class of

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Figure 11: An LIC visualization showing a simulation offlow around a wheel. 59 The appropriate choice of transferfunction results in a sparser noise texture. Image courtesy ofRezk-Salama et al. 59

visualization techniques. Seeding strategies address whereto start streamlines and other integration-based geometricobjects. Selective seeding of geometric objects in 3D is of-ten considered a key to successful visualization. However,knowledge of the proper seed locations is a requisite for thisapproach. And just as proper seed placement is a requi-site when using geometric objects, knowledge of the transferfunction(s) and closed-object clipping geometries is requiredin the case of 3D LIC.

Geometric LIC – We make a distinction between geomet-ric flow visualization and dense, texture-based flow visual-ization. However, these two topics are closely coupled. Con-ceptually, the path from using geometric objects to texture-based visualization is obtained via a dense seeding strategy.That is, densely seeded geometric objects result in an im-age similar to that obtained by dense, texture-based tech-niques 30. Likewise, the path from dense, texture-based visu-alization to visualization using geometric objects is obtainedusing something such as a sparse texture for texture advec-tion 85.

Here we have grouped together techniques that synthesizeLIC results by mapping a pre-computed LIC texture onto ge-ometric primitives such as streamlines. By using geometricprimitives, researchers hope to speed up performance timesof the LIC results. The drawback of these methods is thatthey require careful seeding strategies to gain the completecoverage of the flow field offered by traditional LIC tech-niques.

Motion Map – Jobard and Lefer use a motion map 31 in or-der to animate 2D steady flows. First, the domain is coveredcompletely with streamlines. Next, a color is mapped to thestreamlines and a color-table animation technique is used toanimate the flow. It offers the advantage of saving memoryand computation time since only one image of the flow hasto be computed and stored in the motion map data structure.This technique is not applicable to unsteady flow however. Itrelies on a one-time cost of computing a set of streamlines.

PLIC – Verma et al. present a method for visual compar-ison of streamlines and LIC called PLIC 82 (Pseudo-LIC).They attempt to identify the relevant parameters to generateLIC-like images from a dense set of streamlines and for gen-erating streamline-like images through the use of differentfilters used for convolution. By experimenting with differentinput textures for LIC, both streamline-like images and LIC-like results can be obtained. ELIC (enhanced LIC), placedhere because of its visual comparison with PLIC, builds onthe original LIC algorithm in four ways: (1) by incorporat-ing an algorithm to improve the delineation of streamlines,(2) increasing the image contrast, (3) removing texture dis-tortion introduced by applying LIC to curvilinear grids, and(4) using color to highlight flow separation and reattach-ment boundaries. A visual comparison between UFLIC 65,ELIC 51, and PLIC is shown in Figure 12.

Hierarchical LIC – Bordoloi and Shen 5 introduce a hier-archical approach to LIC based on a quadtree data structureused to support level of detail (LOD). The idea is to replaceportions of the vector field of lower complexity with rectan-gular LIC texture-mapped patches. The LIC texture is takenfrom a previously calculated LIC image of a straight vectorfield. Here, complexity is a direct function of the amount ofcurl in the local vector field.

Decoupled LIC – Li et al. 40 present a technique for the vi-sualization of 3D flow based on texture mapped primitives,namely streamlines. They decouple the visualization intoa pre-processing type stage that computes the streamlinesand a stage which maps various textures to the streamlinescomputed in the first stage. The result is volume renderedat interactive frame rates. To address the perceptual chal-lenges posed by 3D visualization, depth cues, lighting ef-fects, silhouettes, shading, and interactive volume culling aredescribed.

3.3. Texture Advection and GPU-Based Techniques

In this section we describe research based on moving tex-els or moving groups of texels, i.e., texture-mapped poly-gons whose motion is directed by the vector field. Figure 13shows an overview of the different techniques and classifiesthem according to two properties: (1) the advection schemeused and (2) the primitive used during advection. Some ofthe literature focuses mainly on the integration scheme usedto advect textures or texels. By the term texel means texture

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Figure 12: A comparison of 3 LIC techniques: (left) UFLIC 65, (middle) ELIC 51, and (right) PLIC 82. Image courtesy of Vermaet al. 82.

Moving Textures

Texture Advection

LEA 3D IBFV

IBFVAdvectionForward

BackwardAdvection

2D

2.5D

3D

Unsteady

LEGEND

UFAC

3D Texture Advection

Texel Textured Polygons

Advection Primitive

ISA and IBFVS

Figure 13: The classification of texture advection and GPU-based techniques. The columns indicate the primitive used duringadvection while the rows indicate the advection scheme.

element. Some methods focus on the mapping to advectedprimitives and some focus on both. Figure 13 also showsthe dimensionality of the flow data. In our discussion, wevisit the methods in clockwise order starting at 12 o’clock.Within each sub-block the methods are listed in chronologi-cal order. This is because the mapping of texel properties be-tween two time steps in the visualization is not 1-to-1 in thiscase. For a more detailed discussion see Jobard et al 28 29.

One characteristic common to many of the texture ad-vection techniques in this section 28 29 38 48 is the use ofbackward coordinate integration (or backward advection).None of the methods described here use forward advection(i.e., forward integration) and individual texels as a primi-tive. This is because the combination of forward integrationand texel primitives leaves holes in the visual domain afterthe forward integration computation 29. Given a position,x0 i j #$ i j of each particle in a 2D flow, backward in-tegration over a time interval h determines its position at aprevious time step 28:

x % h i j x0 i j h

τ 0v % τ x % τ i j dτ (8)

where h is the integration step, x % τ i j represents interme-diary positions along the pathline passing through x0 i j ,and vτ is the vector field at time τ. We note that the methodsin this category are generally implemented in an iterativefashion. That is for each animated frame an integration isperformed over a small time-step h, followed by an updateof visual properties. This is opposed to geometric methodsin which a longer particle path may be computed over sev-eral time steps before the results are displayed.

IBFV – Image Based Flow Visualization (IBFV) by VanWijk 80 is one of the faster algorithms for dense, 2D, un-steady vector field representations. It is based on the advec-tion and decay of textures in image space. Each frame ofthe visualization is defined as a blend between the previousimage, warped according to the flow direction, and a numberof background images composed of filtered white noise tex-tures. One reason it is faster than many texture-based flowvisualization methods is because it reduces the number ofintegration computations that need to be performed via ad-vecting small quadrilaterals rather than individual pixels.

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Figure 14: Snapshots from the visualization of a time-dependent surface mesh composed of 79K polygons with dynamic geom-etry and topology 38.

Moving Textures – Max and Becker were early to intro-duce the idea of moving textures in order to visualize vectorfields 48. One of the primary goals of this work was to usetextures in motion to produce near-real-time animation offlow. Texture-mapped triangles are advected, or distorted, inthe direction of the flow. Also, applying this technique to 3Dflows with no modification provides results that are difficultto perceive, at least in the case of a still image.

ISA and IBFVS – IBFV has been extended to the visualiza-tion of flow on surfaces 38 81. Van Wijk presents an extensioncalled IBFVS, IBFV for Surfaces. Laramee et al. 38 present asimilar dense, texture-based visualization technique on sur-faces for unsteady flow called ISA: Image Space Advection.Both methods produce animated textures on arbitrary 3Dtriangle meshes in the same manner as the original IBFVmethod. Textures are generated, advected, and blended inimage space. The methods generate dense representations oftime-dependent vector fields with high spatio-temporal cor-relation. While the 3D vector fields are associated with ar-bitrary triangular surface meshes, the generation and advec-tion of texture properties is confined to image space. Bothspot noise and LIC-like results can be attained. In both tech-niques, 38 81 fast frame rates are achieved in part by exploit-ing the GPU.

Van Wijk’s method is applied to potential field visualiza-tion and surface visualization. Laramee et al.’s algorithm isapplied to unsteady flow on boundary surfaces of large, com-plex meshes from computational fluid dynamics, dynamicmeshes with time-dependent geometry and topology, medi-cal data, as well as isosurfaces 39. Figure 14 shows the resultsapplied to a time-dependent geometry and topology.

3D IBFV – IBFV has also been applied to the visualizationof 3D flow 75. The problem of how to see inside the flowvolume is addressed by varying both the noise sparsity, rem-iniscent of Interrante and Grosch 26, and through varying theopacity of the rendered volume similar to Rezk-Salama etal 59. In order to achieve sparseness, Telea and Van Wijk in-ject empty holes of noise into the 3D field, in addition to the

noise described by the original IBFV. One important com-ponent of their method is to define a threshold value whicheliminates all close-to-transparent texel values. One disad-vantage of the method is that the range of velocity values itcan display is limited: A texel property cannot be advectedby more than one slice along the z axis of the volume in oneanimation frame. This problem is addressed by Weiskopfand Ertl 88.

3D Texture Advection – Kao et al. discuss the use of 3Dand 4D texture advection for the visualization of 3D fluidflows 32. The results show sparse texture noise in order to vi-sualize inside the 3D vector field. Formidable challenges areintroduced by the memory requirements involved in using3D and 4D textures. The proposed method does not workwell for the case of flows containing critical points for in-coming flows from the grid boundary.

GPU-Based LIC – Heidrich et al. 23 exploit pixel tex-tures to accelerate LIC computation. Pixel textures are anOpenGL extension by SGI that provides the functionality ofdependent textures in combination with multi-pass render-ing. Heidrich et al.’s implementation supports 2D, steadyvector fields only, and achieves sub-second computationtimes for LIC image generation. While this method couldbe categorized as a GPU-accelerated LIC technique, we po-sition it here due to its comparability with the following tex-ture advection techniques 27 89 that use the same proposedOpenGL extension, handle unsteady flow, and thus can beconsidered an extension of this technique.

LEA – Jobard et al. 27 introduce a GPU-assisted textureadvection technique for the dense visualization of 2D, un-steady flow. While the method of Max and Becker 49 ad-vects textures based on coarse triangular meshes, Jobard etal. advect textures on a per-pixel basis by means of pixeltextures, which are used in a similar way as by Heidrich etal 23. The gray-scale texture from the previous time step isdragged along the flow field by modifying the texture coordi-nates for the dependent texture lookup according to the flow

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Figure 15: Three images taken from an animation of an unsteady vector field created with the Lagrangian-Eulerian advectionalgorithm. 28 29 Image courtesy of Jobard et al.

data. Nearest-neighbor sampling is combined with an updateof fractional texture coordinates to represent subtexel motionand, at the same time, maintain a high contrast. An iterativeinjection of additional noise is used to compensate for a pos-sible loss of contrast over time. Jobard et al. also discuss thetreatment of inflow at boundaries, image enhancement bycolor masking, and the use of dye advection. Because of thelimited functionality of the graphics hardware that supportspixel textures, the implementation requires many renderingpasses and advects a texture of size 2562 at approximatelytwo frames per second. Moreover, the maximum resolutionof textures is restricted to 2562.

Jobard et al. extend this method to the more flexibleLagrangian-Eulerian Advection (LEA) scheme 28 for the vi-sualization of unsteady, 2D flow. Here, they rely on a CPUimplementation that leads to better advection quality, higherspeed, and no limitations of the maximum flow size. Par-ticle paths are integrated as a function of time, referred toas the Lagrangian step, while the color distribution of theimage pixels is stored in a texture and updated in place (Eu-lerian step). The temporal coherence of the advected noisetextures is transformed into spatial coherence by blendingtextures from subsequent time steps, i.e., each still framedepicts the instantaneous structure of the flow, whereas ananimated sequence of frames still reveals the motion of theadvected texture. Jobard et al. demonstrate that the combi-nation of noise and dye advection is useful for an effectivevisualization and exploration of unsteady flow. Some resultsfrom the technique are shown in Figure 15. This work is ex-tended by Jobard et al. 29 in order to improve the quality ofdye advection.

Weiskopf et al. 87 present a GPU-accelerated version ofthe LEA algorithm using per-fragment operations. TheGPU-based texture advection by Weiskopf et al. 89 sup-ports bilinear dependent texture lookups without taking intoaccount the update of fractional coordinates. Therefore,this approach is mainly suitable for dye advection at highframe rates. Weiskopf et al. also demonstrate how GPU-

accelerated visualization of unsteady, 3D flows can be im-plemented with pixel textures.

UFAC – Weiskopf et al. 86 introduce a generic texture-based framework for visualizing 2D, time-dependent vectorfields. They propose Unsteady Flow Advection-Convolution(UFAC) as an application of the framework for visualizingunsteady fluid flow. Also, their approach can reproduceother techniques such as LEA 29, IBFV 80, UFLIC 65, andDLIC 71. Weiskopf et al. describe a GPU-accelerated imple-mentation that, among other things, allows the user to trade-off quality for speed.

3.4. Related Dense, Texture-Based Methods

The literature described here is not, in general, as stronglyinter-related as the literature in the spot noise, LIC, textureadvection, and GPU-based categories. For this reason wesought an alternative schema in order to relate the differenttechniques. Figure 16 shows the related methods and classi-fies them based on the density of their results. In this caseeach technique is given a subjective rating on a sparse-to-dense scale. Sparse results look more like the results fromflow visualization using geometric objects whereas densetechniques produce results resembling spot noise or LIC.These methods do not fit cleanly into one of the previouscategories, nonetheless, they are important to the dedicatedtopic and are briefly outlined here. Reading from top to bot-tom in Figure 16, we visit the techniques in chronologicalorder.

Texture Splats – As an extension of the technique of splat-ting from volume rendering, Crawfis and Max 9 introducethe notion of texture splats for flow visualization. Being avolume rendering technique, it is targeted at the depiction of3D vector fields. As with Rezk-Salama et al. 59, it is a selec-tive transfer function that ultimately decides which subsetsof the 3D data are shown and which are not. The transferfunctions are used to emphasize or suppress spatial regionsas opposed to ranges of data values.

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MRF Textures

High DensityMediumSparse

Texture Splats

2D

2.5D

3D

Unsteady

LEGEND Texture Transport

Diffusion

Unsteady Diffusion

Contrast Analysis

Furlike Texture

Figure 16: Related dense, texture-based flow visualizationmethods. Each method is compared with respect to the den-sity of the resulting visualization.

Texture Transport – The texture transport method ofBecker and Rumpf 3 introduces a mathematical frameworkbased on the solution of a time-dependent transport equa-tion. Lagrangian coordinates are computed from the trans-port equation and visualized using a texture mapping. Theresults in this case resemble those from the geometric classof solutions. Individual lines in the texture can be distin-guished. The major drawback of this approach is the com-putation time required.

Furlike Texture – Khouas et al. synthesize LIC-like imagesin 2D with furlike textures 33. Their technique is able to lo-cally control attributes of the output texture such as orien-tation, length, density, and color via a model based on fila-ments resembling fur.

Diffusion and Unsteady Diffusion – Preußer and Rumpf 58

as well as Diewald et al. 18 borrow a well known techniquefrom image analysis for visualization of fluid flow. The non-linear, anisotropic diffusion equations from image analysisare adopted and applied to vector fields. A noisy texture cov-ering the domain is strongly smoothed along integral lineswhile still retaining and enhancing edges in directions or-thogonal to the flow, i.e., streamline-aligned diffusion. Suc-cessively coarse patterns representing the vector field canalso be generated. It is applied to 2D, 2.5D, and 3D vectorfields 18 58. In the case of 3D, the resulting enhanced edgesare discretized and resemble streamlines or streamribbons.In this case, occlusion becomes an important issue becausethe 3D results appear somewhat cluttered.

Bürkle et al. extend this technique to the case of time-dependent flow 6. Instead of streamline-like patterns, streak-line patterns are generated. A blending strategy, comparableto noise or dye injection, is introduced in order to provide thenew time-dependent texture necessary for the case of long-term flow evolution. They propose a solution based on the

blending of different results from the transport diffusion evo-lution started at successively incremented times. Again, thedisadvantage of this approach is the required computationaltime. Also, no attempt is made to apply this method to time-dependent 3D flow, a formidable challenge.

Contrast Analysis – Sanna et al. 63 focus on the issue ofencoding another scalar value into the texture used to visu-alize the flow, in addition to flow direction, orientation, andlocal magnitude of the field. It is an extension of a previ-ous technique called TOSL–Thick Oriented Streamline Al-gorithm 62. Areas of higher scalar values are characterizedby higher contrast levels in the texture and streamline tonesare generated in order to highlight these areas. The goal isto allow an additional variable into the visualization beyondprevious techniques.

MRF – Taponecco and Alexa apply Markov Random Field(MRF) texture synthesis methods to vector fields 72. Theresults resemble a mixture of traditional texture-based meth-ods and geometric methods. In the resulting texture, dis-tinct streamline patterns can be seen. One drawback to thismethod is performance. MRF texture synthesis methodsmay require hours of computation time. How it may be ap-plied to unsteady flow is an open question.

4. Comparisons and Discussion

In this section we briefly introduce literature that comparesand discusses dense, texture-based techniques at a meta-level. Sanna et al. also provide a summary of this area ofresearch, with a different classification 61. The methods areclassified according to the dimensionality outlined here inSection 1.2.

Flow Textures – Erlebacher et al. 19 present a class of flowvisualization algorithms called flow textures within a com-mon conceptual framework. Flow textures are textures thatencode dense, 2D, time-dependent representations of flow.The framework allows important ingredients of flow texturealgorithms to be understood with respect to spatial and tem-poral correlation. A subset of the more recent visualizationtechniques is described.

User Studies – Laidlaw et al. 35 present one of the few find-ings related to human-computer interaction (HCI). They at-tempt to assess some different visualization techniques fromthe viewpoint of the user in terms of searching for and clas-sifying critical points in the flow and predicting where a par-ticle may end after advection. Error was highest for the LICtechnique in conjunction with classifying critical points andthe prediction of particle advection. This is probably dueto the fact that LIC images do not distinguish between up-stream and downstream flow. User error was higher than ex-pected for all methods. Hedgehog techniques and LIC werealso associated with high error for locating critical points.The authors postulate that this was because in many cases

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critical points near the borders of the vector field were diffi-cult to identify.

5. Conclusions and Future Prospects

Texture-based algorithms are effective, versatile, and appli-cable to a wide spectrum of applications. A large numberof techniques have been developed and refined. In general,which techniques are best depends strongly on the goal ofthe visualization, such as for exploration, detailed analysis,or presentation and on the kind of data involved. Therefore,we believe that a large variety of techniques should be avail-able in order to allow researchers to choose the most suitableone.

The problem of dense, 2D, unsteady flow visualizationis close to being solved 80. And with recent follow-upwork 38 81, unsteady flow visualization on surfaces is notfar behind. However, the generalization to 3D flow fields isstill a big challenge, especially in the case of unsteady flow.Hardware, arguably, will not be the primary bottleneck tosolving this challenge, but perceptual issues will. Perceivingthree spatial and three data dimensions directly is a difficultjob for the human eye and brain. So far, techniques based ongeometric objects and particle animation generalize better to3D fields.

The scale of numerical flow simulations, and thus thesize of the resulting datasets, continues to grow rapidly -generally faster than the size of computer memory. For thesereasons more simplification strategies must be conceived,such as spatial selection (slicing, regions of interest), geom-etry simplification, and feature extraction.

Slicing in a 3D field reduces the problem to 2D, allowinguse of good 2D techniques, but care must be taken with in-terpretation, as the loss of the third dimension may lead tophysically irrelevant results and wrong interpretation. Tak-ing a single 3D time slice from a 3D time-dependent datasethas similar dangers. Other spatial selections such as 3Dregion-of-interest selection are less risky, but may lead toloss of context. Reduction of data dimension, such as re-ducing vector quantities to scalars will give more freedomof choice in visualization techniques (such as using volumerendering), but will not lead to much data reduction. Ge-ometry simplification techniques such as polygon mesh dec-imation, levels-of-detail, or multiresolution techniques willbe effective in managing very large datasets and interactiveexploration, enabling users to trade accuracy with responsetime.

Some areas that need additional work are: multi-field visualization with scalar, vector, and tensor

data, handling and exploring huge time-dependent flowdatasets, user studies for evaluation, validation, and field testing offlow visualization techniques, visualization of inaccuracy and uncertainty 42 60,

more robust feature extraction techniques, especially inthe case of 3D flow.

We also note that much of the research literature presentedhere demonstrates methods operating on structured, uniformresolution grids. However, the grids used in the private, com-mercial industry sector are often adaptive resolution and un-structured, especially in the case of CFD 37 38. Thus furtherresearch is necessary in order to integrate many of the thesemethods into practical industrial applications.

6. Acknowledgements

The authors thank all those who have contributed to this re-search including AVL (www.avl.com) , the Austrian gov-ernmental research program called K plus (www.kplus.at),and the VRVis Research Center (www.VRVis.at). Further-more, the authors thank all the colleagues from the researchcommunity who permitted to use the images as shown in thepaper. CFD simulation data used in Figures 2, 6, 10 and 14courtesy of AVL.

This project was partly supported by the Netherlands Or-ganization for Scientific Research (NWO) on the NWO-EWComputational Science Project, “Direct Numerical Simu-lation of Oil/Water Mixtures Using Front Capturing Tech-niques”, and by the Landesstiftung Baden-Württembergwithin the “Eliteförderprogramm für Postdoktoranden”.

For supplementary material, including additional, higherresolution images and animations, please visit:http://www.vrvis.at/ar3/pr2/star/

References

1. D. Arrowsmith and C. Place. An Introduction to DynamicalSystems. Cambridge University Press, USA, 1990. 2

2. H. Battke, D. Stalling, and H. Hege. Fast Line Integral Convo-lution for Arbitrary Surfaces in 3D. In Visualization and Math-ematics, pages 181–195. Springer-Verlag, Heidelberg, 1997.7, 9

3. J. Becker and M. Rumpf. Visualization of Time-DependentVelocity Fields by Texture Transport. In Visualization in Sci-entific Computing ’98, Eurographics, pages 91–102, 1998. 14

4. S. Berger and E. Gröller. Color-Table Animation of Fast Ori-ented Line Intgral Convolution for Vector Field Visualization.In WSCG 2000 Conference Proceedings, pages 4–11, 2000. 9

5. U. Bordoloi and H. W. Shen. Hardware Accelerated Interac-tive Vector Field Visualization: A level of detail approach. InEurographics 2002 Proceedings, volume 21(3) of ComputerGraphics Forum, pages 605–614, 2002. 10

6. D. Bürkle, T. Preußer, and M. Rumpf. Transport andAnisotropic Diffusion in Time-Dependent Flow Visualization.In Proceedings IEEE Visualization ’01, pages 61–67. IEEEComputer Society, 2001. 14

7. B. Cabral and C. Leedom. Highly Parallel Vector VisualizationUsing Line Integral Convolution. In Proceedings of the 27th

submitted to COMPUTER GRAPHICS Forum (3/2004).

Page 16: Flow Visualization-STAR: Dense and Texture-Based Techniques · The State of the Art in Flow Visualization: Dense and Texture-Based Techniques Robert S. Laramee,1 Helwig Hauser,1 Helmut

16 Laramee, Hauser, Doleisch, Vrolijk, Post, Weiskopf / Flow Visualization-STAR: Dense and Texture-Based Techniques

Conference on Parallel Processing for Scientific Computing,pages 802–807, Philadelphia, PA, USA, 1995. SIAM Press. 7

8. B. Cabral and L. C. Leedom. Imaging Vector Fields UsingLine Integral Convolution. In Poceedings of ACM SIGGRAPH1993, Annual Conference Series, pages 263–272. ACM Press/ ACM SIGGRAPH, 1993. 5, 6

9. R. A. Crawfis and N. Max. Texture Splats for 3D Scalar andVector Field Visualization. In Proceedings IEEE Visualization’93, pages 261–267. IEEE Computer Society, Oct. 1993. 13

10. W. de Leeuw and R. van Liere. Visualization of Global FlowStructures Using Multiple Levels of Topology. In Data Vi-sualization ’99, Eurographics, pages 45–52. Springer-VerlagVienna, May 1999. 6

11. W. de Leeuw and R. van Liere. Multi-level Topology for FlowVisualization. Computers and Graphics, 24(3):325–331, June2000. 6

12. W. de Leeuw and J. van Wijk. Enhanced Spot Noise for VectorField Visualization. In Proceedings IEEE Visualization ’95,pages 233–239. IEEE Computer Society, Oct. 1995. 5

13. W. C. de Leeuw. Divide and Conquer Spot Noise. In Proceed-ings of Supercomputing’97 (CD-ROM), San Jose, CA, Nov.1997. ACM SIGARCH and IEEE. 5

14. W. C. de Leeuw, H. Pagendarm, F. H. Post, and B. Waltzer.Visual Simulation of Experimental Oil-Flow Visualization bySpot Noise from Numerical Flow Simulation. In Visualizationin Scientific Computing ’95, pages 135–148. Springer-VerlagVienna, May 1995. 5

15. W. C. de Leeuw, F. H. Post, and R. W. Vaatstra. Visualizationof Turbulent Flow by Spot Noise. In Virtual Environments andScientific Visualization ’96, pages 286–295. Springer-VerlagVienna, Apr. 1996. 6

16. W. C. de Leeuw and R. van Liere. Spotting Structure in Com-plex Time Dependent Flow. In H. Hagen, G. M. Nielson, andF. H. Post, editors, Scientific Visualization, pages 9–13. IEEE,June 1997. Dagstuhl Seminar 9724. 5

17. W. C. de Leeuw and R. van Liere. Comparing LIC and SpotNoise,. In Proceedings IEEE Visualization ’98, pages 359–366. IEEE Computer Society, 1998. 6

18. U. Diewald, T. Preußer, and M. Rumpf. Anisotropic Diffusionin Vector Field Visualization on Euclidean Domains and Sur-faces. In IEEE Transactions on Visualization and ComputerGraphics, volume 6 (2), pages 139–149. IEEE Computer So-ciety, 2000. 14

19. G. Erlebacher, B. Jobard, and D. Weiskopf. Flow Textures.In C. R. Johnson and C. D. Hansen, editors, The VisualizationHandbook. Academic Press, Oct 2003. 14

20. L. K. Forssell. Visualizing Flow over Curvilinear Grid Sur-faces Using Line Integral Convolution. In Proceedings IEEEVisualization ’94, pages 240–247, Los Alamitos, CA, Oct.1994. IEEE Computer Society. 7, 9

21. L. K. Forssell and S. D. Cohen. Using Line Integral Con-volution for Flow Visualization: Curvilinear Grids, Variable-Speed Animation, and Unsteady Flows. IEEE Transactionson Visualization and Computer Graphics, 1(2):133–141, June1995. 7, 9

22. H. Hege and D. Stalling. Fast LIC with Piecewise PolynomialFilter Kernels. In Mathematical Visualization, pages 295–314.Springer Verlag, Heidelberg, 1998. 7, 8

23. W. Heidrich, R. Westermann, H.-P. Seidel, and T. Ertl. Appli-cations of Pixel Textures in Visualization and Realistic ImageSynthesis. In ACM Symposium on Interactive 3D Graphics,pages 127–134, 1999. 12

24. L. Hesselink, F. H. Post, and J. van Wijk. Research issues invector and tensor field visualization. IEEE Computer Graph-ics and Applications, 14(2):76–79, Mar. 1994. 1

25. V. Interrante and C. Grosch. Strategies for Effectively Visual-izing 3D Flow with Volume LIC. In Proceedings IEEE Visu-alization ’97, pages 421–424, 1997. 7, 8

26. V. Interrante and C. Grosch. Visualizing 3D flow. IEEE Com-puter Graphics & Applications, 18(4):49–53, 1998. 7, 8, 9,12

27. B. Jobard, G. Erlebacher, and M. Y. Hussaini. Hardware-Accelerated Texture Advection. In Proceedings IEEE Visual-ization 2000, pages 155–162. IEEE Computer Society, 2000.12

28. B. Jobard, G. Erlebacher, and M. Y. Hussaini. Lagrangian-Eulerian Advection for Unsteady Flow Visualization. In Pro-ceedings IEEE Visualization ’01, San Diego, California, Oc-tober 2001. IEEE. 7, 11, 13

29. B. Jobard, G. Erlebacher, and Y. Hussaini. Lagrangian-Eulerian Advection of Noise and Dye Textures for UnsteadyFlow Visualization. In IEEE Transactions on Visualizationand Computer Graphics, volume 8(3), pages 211–222, 2002.7, 11, 13

30. B. Jobard and W. Lefer. Creating Evenly–Spaced Stream-lines of Arbitrary Density. In Proceedings of the EurographicsWorkshop on Visualization in Scientific Computing ’97, vol-ume 7, Boulogne-sur-Mer, France, April 28-30 1997. Euro-graphics, Springer-Verlag. 10

31. B. Jobard and W. Lefer. The Motion Map: Efficient Com-putation of Steady Flow Animations. In Proceedings IEEEVisualization ’97, pages 323–328, Los Alamitos, Oct. 19–241997. IEEE Computer Society. 2, 10

32. D. Kao, B. Zhang, K. Kim, and A. Pang. 3D Flow Visual-ization Using Texture Advection. In International Conferenceon Computer Graphics and Imaging ’01, Honolulu, Hawaii,August 2001. 12

33. L. Khouas, C. Odet, and D. Friboulet. 2D Vector Field Visu-alization Using Furlike Texture. In Joint Eurographics-IEEETVCG Symposium on Visualization (VisSym ’99), Eurograph-ics, pages 35–44. Springer-Verlag Vienna, May 1999. 14

34. M. Kiu and D. C. Banks. Multi-frequency Noise for LIC.In Proceedings IEEE Visualization ’96, pages 121–126, LosAlamitos, Oct. 27–Nov. 1 1996. IEEE. 8

35. D. H. Laidlaw, R. M. Kirby, J. S. Davidson, T. S. Miller,M. da Silva, W. H. Warren, and M. Tarr. Quantitative Com-parative Evaluation of 2D Vector Field Visualization Methods.In Proceedings IEEE Visualization 01, pages 143–150, SanDiego, CA, October 2001. IEEE Computer Society. 14

submitted to COMPUTER GRAPHICS Forum (3/2004).

Page 17: Flow Visualization-STAR: Dense and Texture-Based Techniques · The State of the Art in Flow Visualization: Dense and Texture-Based Techniques Robert S. Laramee,1 Helwig Hauser,1 Helmut

Laramee, Hauser, Doleisch, Vrolijk, Post, Weiskopf / Flow Visualization-STAR: Dense and Texture-Based Techniques 17

36. D. A. Lane. Scientific Visualization of Large-Scale UnsteadyFluid Flows, chapter 5, pages 125–145. Scientific Visualiza-tion: Overviews, Methodologies, and Techniques. IEEE Com-puter Science Press, Los Alamitos, 1997. 4

37. R. S. Laramee. FIRST: A Flexible and Interactive Resam-pling Tool for CFD Simulation Data. Computers & Graphics,27(6):905–916, 2003. 15

38. R. S. Laramee, B. Jobard., and H. Hauser. Image Space BasedVisualization of Unsteady Flow on Surfaces. In ProceedingsIEEE Visualization ’03, pages 131–138. IEEE Computer So-ciety, 2003. 7, 11, 12, 15

39. R. S. Laramee, J. Schneider, and H. Hauser. Texture-BasedFlow Visualization on Isosurfaces from Computational FluidDynamics. In Joint Eurographics-IEEE TVCG Symposium onVisualization (VisSym ’04), Konstanz, Germany, May 19-212004. forthcoming. 12

40. G. S. Li, U. Bordoloi, and H. W. Shen. Chameleon: AnInteractive Texture-based Framework for Visualizing Three-dimensional Vector Fields. In Proceedings IEEE Visualization’03, pages 241–248. IEEE Computer Society, 2003. 10

41. Z. P. Liu and R. J. Moorhead, II. AUFLIC: An AcceleratedAlgorithm for Unsteady Flow Line Integral Convolution. InProceedings of the Joint Eurographics - IEEE TCVG Sympo-sium on Visualizatation (VisSym ’02), pages 43–52, 2002. 9

42. S. K. Lodha, A. Pang, R. E. Sheehan, and C. M. Wittenbrink.UFLOW: Visualizing Uncertainty in Fluid Flow. In Proceed-ings IEEE Visualization ’96, pages 249–254, Los Alamitos,Oct. 27–Nov. 1 1996. 15

43. H. Löffelmann, T. Kucera, and E. Gröller. Visualizingpoincaré maps together with the underlying flow. In Mathe-matical Visualization, pages 315–328. Springer Verlag, Hei-delberg, 1998. 6

44. H. Löffelmann, L. Mroz, E. Gröller, and W. Purgathofer.Stream arrows: Enhancing the use of streamsurfaces for thevisualization of dynamical systems. The Visual Computer,13:359–369, 1997. 6

45. H. Löffelmann, Z. Szalavàri, and E. Gröller. Local Analysis ofDynamical Systems – Concepts and Interpretation. In WSCG1996 Conference Proceedings, pages 170–180, Feb. 1996. 4

46. X. Mao, L. Hong, A. Kaufman, N. Fujita, and M. Kikukawa.Multi-granularity noise for curvilinear grid LIC. In GraphicsInterface, pages 193–200, June 1998. 9

47. X. Mao, M. Kikukawa, N. Fujita, and A. Imamiya. Line Inte-gral Convolution for 3D Surfaces. In Visualization in ScientificComputing ’97. Proceedings of the Eurographics Workshop,pages 57–70. Eurographics, 1997. 9

48. N. Max and B. Becker. Flow Visualization Using Moving Tex-tures. In Proceedings of the ICASW/LaRC Symposium on Vi-sualizing Time-Varying Data, pages 77–87, Sept. 1995. 11,12

49. N. Max, B. Becker, and R. Crawfis. Flow volumes for inter-active vector field visualization. In Proceedings IEEE Visu-alization ’93, pages 19–24, San Jose, CA, Oct. 1993. IEEEComputer Society. 12

50. N. Max, R. Crawfis, and D. Williams. Visualizing Wind Ve-locities by Advecting Cloud Textures. In Proceedings IEEEVi-sualization ’92, Boston, Massachusetts, 1992. IEEE ComputerSociety. 5

51. A. Okada and D. L. Kao. Enhanced Line Integral Convolutionwith Flow Feature Detection. In SPIE Vol. 3017 Visual DataExploration and Analysis IV, pages 206–217, Feb. 1997. 10,11

52. D. R. Peachey. Solid Texturing of Complex Surfaces.Computer Graphics (Proceedings of ACM SIGGRAPH 85),19(3):279–286, 1985. 9

53. F. H. Post and T. van Walsum. Fluid flow visualization. InFocus on Scientific Visualization, pages 1–40. Springer, 1993.4

54. F. H. Post and J. van Wijk. Visual Representation of VectorFields: Recent Developments and Research Directions, chap-ter 23, pages 367–390. Springer, 1994. in: L. Rosenblum etal. (eds.), Scientific Visualization: Advances and Challenges.4

55. F. H. Post, B. Vrolijk, H. Hauser, R. S. Laramee, andH. Doleisch. Feature Extraction and Visualization of FlowFields. In Eurographics 2002 State-of-the-Art Reports, pages69–100, Saarbrücken Germany, 2–6 September 2002. The Eu-rographics Association. 2, 6

56. F. H. Post, B. Vrolijk, H. Hauser, R. S. Laramee, andH. Doleisch. The State of the Art in Flow Visualization: Fea-ture Extraction and Tracking. Computer Graphics Forum,22(4):775–792, Dec. 2003. 2, 6

57. W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flan-nery. Numerical Recipes in C++: The Art of Scientific Com-puting. Cambridge University Press, Cambridge, 2 edition,2002. 4

58. T. Preußer and M. Rumpf. Anisotropic Nonlinear Diffusion inFlow Visualization. In Proceedings IEEE Visualization ’99,pages 325–332. IEEE Computer Society, Oct. 1999. 14

59. C. Rezk-Salama, P. Hastreiter, C. Teitzel, and T. Ertl. Interac-tive exploration of volume line integral convolution based on3D-texture mapping. In Proceedings IEEE Visualization ’99,pages 233–240, San Francisco, 1999. IEEE Computer Society.9, 10, 12, 13

60. P. J. Rhodes, R. S. Laramee, R. D. Bergeron, and T. M. Sparr.Uncertainty Visualization Methods in Isosurface Rendering.In M. Chover, H. Hagen, and D. Tost, editors, Eurographics2003, Short Papers, pages 83–88, Granada, Spain, September1-5 2003. The Eurographics Association. 15

61. A. Sanna, B. Montrucchio, and P. Montuschi. A survey onvisualization of vector fields by texture-based methods. Re-search Developments in Pattern Recognition, 1(1), 2000. pub-lisher: www.transworldresearch.com. 14

62. A. Sanna, B. Montrucchio, P. Montuschi, and A. Sparavigna.Visualizing vector fields: the thick oriented stream-line algo-rithm (TOSL). Computers and Graphics, 25(5):847–855, Oct.2001. 14

63. A. Sanna, C. Zunino, B. Montucchio, and P. Montuschi.

submitted to COMPUTER GRAPHICS Forum (3/2004).

Page 18: Flow Visualization-STAR: Dense and Texture-Based Techniques · The State of the Art in Flow Visualization: Dense and Texture-Based Techniques Robert S. Laramee,1 Helwig Hauser,1 Helmut

18 Laramee, Hauser, Doleisch, Vrolijk, Post, Weiskopf / Flow Visualization-STAR: Dense and Texture-Based Techniques

Adding a scalar value to texture-based vector field representa-tions by local contrast analysis. In Proceedings of the Joint Eu-rographics - IEEE TCVG Symposium on Visualizatation (Vis-Sym ’02), pages 35–41, 2002. 14

64. G. Scheuermann, H. Burbach, and H. Hagen. Visualizing Pla-nar Vector Fields with Normal Component Using Line IntegralConvolution. In Proceedings IEEE Visualization ’99, pages255–262, San Francisco, 1999. IEEE Computer Society. 7, 8

65. H. Shen and D. L. Kao. A New Line Integral ConvolutionAlgorithm for Visualizing Time-Varying Flow Fields. IEEETransactions on Visualization and Computer Graphics, 4(2),Apr. – June 1998. 9, 10, 11, 13

66. H. W. Shen, C. R. Johnson, and K. L. Ma. Visualizing VectorFields Using Line Integral Convolution and Dye Advection.In 1996 Volume Visualization Symposium, pages 63–70. IEEE,Oct. 1996. 8, 9

67. H. W. Shen and D. L. Kao. UFLIC: A Line Integral Convolu-tion Algorithm for Visualizing Unsteady Flows. In Proceed-ings IEEE Visualization ’97, pages 317–323. IEEE ComputerSociety, 1997. 9

68. D. Silver, F. Post, and I. Sadarjoen. Flow Visualization, vol-ume 7 of Wiley Encyclopedia of Electrical and Electronics En-gineering, pages 640–652. John Wiley & Sons, New York,1999. 4

69. D. Stalling. LIC on Surfaces. In Texture Synthesis with LineIntegral Convolution, pages 51–64. ACM SIGGRAPH 97, In-ternational Conference on Computer Graphics and InteractiveTechniques, 1997. 9

70. D. Stalling and H. Hege. Fast and Resolution IndependentLine Integral Convolution. In Proceedings of ACM SIG-GRAPH 95, Annual Conference Series, pages 249–256. ACMSIGGRAPH, ACM Press / ACM SIGGRAPH, 1995. 6, 7

71. A. Sundquist. Dynamic Line Iintegral Convolution for Visual-izing Streamline Evolution. In IEEE Transactions on Visual-ization and Computer Graphics, volume 9(3), pages 273–282,2003. 8, 13

72. F. Taponecco and M. Alexa. Vector Field Visualization usingMarkov Random Field Texture Synthesis. In Proceedings ofthe Joint Eurographics - IEEE TCVG Symposium on Visual-izatation (VisSym ’03), pages 195–202. Springer-Verlag, may2003. 14

73. C. Teitzel, R. Grosso, and T. Ertl. Line Integral Convolutionon Triangulated Surfaces. In WSCG 1997 Conference Pro-ceedings, pages 572–581, 1997. 9

74. A. Telea and J. van Wijk. Simplified Representation of VectorFields. In Proceedings IEEE Visualization ’99, pages 35–42,San Francisco, 1999. IEEE Computer Society. 6

75. A. Telea and J. J. van Wijk. 3D IBFV: Hardware-Accelerated3D Flow Visualization. In Proceedings IEEE Visualization’03, pages 233–240. IEEE Computer Society, 2003. 12

76. T. Urness, V. Interrante, I. Marusic, E. Longmire, and B. Gana-pathisubramani. Effectively Visualizing Multi-Valued FlowData using Color and Texture. In Proceedings IEEE Visual-ization ’03, pages 115–122. IEEE Computer Society, 2003. 8

77. M. van Dyke. An Album of Fluid Motion. The Parabolic Press,1982. 2

78. J. van Wijk. Implicit Stream Surfaces. In Proceedings of theVisualization ’93 Conference, pages 245–252, San Jose, CA,Oct. 1993. IEEE Computer Society. 4

79. J. J. van Wijk. Spot noise-Texture Synthesis for Data Visual-ization. In T. W. Sederberg, editor, Computer Graphics (Pro-ceedings of ACM SIGGRAPH 91), volume 25, pages 309–318.ACM, 1991. 4, 5

80. J. J. van Wijk. Image Based Flow Visualization. ACM Trans-actions on Graphics, 21(3):745–754, 2002. 7, 11, 13, 15

81. J. J. van Wijk. Image Based Flow Visualization for CurvedSurfaces. In Proceedings IEEE Visualization ’03, pages 123–130. IEEE Computer Society, 2003. 12, 15

82. V. Verma, D. Kao, and A. Pang. PLIC: Bridging the Gap Be-tween Streamlines and LIC. In Proceedings IEEE Visualiza-tion ’99, pages 341–348, N.Y., Oct. 25–29 1999. 10, 11

83. H. K. Versteeg and W. Malalasekera. Addison-Wesley, Febru-ary 1996. 3

84. R. Wegenkittl and E. Gröller. Fast Oriented Line Integral Con-volution for Vector Field Visualization via the Internet. In Pro-ceedings IEEE Visualization ’97, pages 309–316, Los Alami-tos, Oct. 19–24 1997. IEEE Computer Society. 9

85. R. Wegenkittl, E. Gröller, and W. Purgathofer. AnimatingFlow Fields: Rendering of Oriented Line Integral Convolu-tion. In Computer Animation ’97 Proceedings, pages 15–21.IEEE Computer Society, June 1997. 9, 10

86. D. Weiskopf, G. Erlebacher, and T. Ertl. A Texture-BasedFramework for Spacetime-Coherent Visualization of Time-Dependent Vector Fields. In Proceedings IEEE Visualization’03, pages 107–114. IEEE Computer Society, 2003. 13

87. D. Weiskopf, G. Erlebacher, M. Hopf, and T. Ertl. Hardware-Accelerated Lagrangian-Eulerian Texture Advection for 2DFlow Visualizations. In Proceedings of the Vision Model-ing and Visualization Conference 2002 (VMV-01), pages 439–446, Nov. 21–23 2002. 13

88. D. Weiskopf and T. Ertl. GPU-Based 3D Texture Advec-tion for the Visualization of Unsteady Flow Fields. In WSCG2004 Conference Proceedings, Short Papers, pages 259–266,February 2004. 12

89. D. Weiskopf, M. Hopf, and T. Ertl. Hardware-Accelerated Vi-sualization of Time-Varying 2D and 3D Vector Fields by Tex-ture Advection via Programmable Per-Pixel Operations. InProceedings of the Vision Modeling and Visualization Confer-ence 2001 (VMV 01), pages 439–446, Nov. 21–23 2001. 12,13

90. M. Zöckler, D. Stalling, and H.-C. Hege. Parallel Line IntegralConvolution. Parallel Computing, 23(7):975–989, 1997. 7

submitted to COMPUTER GRAPHICS Forum (3/2004).