Illustrative Flow Visualization: State of the Art, Trends and Challenges Andrea Brambilla

Illustrative Flow Visualization: State of the Art, Trends and Challenges Andrea Brambilla
EUROGRAPHICS 2012/ M.-P. Cani, F. Ganovelli
STAR – State of The Art Report
Illustrative Flow Visualization: State of the Art, Trends and
Andrea Brambilla1 , Robert Carnecky2 , Ronald Peikert2 , Ivan Viola1 , Helwig Hauser1
University of Bergen, Norway
2 ETH Zurich, Switzerland
Flow visualization is a well established branch of scientific visualization and it currently represents an invaluable
resource to many fields, like automotive design, meteorology and medical imaging. Thanks to the capabilities of
modern hardware, flow datasets are increasing in size and complexity, and traditional flow visualization techniques
need to be updated and improved in order to deal with the upcoming challenges. A fairly recent trend to enhance
the expressiveness of scientific visualization is to produce depictions of physical phenomena taking inspiration
from traditional handcrafted illustrations: this approach is known as illustrative visualization, and it is getting a
foothold in flow visualization as well.
In this state of the art report we give an overview of the existing illustrative techniques for flow visualization,
we highlight which problems have been solved and which issues still need further investigation, and, finally, we
provide remarks and insights on the current trends in illustrative flow visualization.
Categories and Subject Descriptors (according to ACM CCS): I.3.6 [Computer Graphics]: Methodology and
Techniques—I.3.8 [Computer Graphics]: Applications—
1. Introduction
Van Dyke’s book [VD82] from 1982 begins with the following statement: “We who work in fluid mechanics are fortunate [. . . ] that our subject is easily visualized”. This is indeed
reflected by the many years of successful research in flow
visualization: with the help of visualization techniques, flow
phenomena have been deeply studied and many unclear aspects of their behaviour have been explained. Over the years,
this continuous investigation process have produced a considerable amount of knowledge and, in the meantime, the
computational power of the hardware has been growing exponentially. Nowadays we are able to produce, through measurements or simulations, extremely faithful and high quality flow datasets, which are usually very dense, multidimensional and multivariate. It is, therefore, almost impossible to
get any insight out of them without the help of automatic or
semi-automatic tools.
The analysis/postprocessing phase can be more or less
complex and, based on several years of expertise and research in visualization, we propose to describe it through the
c The Eurographics Association 2012.
data abstraction pyramid metaphor, in Figure 1. At the lowest level, an acquisition step produces the so called raw data,
which is an initial representation of the phenomenon of interest. At this point different processing steps can be taken:
gradients and local properties can be computed in order to
enrich the data, a domain-specific model can help identifying
relevant feature, and so on. After every step a more abstract
representation of the underlying phenomenon is obtained.
The purpose of visualization techniques is to take data at
a certain abstraction level and show it in a way that allow
users to gain insights out of it.
Traditional flow visualization techniques have been quite
effective in making flow data understandable, but they
struggle to deal with the increased complexity of the
most recent datasets. A novel category of visualization
approaches, that has already been successful in medical
[SES05, VKG05, TSS∗ 06] and other visualization subfields
[WBE∗ 06, HBP∗ 07, PGT∗ 08], is illustrative visualization.
This discipline aims at visualizing the data in a clear and
understandable way through the use of techniques from tra-
A. Brambilla et al. / Illustrative Flow Visualization
importance mapping
intent specification
domain objects
model mapping
data markups
data enhancement
raw data
abstraction methods
abstraction levels
data amount
Figure 1: The data abstraction pyramid.
ditional handcrafted illustrations. Illustrative visualization
techniques explicitly address issues like cluttering, occlusion
and depth perception, which are typical for flow visualization as well. Exploiting illustrative approaches in this field
allows for quick exploration and in-depth analysis of dense
flow datasets, consequently producing a significant amount
of knowledge which would be otherwise unattainable.
The rest of the paper is organized as follows: brief
overviews of the basics and most common approaches in
both flow and illustrative visualization are given in Section
2 and Section 3, respectively. Section 4 is dedicated to the
classification and description of currently existing illustrative flow visualization approaches, and, finally, Section
5 summarizes the present state of the art and suggests
directions for possible future developments.
Illustrative flow visualization is a newborn discipline and, as
such, it still lacks of a formal structural organization and well
defined boundaries. In light of this consideration, the main
contributions and novelties of this STAR can be summarized
as follows:
• For the first time illustrative flow visualization is thoroughly analysed and formally organised.
• We propose a user-centric classification of the techniques
in this field, in order to help application experts (our users)
to choose the ones that best suit their needs.
• In the context of this classification, we review the existing
approaches and the most recent developments in the field.
• We give an overview of illustrative visualization focused
on showing the advantages of this category of techniques
over traditional visualization.
2. Traditional flow visualization
The term flow denotes an abstract concept adopted in many
application fields. Fluid dynamics, for instance, is concerned
with the study of fluid flows, i.e. the motion of fluids: typical
examples include the motion of water in a pump or a turbine,
the stream of air around a car or an airplane, blood in a vessel, oil or gas in a pipe, and so on. However, the concept of
flow is much broader and different definitions arise in every
area of application, such as physics or mathematics. Flow
visualization usually deals with data generated via measurements, simulations or modeling, and the results are commonly expressed as vector fields. In the following, the formal
mathematical background is discussed, then an overview of
flow visualization is presented, focusing on what are the existing techniques, how they can be classified, and which are
the pressing challenges.
2.1. Flow and vector fields
Firstly it is worth pointing out that the mathematical theories
behind flows and vector fields are extensive and beyond the
scope of this paper, here only a brief overview is given; for
a more detailed introduction on the subject, the reader can
refer to Asimov’s tutorial from 1993 [Asi93].
Given a dense set of massless particles i = 0, 1, 2, . . . moving in the spatial domain Ω ⊆ Rn , an n-dimensional steady
flow v is typically described with a differential equation of
the particles locations xi ∈ Ω with respect to the time t ∈ R:
dxi (t)
= v(xi (t))
In other words, a steady flow is associated with a vector field
that describes the instantaneous velocities of the particles
moving in the Euclidean space Rn :
v : Ω → Rn
The term steady means that the velocity vectors are constant over time; in contrast an unsteady vector field is timedependent and is defined as:
v : Ω × R → Rn
The related differential equation describing the motion of the
particles is
dxi (t)
= v(xi (t),t)
The differential equations 1 and 4 are solved via integration. In particular, a streamline is obtained by integration on
a steady vector field and it represents the path of a particle
in the steady flow; a pathline is the equivalent for unsteady
flows. There are two other types of commonly used curves
obtained through integration: a streakline is the imaginary
line created by particles continuously seeded at a certain position, and it is closely related to the physical experiment
of releasing dye into a fluid. A timeline instead is obtained
by integrating a set of particles simultaneously released in
the flow along a certain line or curve. Stream-, path-, streakand timelines are commonly known as integral lines (or integral curves), and they can be extended to higher dimension
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A. Brambilla et al. / Illustrative Flow Visualization
(-surfaces, -volumes). In the following, integral lines, integral surfaces and integral volumes are referred to as integral
Vector fields and integral structures are both well defined
concepts but their expressiveness is limited; essentially, the
resulting visualizations may be not able to fully represent
certain relevant aspects of the flow behaviour. The most recurrent strategy to address this issue is to look for objects
of particular interest in the vector field, the so called flow
features. In accordance with the state of the art report on
feature-based flow visualization by Post et al. [PVH∗ 03], the
most common types of flow features include:
Vortices: areas associated with swirling motion, they are almost ubiquitous in flows and are of vital importance in
many applications. The main problem is that a formal,
well accepted definition of vortex has yet to be found.
Vector field topology (VFT): obtained by integrating selected streamlines close to critical points (i.e. points p ∈
Rn where v(p) = 0), usually referred to as separatrices.
They partition the vector field in areas that asymptotically show coherent behavior. VFT is very effective for
2D steady flows, but its extension to 3D is problematic
because of cluttering and occlusion issues. More details
on this subject can be found in the works of Helman and
Hesselink [HH89, HH91] or in the survey from Laramee
et al. [LHZP07].
Lagrangian Coherent Structures (LCS): from a conceptual point of view, they are an attempt to extend VFT
to unsteady flows. A formal definition has not yet been
given and the research on this subtopic is very active.
Useful information can be found in related literature
[Hal01, SLM05, PPF∗ 11].
Shock waves: typical of flows around aircraft, they are
characterized by sharp discontinuities in physical flow attributes. A straightforward way to detect them is to look
for edges in scalar quantities such as pressure, density or
velocity magnitude.
Separation and attachment lines: only present in conjunction with solid bodies or boundaries, these are the
curves where the flow abruptly moves away (separation)
or towards (attachment) the surface of the solid object.
2.2. Vector field discretization
Focusing now on a more practical topic, flow visualization
approaches have to take into account a specific issue: data
obtained from simulations or measurements is almost never
given in analytic form, but sampled at specific locations in
the spatial and temporal domain. The set of sampling points
is usually topologically organized according to a more or
less structured grid (also called mesh), ranging from Cartesian to curvilinear, or even to completely unstructured grids.
Even assuming that the Nyquist frequency condition is
fulfilled, a series of problems arises: for example, point loc The Eurographics Association 2012.
cation, i.e. determining the grid cell which contains a certain point, is not trivial, especially for unstructured grids.
Special data structures are often employed in order to speed
up the search. Moreover, since the vector field is sampled
only at specific points, there is also the need for a reconstruction strategy to determine flow attributes at generic locations of the domain. Reconstruction algorithms heavily
depend on the cell shape and are usually based on linear
or higher order interpolation techniques. The reconstruction problem can also cause collateral effects on the computation of derivatives and integral structures, therefore special attention is often needed when designing these algorithms. A more detailed overview of sampling grids and
related issues can be found in previous state of the art reports [PVH∗ 02, LHD∗ 04].
For the sake of completeness, it is worth mentioning that,
even though sampling grids are widely used, other types of
representations exist, like particle-based or functional representations, and each one has its own set of related challenges.
2.3. Flow visualization techniques
One of the first attempts to formally classify and summarize decades of work in flow visualization has been proposed
by Hesselink, Post and van Wijk in 1994 [HPvW94]: they
suggest to differentiate existing approaches according to the
type of data (scalar, vector, tensor), the dimensionality of the
domain (point, line, surface, volume) and the “information
level”, i.e. if the displayed data is either raw (elementary),
derived from a small neighbourhood (local), or dependent
on the entire dataset (global). The first two criteria are still
widespread nowadays, with the second one now taking into
account the temporal dimension as well, and they are often
combined with other classification directives.
In 2002, Post et al. [PVH∗ 02] proposed one of the most
widely accepted categorizations of flow visualization techniques:
Direct Visualization: the data is directly mapped to a visual representation, without complex conversions or extraction steps. Arrow glyphs, color coding and volume
rendering are the core of this category.
Texture-based Visualization: a dense representation of the
flow is obtained using local flow attributes to create and/or
warp a noise texture; more details on this topic can be
found in [SMM00] and [LHD∗ 04].
Geometric Visualization: in order to better convey flow
dynamics, integral structures are used as a basis for the
graphical representation; a recent survey by McLoughlin
et al. [MLP∗ 10] thoroughly describes this category of approaches.
Feature-based Visualization: a sparse visualization is obtained focusing only on the most significant areas of the
vector field; a comprehensive survey on features extraction and related visualization techniques has been presented in 2003 by Post et al. [PVH∗ 03].
A. Brambilla et al. / Illustrative Flow Visualization
More recently, Salzbrunn et al. [SJWS08] propose to add a
new category, i.e. Partition-based Visualization, which includes all those approaches aimed at effectively partitioning
the spatial and temporal domain according to flow properties.
For reasons that will become clear in Section 4 we do not
fully adopt this classification, but we adjust it in order to better reflect the data abstraction scheme previously introduced
through the pyramid metaphor.
2.4. Challenges in flow visualization
Flow visualization has been an active research field for many
years now and satisfactory solutions have been found for
many problems, like the direct or texture-based visualization
of 2D steady flows. However, a lot of questions still have to
be answered. This topic is extensively discussed in the survey by McLoughlin et al. [MLP∗ 10], here we provide a just
short list of selected challenges.
Already at the raw data level interesting research opportunities can be found: first of all, the generation of a dataset,
through simulations or measurements, can take days and
generate terabytes of data; in contrast, the visualization process has to be possibly interactive and, since disk access is
a time-consuming operation, it can only rely on a few gigabytes of main memory.
Furthermore, data is usually defined according to a certain grid, as mentioned before, and the type of the grid has a
significant impact on the visualization as well: for instance,
raycasting through a Cartesian grid is straightforward, but
it becomes progressively more complex with less structured
grids. In general, approaches designed for a certain type of
grid structure are not guaranteed to work well with more
complex ones, at least not at the same frame rate.
From a visualization-related point of view, one of the most
difficult challenges is associated with three-dimensional
datasets: vector fields are usually very densely sampled,
therefore cluttering and occlusion are almost ubiquitous. In
3D, integral structures and certain flow features, like LCS,
often present twists, folds and self intersections, which make
depth and shape perception very difficult.
Adding the temporal dimension makes the situation even
more complicated: animation is the traditional tool to depict
time-dependent information, but it can only depict one instant at a time, the temporal context is limited; on the other
hand, pathlines and streaklines can be used to show the trajectory of one or more particles, but the global flow behavior
cannot be effectively conveyed. In the next section we discuss how illustrative visual abstractions can be used to solve
some of these open issues.
3. The illustrative paradigm
Illustrative visualization is an emerging branch of the visualization research field that focuses on interactive and expressive visualizations typically inspired by works from artists
and illustrators [RBGV08]. Its main goal is maximizing the
amount of information effectively conveyed utilizing visual
abstraction techniques.
In traditional craft, the illustrator employs drawing styles
such as pencil, brush, or watercolor styles; in illustrative visualization, algorithms that are concerned with visual styles
are referred to as low-level visual abstractions [VGH∗ 05].
Line drawings techniques, contours or silhouettes [IFH∗ 03],
and handcrafted shading, such as stippling, hatching, or toon
shading [GGSC98], provide enhanced shape, depth and directional cues in order to improve the perceptual effectiveness of the results. Low-level visual abstractions, such as
those mentioned above, define how to depict a certain structure and have been the primary focus of non-photorealistic
rendering (NPR).
When dealing with large and dense amounts of data, illustrators work with expressive techniques that change the
layout or deform features to increase the communicative intent of the illustration; these approaches are commonly referred to as high-level visual abstractions. Selective visualization, cutaways, close-ups, or exploded views are examples of illustrative concepts that can be simulated with computerized techniques with different purposes in mind. In particular, visibility management (also known as smart visibility) techniques [VG05, ET08] are aimed at improving the
overall visibility of the data through an optimal use of the
visual space. In contrast, focus emphasis (or focus+context)
approaches [Hau03, VKG05] acknowledge that portions of
the data are deemed more important than others. The focus,
i.e. the relevant part of the dataset, has to be visually emphasized, while less important information should be used to
provide the context. The mapping between domain knowledge and visual appearance is expressed by an importance
Closely related to high-level visual abstractions, are
guided visualization [KBKG07,VFSG06] and interactive visual storytelling techniques [WH07, MLF∗ 12]. The former
guides the viewer’s attention to the relevant structures by
computing informative viewpoints and camera paths for refocusing from one object of interest to another. Interactive
storytelling enables the user to set up a story related to a phenomenon of interest by setting up story-nodes and transitions
between them. All the aspects of the story, from the rendering style to the camera parameters, can be interactively modified, so every user can adapt the narrative process to his or
her own needs on the fly. Both these categories of approaches
share the common goal of providing an effective visual description of the phenomenon of interest, therefore we refer
to them as visual explanation techniques.
Notice that different amounts of domain knowledge are
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A. Brambilla et al. / Illustrative Flow Visualization
cut-aways and clip planes effectively improve visibility and
reduce occlusions. Nowadays the quality and the amount of
available computational resources are respectively better and
larger than 30 (or 500) years ago, but those concepts and
guidelines are still the key to produce intuitive, effective and
aesthetically pleasing visualizations.
4.1. A user-centric classification
Figure 2: (a) Hand-drawn illustration of water flow behind
an obstacle by Leonardo da Vinci [dV09]. (b) Depiction of
a dynamical system with stream arrows (image courtesy of
Abraham and Shaw [AS82] 1982
needed in every category in order to achieve expressive visualizations: this property is nicely aligned with the idea of
knowledge and information-assisted visualization expressed
by Chen et al. [CEH∗ 09]. Table 1 summarizes the illustrative
visualization categories just introduced, emphasizing what
are their strong points with respect to traditional visualization, and what kind of knowledge about the data they take
into account. For more details about illustrative visualization and a review of the best known techniques, the reader
can refer to [VGH∗ 05, SEV∗ 08].
Before proceeding to the next section, we would like to
spend a few words about interactivity: besides solving occlusion problems, interactive navigation through the spatial
domain is one of the most effective ways to perceive the location and the shape of an object. Its central role has been
already identified 30 years ago [HS89], and it is still one
of the most sought after features of a visualization system.
Even though expressiveness is frequently much more discussed, illustrative visualization heavily relies on interactivity as well.
4. Illustrative Flow Visualization
The idea of using illustrations to depict and investigate flow
behavior is not new, on the contrary, it has been around for
more or less 500 years: Figure 2a is an illustration from
Leonardo da Vinci (1452-1519) showing the motion of water behind a solid obstacle. More recently (1982), Abraham
and Shaw extensively used hand-drawn pictures to visualize
flow structures in their book [AS82] (see Figure 2b). Neither
da Vinci nor Abraham and Shaw had access to fancy graphics hardware, but they were still able to effectively convey
relevant flow information; so, how did they do it?
Analyzing their pictures, some of the concepts introduced
in the previous section can be easily recognised: hatching
and stippling are used to improve depth perception, only
portions of the data are shown so that cluttering is avoided,
c The Eurographics Association 2012.
Being at the crossroad of two disciplines, it seems natural
to classify illustrative flow visualization techniques according to two different characteristics, one from the flow and
one from the illustrative domain. While designing this categorization we have taken into account the following guidelines:
1. the two classification criteria should be as independent as
2. the advantages of using illustrative visualization, as compared to more traditional visualization, should be clearly
3. the classification should help a potential user (with possibly limited knowledge of visualization) to find which
techniques suit his/her needs best.
Regarding the flow perspective, we realized that the traditional subdivision into direct, texture-based, geometric and
feature-based visualization is not optimal since, even though
perfectly clear to a visualization expert, it does not well reflect the point of view of a user. Doctors, engineers and meteorologists need a clear depiction of some specific aspects of
the data, the visual tools employed are only partially relevant
to them. On the other hand, they are usually well aware of
what kind of data they are dealing with and which processing steps are meaningful for their applications, therefore we
propose a slightly different classification based on what are
the domain objects the user wants to see in a visualization:
Raw data refers to the original data produced by simulations or measurements (such as velocity or pressure), together with the information directly derivable from it (like
curl or gradients); this kind of data is usually defined at the
vertices or cells of the sampling grid and it can be easily
visualized, for instance, via volume rendering or glyphs.
Integral structures are well known concepts in the flow
community and are extensively used to investigate flow
behavior; they are usually displayed as linear structures
(lines, tubes, ribbons) or surfaces.
Flow features are subsets of the data perceived as particularly relevant by the user; according to the specific application domain different definitions arise and different
visualization techniques are used.
These categories on the flow axis go along very well with
the illustrative visual abstraction levels presented in Section
3: there is no mutual dependency between the two classifications, and the user, in order to satisfy his or her visualization needs, has just to answer the questions “what flow representation do I want to refer to?” and “what visualization
A. Brambilla et al. / Illustrative Flow Visualization
Visual Abstraction
Advantages over traditional visualization
Knowledge about the data
Perceptual Enhancement
Depth and/or shape perception is enhanced, local
properties of the data are effectively conveyed
No domain knowledge about the data is
usually taken into account
Visibility Management
Occlusion and cluttering are reduced, the expressiveness of the visual space is maximized
The data reflects the inherent complexity of the phenomenon of interest
Focus Emphasis
The data aspects in focus are always clearly visible, well depicted and not occluded by the context
A portion of the data (the focus) is
deemed more important than the rest
Visual Explanation
A description of the phenomenon is presented to
the user according to his or her needs
A domain-specific semantic is associated with the data
Table 1: The illustrative visual abstraction categories, with their advantages over traditional visualization and the kind of knowledge about the data they take into account.
enhancement do I need?”. Table 2 summarizes this classification and presents a possible categorization of existing illustrative flow visualization techniques according to the two
criteria just introduced.
We would like to point out that there is also an alternative
interpretation to our classification: the flow axis can be seen
as the amount of processing that the data has been undergoing, while the illustrative categories relate to the amount of
knowledge about the data taken into account during the visualization process. These are the same concepts mentioned
before regarding, respectively, the abstraction pyramid (see
Section 1) and the knowledge and information-assisted visualization (see Section 3).
4.2. Perceptual Effectiveness
This subsection gives an overview of the approaches focused
on improving the perception of the flow data through the use
of depth, shape and directional cues. This necessity has been
identified in flow visualization a long time ago, here we review those approaches that clearly show some illustrative aspect, even though they have been proposed before illustrative
visualization was formally introduced.
similar idea has been adopted in the work of Ebert and Shaw
in 2001 [ES01], where arrows and superquadric shapes are
used to convey flow properties in a three-dimensional immersive environment. Notice that these techniques essentially differ from the traditional (non-illustrative) arrow plotting techniques since particular attention is posed on the expressiveness (shape, appearance, position and so on) of the
The natural extension of color coding to 3D is volume
rendering. This technique is known to generate cluttering
and occlusion if used unwisely, therefore particular attention
should be paid in the setup phase. Stompel et al. [SLM02]
propose different NPR techniques for volumetric data, with
the goal of improving the readability of the results. In contrast, Park et al. [PBL∗ 04] use raw and derived data as input of a customizable n-dimensional transfer function, allowing for expressive and uncluttered visualization. An inbetween approach has been proposed in 2005 by Svakhine et
al. [SJEG05]: only 2 variables are used to control color and
transparency, therefore the long and cumbersome fine-tuning
of the transfer function needed in [PBL∗ 04] is avoided. As
can be seen in Figure 3b, simple illustrative techniques, like
silhouette enhancing, are applied in order to improve the appearance of the results.
4.2.1. Improving perception of raw data
The techniques in this category are mostly based on
well known visualization concepts, like directional glyphs
(hedgehog), transfer functions or texture advection. The
mapping between the data and its visual counterpart is usually very tight, and it typically leads to very dense representations of the dataset. For example, the approach proposed
in [KML99] is built on a direct correspondence between
flow properties and visual resources: Figure 3a has been obtained by mapping velocity direction and magnitude to direction and size of arrows, while colors represent the vorticity and ellipses represent strain, divergence and shear. A
This last work has also been extended to tetrahedral grids
in 2006 [SET∗ 06] but, since then, volume rendering of flows
hasn’t attracted too much attention, probably because it is
not well suited for conveying directional information. On the
other hand, volume rendering is an active research field on
its own, and techniques developed for volumetric data are
often used in flow visualization to show scalar variables like
pressure or temperature.
Another category of approaches aimed at effectively conveying flow properties is texture-based visualization: the basic idea is to generate a noise texture and then use local charc The Eurographics Association 2012.
A. Brambilla et al. / Illustrative Flow Visualization
Raw Data
Integral Structures
Flow Features
[vW91] [CL93] [IG97]
[dLvL97] [HWSE99]
[KML99] [RSHTE99]
[DPR00] [ES01] [JEH01]
[WFK∗ 02] [SLM02]
[vW02] [WEE03] [PBL∗ 04]
[SJEG05] [SET∗ 06]
[SVL91] [USM96] [ZSH96]
[SM04] [SKH∗ 04] [XZC04]
[MPSS05] [SGS05] [vFWTS08]
[BFTW09] [KGJ09] [EBRI09]
[LKG98] [UIM∗ 03]
[UIL∗ 04] [vPBB∗ 10]
[MCG94] [LMG97] [LDG98]
[HWHJ99] [TVW99] [GPR∗ 01]
[JL97] [GPR∗ 04] [LS07]
[YWM07] [LHS08] [BWF∗ 10]
[HGH∗ 10] [MCHM10]
[CYY∗ 11] [LMSC11]
[vPGtHRV11] [WTS11]
[RPS01] [HMCM10]
[SJM96] [TvW03] [HM03]
[SLB04] [WE04] [WBE05]
[CSC07] [WSE07] [FW08]
[IEGC08] [LTH08]
[WYM08] [WYG∗ 11]
[FG98] [HM03] [MTHG03]
[KKKW05] [WS05] [STWE07]
[FBTW10] [JM10] [WWYM10]
[AWM10] [PTA∗ 11]
Table 2: Classification of illustrative flow visualization approaches according to the abstraction level of the visualized data and
the kind of visual abstraction they adopt. The different categories are thoroughly described in Section 4
acteristics of the vector field to warp or filter it. This kind of
techniques is widely used in flow visualization, mainly for
2D flows or on curved surfaces in 3D, since they are able
to clearly represent directional information with minimal visual resources. The direct consequence is that they can be
easily combined with other techniques, like color mapping,
glyphs, or even other textures, to obtain highly expressive
results (see Figure 3c).
One of the first texture-based techniques, introduced by
van Wijk in 1991 [vW91], is spot noise: a set of intensity
functions (the spots) are warped over a small time step according to the velocity vectors, therefore generating a dense
texture which encodes both the direction and the magnitude
of the local flow. Two years later a similar technique was
presented: Line Integral Convolution (LIC) [CL93] fetches
intensity values from a random noise textures and convolves
them along the streamlines of the vector field; in contrast to
spot noise, LIC does not reflect the magnitude of velocity,
c The Eurographics Association 2012.
but makes the location of critical points easier. These techniques have been later extended in many ways:
1. [dLvL97] deals with unsteady vector fields.
2. [HWSE99] proposes a GPU implementation of LIC.
3. [IG97, RSHTE99] apply LIC to 3D flows using 3D textures. In this case the results suffer of serious cluttering
and occlusion problems, so halos and clipping planes are
used to enhance the overall readability (see Figure 3d).
Other notable techniques in this category are based on
anisotropic non-linear diffusion [DPR00], Image Based
Flow Visualization (IBFV) [vW02], Lagrangian-Eulerian
Advection (LEA) [JEH01], and especially Unsteady Flow
Advection-Convolution (UFAC) [WEE03], which is able to
emulate most of the previously introduced approaches. Research in texture-based flow visualization has been very active until a few years ago and is now considered an almost
closed topic; for a comprehensive overview of the substan-
A. Brambilla et al. / Illustrative Flow Visualization
Figure 3: (a) Visualization of multiple flow attributes: arrows represent velocity, colors represent vorticity and ellipses represent
strain, divergence and shear (image courtesy of Kirby et al. [KML99] 1999
IEEE). (b) Illustrative volume rendering of flow
data (image courtesy of Svakhine et al. [SJEG05] 2005
IEEE). (c) Texture-based visualization with color-coding of local
flow properties (image courtesy of Urness et al. [UIM∗ 03] 2003
IEEE). (d) 3D-LIC of flow around a wheel, visualized with
the aid of a clipping plane (image courtesy of Rezk-Salama et al. [RSHTE99] 1999
tial amount of work on this topic the reader can refer to the
state of the art report by Laramee at al. [LHD∗ 04].
To conclude this section, we would like to emphasize that
the different techniques introduced up to now can also be
used as “building blocks” of more comprehensive visualizations: [WFK∗ 02], for instance, employs textures, hue and
intensity to visualize 3 different flow aspects, and mix them
using partial transparency and 3D height fields.
4.2.2. Effective integral structures
Integral structures are widely used in flow visualization because of their inherent ability of clearly depicting the trajectories of particles in the flow, a task that cannot be achieved
with raw data alone. The first attempt to improve the expressive power of integral lines was the Stream Polygon
[SVL91], proposed in 1991 by Schroeder et al.: an n-sided
polygon is swept along a streamline and it is deformed according to local flow properties, like the normal or shear
strain; moreover, once the deformed polygons have been
computed at every point of the streamline, they can be connected, generating a streamtube. This idea became very popular and different improvements and variants have been proposed: notably [USM96] presents an extension to unstructured grids, while [SKH∗ 04] describes a method similar to
billboarding aimed at speeding up the rendering. More recently Stoll et al. [SGS05] introduced a novel rendering algorithm that allows to control different properties of tubelike structures and supports effects like halos, shadows and
texturing to improve the visual appearance of the results (see
Figure 4).
Instead of dealing with geometrical structures, another
well known category of approaches focuses on shading techniques for (infinitesimally thin) lines. For example Zöckler
et al. in 1996 propose a method for computing Phong illumination on streamlines, obtaining the so called Illuminated Streamlines [ZSH96]. Similar results are presented
in [MPSS05], which reviews Zöckler’s work in order to enhance depth perception, and in [SM04], which samples the
lines into an anisotropic voxel representation; the voxels are
then displayed via volume rendering, allowing for the visualization of whole datasets at nearly interactive rates.
A slightly different and very interesting approach has
been proposed by Everts et al. [EBRI09]: they display dense
bundles of lines with a simple pen-and-ink style (black and
white), while depth information is effectively conveyed by a
smart use of halos. In general, the main difference between
geometric and shading approaches is that, while the former
are able to convey local properties of the flow, the latter can
guarantee a denser coverage of the spatial domain.
Focusing now on 2D integral structures, it immediately
stands out that the illustrative visualization of flow surfaces
has followed a completely different path as compared to integral lines. This is actually not so surprising: even a minimal swirling motion can make an integral surface roll up,
occluding itself. Moreover, in the case of pathsurfaces, self
intersections occur quite frequently. The direct consequence
is that “visibility” issues, discussed in the next section, have
Figure 4: Different visual enhancements applied to integral
lines (image courtesy of Stoll et al. [SGS05] 2005
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A. Brambilla et al. / Illustrative Flow Visualization
been much more investigated than “perceptual” ones. Here
we present three techniques focused on the interactive illustrative visualization of time- and streaksurfaces.
As already stated at the end of Section 3, interaction is
extremely effective in improving depth and shape perception, but, due to their high computational cost, visualizing time- and streaksurfaces at interactive rates has been
a difficult challenge. The approach by von Funck et al.
[vFWTS08] consists of a rendering technique that gives surfaces a smoke-like appearance. Besides the visually pleasant look, the main advantage is that the algorithm for surface construction can be largely simplified, since the resulting artifacts are not shown by the smoke-like rendering. In contrast, the other two approaches [BFTW09,KGJ09]
explicitly review the surface construction procedure, computing it on the GPU and employing different optimizations and workarounds. They also apply different illustrative
techniques, like transparency, silhouette enhancement and
ribbon-like textures, while still achieving interactive frame
Integral volumes were introduced in 1993 by Max et al
[MBC93], but they have never received too much attention,
probably because their inherent complexity is not matched
by a significant improvement of expressiveness. However, it
is worth mentioning the approach by Xue et al. [XZC04],
which computes streamvolumes and visually enhances them
with texture advection techniques.
4.2.3. Appearance of flow features
To our knowledge, there is no technique which explicitly
addresses the perceptual effectiveness of flow feature visualizations. A possible reason could be that many kinds of
features, like vortices or shock waves, can be mapped to
sparse and easy to understand visual representations, therefore they rarely present perceptual problems. This situation
may soon change as a consequence of the recent increasing
interest in Lagrangian Coherent Structures: LCS are typically represented by very complex surfaces, which can be
self-intersecting, self-occluding, or even non-manifold. As
this kind of features will grow in popularity, we expect that
different approaches will be developed in order to visualize
them in an effective way.
4.3. Visibility Management
Visibility management includes all those approaches that explicitly address visibility, occlusion and cluttering issues. It
is important to point out that, at this abstraction level, only
the visual appearance of the result is taken into account. The
fact that some portions of the data can be more relevant than
others is discussed later, in the “Focus Emphasis” section.
Notice that in this category, a particular class of illustrative
techniques can be identified, i.e. temporal implosion. Since
this idea has been applied to all the three kinds of flow entities, we discuss it in a separate subsection.
c The Eurographics Association 2012.
4.3.1. Raw data visibility
Raw data is usually dense and this entails different consequences depending on the dimensionality of the dataset.
In 2D the whole data can be easily displayed on a plane,
therefore visibility issues are minimal. It is however worth
mentioning the Color Weaving technique by Urness et al.
[UIM∗ 03]. In their work a texture-based visualization conveys directional information, while multiple color maps
are used to represent different local properties of the flow.
Thanks to a smart interleaving algorithm, color mixing is
avoided and many attributes can be visualized at once: in
Figure 3c red and blue denote areas of respectively positive and negative vorticity, green represents the shear stress,
while orange and magenta highlight swirling regions. The
expressiveness of this technique has been further improved
one year later [UIL∗ 04], adding shading effects based on
contrast, luminance and embossing.
In 3D the situation is much more complex: the degree of
occlusion is extremely elevated and visualizing the data as
a whole is, at least, highly challenging. A quite typical approach is clipping portions of the dataset or showing only
sections of it. Löffelmann et al. [LKG98] apply this concept for the visualization of Poincaré maps, i.e. functions
describing the behavior of an orbit through a lower dimensional space, a plane in this case. They visualize a section of
the flow with glyphs or spot noise, while the orbit-plane intersections are highlighted with colored dots. Another example is given in the recent work by van Pelt et al. [vPBB∗ 10],
who use cross-sections to emphasize the direction and intensity of blood flow in a vessel.
In the case of raw data, visibility management hasn’t attracted too much attention. Taking into account some kind of
importance measure can greatly increase the effectiveness of
the results, therefore focus emphasis approaches are much
more widespread for this kind of flow representation.
4.3.2. Visibility enhancement for integral structures
In this category a large number of approaches is concerned
with the optimal placement of integral lines. There are two
main issues that have to be considered:
1. too many lines would lead to cluttered results with high
degree of occlusion;
2. uniformly placing seeding points in the space does not
guarantee that the lines will be uniformly distributed as
The need for a seeding strategy was already identified in
the early 90ies: for example Max et al. [MCG94] suggest to
visualize particles and streamlines only close to previously
computed surfaces. Similarly Löffelmann et al. [LDG98]
suggest to seed streamlines in the proximity of selected critical points, which are usually relevant areas of the flow.
Another group of techniques try instead to partition the
flow according to a specific clustering criteria, and then dis-
A. Brambilla et al. / Illustrative Flow Visualization
guarantees that the resulting placement reflects any particular flow aspect or that the visibility is effectively optimized.
Approaches exist to explicitly address the distribution
and the appearance of the streamlines in the final image: a
notable example for 2D flows is due to Jobard and Lefer
[JL97], who describe an approach to evenly place streamlines over the image with density specified by the user. In
2008 Li et al. [LHS08] suggest to compute a distance-based
similarity measure, derived from information theory, to determine if a streamline is redundant or if it actually conveys new relevant information. For 3D vector fields, Li and
Shen [LS07] propose a seeding strategy that takes into account image space information in order to avoid visual cluttering.
Figure 5: Streamtape visualization of the solar plume dataset
compared to traditional streamlines (image courtesy of Chen
et al. [CYY∗ 11] 2011
play one streamline (or a piece of it) for every cluster. Two
approaches have been proposed in 1999, based on two different ideas: Heckel et al. [HWHJ99] use a top-down clustering, which iteratively subdivides the domain according to
an error measure. In contrast, Telea and van Wijk [TVW99]
employ a bottom-up strategy, merging the two most similar
clusters at every step. The former has the advantage of showing more information in turbulent areas, but a large number
cluster is needed to effectively represent the flow. The latter,
in contrast, achieves good results with just a few clusters, but
the similarity function requires many parameters to be set.
Three interesting approaches have been recently proposed
that also take into account the communicative power of the
integral curves they visualize; all of them are based on the information theory concept of entropy, which quantify the expected value of information contained in a message. Besides
the different metrics adopted, these works share the idea
of seeding streamlines from areas with high entropy measures. Usually the resulting visualization can still be cluttered, so an additional pruning process is needed. In particular, [MCHM10] use a view-dependent approach similar to [LS07], while [LMSC11] evaluates also the image
space entropy obtained via Maximum Entropy Projection.
Figure 5 instead is obtained with the approach of Chen et
al. [CYY∗ 11], which partitions the high entropy streamlines
using a clustering technique and then visualizes only a few
curves per cluster using the so called Streamtapes.
A more advanced technique has been proposed two years
later by Garcke et al. [GPR∗ 01]: they use a continuous clustering based on the Cahn-Hilliard model, which describes
phase separation in binary alloys. The main idea is to minimize a specific energy function, that can be customized in order to control the clustering process; the resulting partitions
are nicely aligned with the flow and they can be visualized
using either deformed particles or oriented streamline segments. Griebel et al. [GPR∗ 04] instead define an anisotropic
diffusion tensor based on the flow direction, which, in turn,
induce a strong (parallel to flow) and weak (orthogonal to
flow) coupling between neighbour points. Once again the
clusters are displayed using oriented curved arrows aligned
with the streamlines. More recently Yu et al. [YWM07] propose a parallel approach for clustering unsteady vector fields
in 4D, allowing for a cluster-based visualization of pathlines.
All these clustering approaches have the appreciated property of being hierarchical, therefore the density of the generated integral lines can be easily controlled. However, they
have a major downside: even though the lines are usually
nicely distributed over the domain, clustering takes into account only local properties of the vector field, so there are no
Figure 6: Streamsurface of the ellipsoid dataset rendered
with normal-variation transparency, grid-like texture and silhouette enhancement (image courtesy of Hummel et al.
[HGH∗ 10] 2010
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A. Brambilla et al. / Illustrative Flow Visualization
Figure 7: Side-by-side view of a smoke ring extracted from the argon bubble dataset, rendered using different styles (saturation
and silhouettes) for each timestep (image courtesy of Hsu et al. [HMCM10] 2010
Springer Berlin Heidelberg).
Line placement is currently a very active research direction, but optimal visibility can be achieved in other ways as
well. For instance, Weinkauf et al. [WTS11] propose to remove cusps and intersections created when path- and streaklines are projected onto the viewing plane, therefore obtaining a clean and expressive visualization. Regarding integral
surfaces, already in 1997, Löffelmann et al. proposed the
stream arrow metaphor [LMG97] in order to emulate Abraham and Shaw illustrations (like the streamsurface in Figure 2b). More recently, two notable approaches explicitly
address visibility problems for streamsurfaces using different illustrative rendering techniques: Born et al. [BWF∗ 10]
suggest to use contour lines and halftoning to enhance the
overall shape perception. Flow direction on the surface is
depicted with oriented streamlines, while movable cuts and
slabs allows for an interactive exploration of the flow. In
contrast, the work of Hummel et al. [HGH∗ 10] proposes
two novel transparency techniques (angle-based and normalvariation) explicitly designed to expose hidden parts of the
surface. They also employ additional illustrative techniques,
i.e. adaptive stripe textures and silhouette enhancement: Figure 6 shows a streamsurface of a flow behind an ellipsoid
obtained using a grid-like texture, normal-variation transparency and emphasized contours.
4.3.3. A special case: temporal implosion
Temporal implosion is an illustrative technique aimed at depicting the temporal evolution of a certain system in a single,
static image. It is extensively used, for example, in comics
and photos (via post processing) to convey the motion of an
object, and, in the last few years, it has been successfully
employed to visualize the behaviour of dynamical systems.
4D raycasting algorithm which is able to render multiple volumes (corresponding to multiple timesteps) simultaneously.
They also employ an adapted version of the style transfer
functions [BG07] in order to vary the rendering style along
the temporal dimension. Figure 7 has been generated using
the approach by Hsu et al. [HMCM10]: in this case every
timestep is treated separately, so its visual appearance can
be finely tuned and even the final layout can be modified in
order to create either overlapped or side-by-side views.
Recently van Pelt et al. [vPGtHRV11], following the
guidelines in [JR05], propose to convey the motion of blood
using illustration techniques typical of comics and cartoons:
blood particles, represented by spheres, are deformed along
flow direction according to the velocity magnitude, while the
illustrative rendering of reversed pathline effectively depicts
particles trajectories.
4.4. Focus Emphasis
The techniques included in this category are all based on an
importance measure that clearly distinguishes the relevant
portions of the data from the less interesting ones. This concept is actually well-known in data analysis approaches, like
Interactive Visual Analysis (IVA) or Visual Analytics (VA),
to identify significant subsets of the data in usually multiple
linked views. In illustrative visualization the importance values are instead used to explicitly control one or more visual
In flow visualization, temporal implosion is well suited to
show the trajectory of features, like vortices or saddles: a first
approach was proposed in 2001 by Reinders et al. [RPS01],
who employ a prediction and verification method to track the
features over time, and visualize their past, current and predicted positions using 3D elliptical icons. They also detect
events like feature splitting or merging, and summarize the
evolution of the currently tracked features in a graph.
Even though temporal implosion essentially relies on the
tracking of a specific object, the basic idea can be applied
also to raw data: Balabanian et al. [BVMG08] developed a
c The Eurographics Association 2012.
Figure 8: Focus emphasis of swirling areas of the flow (imc
age courtesy of Weiskopf et al. [WSE07] 2007
A. Brambilla et al. / Illustrative Flow Visualization
properties: it is even possible to render parts of the dataset
with completely different techniques according to their importance values.
4.4.1. Raw data with importance values
It is a quite common practice to let the user define what
he deems relevant and what he does not. In the most simple case, the important area is limited to a small number of
isolated locations manually specified in spatio-temporal domain, while everything else is considered uninteresting. This
idea has been exploited, for example, by many texture-based
algorithms in order to simulate the classical experiment of
dye injection in a flow. Already in 1996, Shen et al. [SJM96]
proposed to use a grayscale 3D LIC to show the context
while the dye (the focus) is rendered with colors smeared
according to the velocity vectors. A similar approach was
adopted by Telea and van Wijk [TvW03] in 2003, but their
technique is based on 3D IBFV instead of LIC. One year
later, Weiskopf and Ertl [WE04] proposed another dye advection technique based on 3D IBFV, which is able to visualize even unsteady flow at interactive rates. Two more recent
approach are specifically aimed at making the appearence of
the dye more realistic: Weiskopf et al. [WBE05] suggest to
vary the intensity of the colors in order to explicitly represent the variation of the dye density caused by the convergence and divergence of the flow. Li et al. [LTH08], instead,
introduce a novel 2D dye advection algorithm which, applying concepts typically used in computational fluid dynamics,
is able to generate highly realistic results.
Figure 10: High transfer entropy regions are depicted with
full saturated colors, while context is completely desaturated
(image courtesy of Wang et al. [WYG∗ 11] 2011
Dye injection is justified by historical reasons and it has
indeed proven its usefulness over the years; however, in
a computerized environment, more advanced exploration
techniques can be developed. This is the case, for instance,
of the Chamaleon rendering framework [SLB04]: the focus is represented by the so called trace volume, which encodes particles trajectories and is visualized via volume ren-
dering; a specific texture is used to control the appearance
of the reuslts. The spatial locations included in the trace
volume can be interactively specified and, choosing the appropriate texture, many illustrative effects can be obtained,
like directional glyphs or tone shading. A curious exploration framework has been recently proposed by Isenberg
et al. [IEGC08], whose goal is maximizing user interactions
using a multitouch display: the 2D flow under investigation
can be displayed using a background texture and the user can
interactively place customizable animated glyphs in the area
of interests.
Figure 9: Illustrative deformation of flow in order to avoid
the occlusion of the focus region (image courtesy of Correa
et al. [CSC07] 2007
When analysing complex, multivariate phenomena like
flows, relevant portions of the data cannot be easily identified by their spatial locations alone, usually precise criteria based on one or more variables are needed. A significant work in this direction has been proposed by Hauser and
Mlejnek in 2003 [HM03]: they describe an IVA framework
where the user can select interesting areas in histograms or
scatterplots of the flow variables. Each point of the dataset
is therefore associated with a fuzzy importance value, the
degree of interest (DOI), which is used in the visualization
phase to modulate transparency or to define isosurfaces. A
fuzzy importance measure is adopted also in [WSE07] and
[FW08] to control different visualization parameters. The
proposed visualizations are based on 3D texture advection
and different shading and illumination schemes, and the importance values are directly mapped to appearance and transparency through a transfer function. In Figure 8, for example, swirling areas are emphasized using high opacity and a
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A. Brambilla et al. / Illustrative Flow Visualization
then visualized according to three different criteria: (1) context in front of the focus is suppressed to avoid occlusions;
(2) in the remaining context areas, only a few streamlines
are visualized; (3) the focus areas are rendered with dense
bundles of streamlines.
Figure 11: A streaksurface, in red, is seeded from the FTLE
ridge on the plane, while green arrows convey directional
information on timesurfaces (image courtesy of Ferstl et al.
[FBTW10] 2010
warm colors, while the context is more transparent and less
Figure 9 has been obtained with the approach of Correa
et al. [CSC07]: they employ a fuzzy importance function,
named Level of Desired Attention, and guarantee that the focus is never occluded deforming the context according to
one of the many templates provided. With the due exceptions [AH11], deformations are in general not well suited
for flows, since they alter the directional information, but in
this case only the context is modified, the relevant part of the
data is untouched and effectively emphasized.
All the focus emphasis techniques discussed up to now are
based on a user specified importance measure, but some attempts have been made to automatically identify significant
regions of the dataset. According to the concept of entropy
already introduced in section 4.3.1, Wang et al. [WYM08]
suggest to subdivide the dataset into blocks and evaluate the
amount of information contained in each block over time.
A clustering algorithm groups together blocks with similar
entropy evolutions and the resulting clusters can be then visualized in different ways. This approach has been recently
extended in [WYG∗ 11], adopting an importance function
based on transfer entropy, i.e. a measure of causal dependencies between variables; the normalized importance value
is then used to modulate saturation and opacity, producing
expressive visualizations like the one in Figure 10.
A second category is instead represented by those approaches that use the focus as the seeding area for the integral structures. Based on this idea, [HM03], already mentioned before, seeds streamlines in regions where the DOI
is maximal, while in [MTHG03] the focus can be either
used to increase streamlines density or to seed new streamlines. [KKKW05] follows a similar strategy, but particles are
seeded instead of streamlines, and, in a second phase, different types of particle-based visualizations can be generated,
like oriented glyphs, stream balls or stream ribbons.
Two notable approaches deal instead with the construction of integral surfaces: Schafhitzel et al. [STWE07] construct either stream- or pathsurfaces starting from a curve
selected by the user in the spatial domain; their algorithm is
based on a GPU implementation and runs at interactive rates.
On the other hand, Wiebel and Scheuermann [WS05] suggest to focus on a set of user selected seeding points, the so
called eyelets, and streaklines, pathline and pathsurfaces are
simultaneously computed. They also provide the user with
different guidelines for the selection of the eyelets, in order
to maximize the expressiveness of the resulting structures.
Recently, a more advanced exploration technique has been
proposed by Ferstl et al. [FBTW10] (see Figure 11): the user
first places a 2D plane (the focus) in the 3D spatial domain,
then FTLE values, i.e. a measure of particles’ divergence
over time, are computed on it. Ridges of the FTLE scalar
4.4.2. Focus+context approaches for integral structures
The concept of focus emphasis has been successfully applied
to integral structures as well. In particular, three main directions have been investigated, each one with different goals
and expected results. The first one is based on the simple assumption that the user can freely specify the focus directly
on the spatial domain, and integral structures in that area
have to be visually emphasized. For example, in the work
of Fuhrmann and Gröller [FG98] from 1998, the focus is
specified as a portion of the volume defined by either a 2D
(magic lens) or a 3D (magic box) selection. Streamlines are
c The Eurographics Association 2012.
Figure 12: Flow features tracked over time and visualized together with context information (image courtesy of Muelder
and Ma [MM09] 2009
A. Brambilla et al. / Illustrative Flow Visualization
Figure 13: Visual explanation using the Aniviz framework: visualization templates are arranged along the timeline to produce
an effective presentation of the dataset (image courtesy of Akiba et al. [AWM10] 2010
field are then detected, and the resulting curves are used to
seed streaksurfaces. Moreover, timesurfaces, rendered using
green arrows, are periodically released from the plane. For
more details on FTLE, the reader can refer to [Hal01].
the first in a long series of works on the illustrative depiction
of flow features.
4.5. Visual Explanation
The third and final category includes approaches that use
whole integral curves as the focus of the visualization. In
2010, two notable approaches based on this concept have
been presented: Jones and Ma [JM10] present a flow exploration framework that, among other functionality, allows the
user to select groups of streamlines which will be visualized in a focus+context fashion. In particular, occluding geometries are removed, and additional information, like the
distance from the focus curves, are depicted in the context.
Wei et al. instead [WWYM10] developed a sketch-based
interface for streamlines selection: the user first sketch the
shape of the streamlines he deems interesting, then, according to a similarity measure, the corresponding curves are
highlighted. This direction has not been heavily investigated
yet, but the current results seem very promising and we expect substantial developments in the near future.
4.4.3. Flow features
At this point it should be clear enough that the number of illustrative approaches that deal with flow features is meagre,
but at least one work can be identified that complies with
the focus emphasis principle. This technique has been proposed in 2009 by Muelder and Ma [MM09], and its main
focus is the interactive extraction and tracking of flow features. The details of their algorithm exceed the scope of this
manuscript, what really matters here is that, at the end of the
procedure, flow features are clearly segmented. As can be
seen in Figure 12, this segmentation can be used during the
volume rendering process to emphasize the features of interest while still providing the less relevant context information. Notice that many illustrative visualization techniques
can be easily integrated into volume rendering algorithms,
therefore it is our opinion that this approach would be just
Visual explanation approaches are a superset of Guided Visualization and Interactive Storytelling, and their goal is to
give an explicative visual description of the underlying phenomena. The challenge here is twofold: besides the usual visualization issues, it is also necessary to identify an appropriate set of objects, properties and relations that can lead to an
effective and concise explanation of the phenomenon of interest. A natural and straightforward way to define this piece
of semantic information is to apply one or more selection
criteria to the data according to spatial, temporal or attribute
values. This is the approach adopted by Aniviz [AWM10],
an animation framework designed to highlight different aspects of volume data. The user is presented with multiple
animation templates which can be freely arranged along a
timeline in order to build a visual presentation of the dataset.
The templates and the transitions between them can be controlled by a set of parameters, which can be used to finely
tune what aspects of the data has to be emphasized (see Figure 13). This framework currently deals with raw data only,
but extending it to integral structures or flow features should
be fairly easy.
A recent work by Pobitzer et al. [PTA∗ 11] suggests to
describe the flow using a scale-space approach: they decompose the vector field according to the level of transport energy present in the flow, so the user can choose to focus either on the main transport structures or on the smaller scale
turbulence. Only raw data is taken into account in the computations, but the derived vector fields can be further processed: this can be useful, for instance, to identify which
flow features have a greater transport energy.
Regarding particle integration and integral structures, an
interesting approach has been proposed by Bürger et al.
c The Eurographics Association 2012.
A. Brambilla et al. / Illustrative Flow Visualization
Figure 14: Flow depicted at different levels of detail (image
courtesy of Bürger et al. [BKKW08] 2008
[BKKW08] in 2008. Their work is based on two additional
functions defined on the flow domain: a customizable fuzzy
importance degree and a measure of the local coherence of
the vector field; different visualization techniques are then
employed according to these two parameters. The descriptive part is given mostly by the coherence measure, which in
fact affects the level of detail of the visualization: as can be
seen in Figure 14, where the local coherence is low, streamlines are used to convey the (turbulent) flow behavior. In contrast, in areas where the flow is more stable, oriented glyphs
are placed, and both their size and density are varied as the
coherence value increases. The importance function can be
used either to explore specific locations of the domain or to
emphasize particular aspects of the flow. Notice that the concept of “adaptive visualization”, which is nicely exploited in
this approach, is very effective in conveying different aspects
of the flow simultaneously, and we expect to see future work
based on it.
5. Final remarks and future expectations
We have reviewed and classified many illustrative flow visualization approaches, emphasizing their respective merits and discussing their downsides. The classification introduced at the beginning of Section 4 clearly highlights that
there is no approach that is universally better then the others, many aspects have to be taken into account in every
situation. In our opinion, the answers to “what flow representation do I want to refer to?” and “what visualization enhancement do I need?” are two excellent guidelines to make
a first choice, but further refinements are possible: for example, the personal preferences and habits of the final users
hold a certain relevance. Moreover, since the various algorithms have very different computational complexity, some
considerations have to be made regarding the available hardware and the size and structure of the datasets. It should not
come as a surprise that the best approach varies from case to
case and from user to user.
Over the last decade, illustrative flow visualization techniques have been proposed and applied in many different
contexts, and, looking back, interesting considerations can
be made:
c The Eurographics Association 2012.
• Perceptual effectiveness has been the first illustrative concept being applied to visualization in general. It has been
thoroughly investigated and many effective and useful algorithms have been proposed. Nowadays there is the feeling that these techniques alone are not effective enough,
so they are usually coupled with some higher visual abstraction approaches.
• Smart placement of integral curves were, and still are, one
of the most prominent research directions in the field, but
visibility enhancement for integral surfaces has been recently attracting a lot of attention as well.
• Temporal implosion has not been investigated too much,
probably because of its inherent technical complexity, but
many see a lot of potential in it, especially for the visualization of unsteady flows.
• Focus emphasis techniques are highly appreciated especially for flow exploration and analysis, and we expect
that in the near future any visualization framework will
implement similar functionality.
Visual explanation techniques and illustrative visualization of flow features are still somewhat unexplored, probably because of the same underlying problem: both these
categories rely on a semantic knowledge base of the phenomenon of interest, but our understanding of flows is still
limited. It is our opinion that, as new aspects of flow dynamics are discovered, research in both these areas will grow
In the near future we expect to see a constantly increasing
degree of interaction between the flow and the illustrative visualization branches: existing approaches typically consider
just the raw information encoded in the dataset, but usually
no knowledge about the physical properties of the underlying flow is considered. In an ideal setup, flow investigation
would become an iterative process with continuous interaction between the illustrative flow visualization expert and the
user: the former should initially provide a set of suitable visualization tools, the latter should use them for a preliminary
analysis of the dataset, producing feedback about the tools
and a set of initial findings. Both the feedback and the new
findings will be taken into account to improve the visualization tools, and the whole process will start anew.
Of course illustrative flow visualization cannot answer all
the open questions or solve all the current issues in flow analysis, but hopefully it will help to shed some light on this still
not well understood phenomenon.
The authors would like to thank the anonymous reviewers
for their valuable feedback.
This report has been worked out within the scope of the
SemSeg project and we acknowledge the financial support
of the Future and Emerging Technologies (FET) programme
within the Seventh Framework Programme for Research of
A. Brambilla et al. / Illustrative Flow Visualization
the European Commission, under FET-Open grant number
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Andrea Brambilla is a Ph.D. candidate at the Department
of Informatics, University of Bergen, Norway. He received
a M.Sc. (Laurea Specialistica) in Computer Science in 2009
from the University of Milano - Bicocca, Italy. After obtaining his degree, he spent one year as an external collaborator
at the same university, working on computer graphics and
A. Brambilla et al. / Illustrative Flow Visualization
computer animations. His current research interests include
flow visualization and illustrative rendering techniques.
Robert Carnecky is a graduate student at the ETH Zürich,
Switzerland. He received his masters in Computational Science and Engineering at the ETH in 2007. His research focuses on scientific and illustrative visualization.
Ronald Peikert received his diploma in mathematics in
1979 and his PhD in mathematics in 1985, both from ETH
Zurich. He is currently a titular professor in the computer
science department of ETH Zurich. His research interests include flow visualization, feature extraction techniques, and
industrial applications of visualization.
Ivan Viola is associate professor at University of Bergen,
and Scientific Adviser at Christian Michelsen Research
(CMR), Bergen, Norway. He received M.Sc. in 2002 and
Ph.D. in 2005 from Vienna University of Technology, Austria. His research is focused on application of illustrative visualization for communication of complex scientific data in
medicine and geo-sciences. Viola co-authored several scientific works published in international journals and conferences such as IEEE TVCG, IEEE Visualization, and EuroVis and acted as a reviewer and IPC member for conferences
in the field of computer graphics and visualization. He is
member of Eurographics, NorSIGD, IEEE Computer Society, VGTC, ACM SIGGRAPH.
Helwig Hauser is a professor in visualization at the University of Bergen, Norway ( He graduated in 1998 with a PhD degree from Vienna University of
Technology, where he also worked as an assistant professor
until 2000 ( Afterwards, he lead a research group on visualization at the VRVis Research Center
in Vienna, Austria, before he became the scientific director
of VRVis in 2003 ( His interests are visualization in general and interactive visual analysis, illustrative visualization, flow visualization, medical visualization,
and the combination of scientific and information visualization, in particular. He has rich experience with state of the
art reports as also documented by recent publications in the
respective Eurographics proceedings.
c The Eurographics Association 2012.
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