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1. If visualization is the solution, what is the problem?
Present day scientific and engineering investigators are confronted
with research problems that depend on gaining insight into complex and
voluminous data. Previous publications - particularly [McCormick 871 -
have referred to
- firehoses of data, powerful computers and automatic
experiments, which produce data at a greater rate than the mind can
comprehend, resulting in
- warehouses of data where much is left
untouched, hiding unsuspected insights.
Scientific visualization is devoted to providing visual tools and
methods (and some non-visual ones) to help a scientific or engineering
investigator with analysing data.
Characterising the investigator's problem
There is no single visualization method or tool that can be applied
successfully to all problems of data analysis. Therefore if
visualization is intended to assist with demanding problems, it is
worthwhile beginning by characterising in what way the investigator's
problem is demanding:
- Multidimensional - at the extremes there may be 1 or many
independent variables. A common example is 3 where the independent
variables are spatial dimensions or 2 where the third dimension can be
ignored. Often in the past, the 3rd dimension has been ignored not
only because the computation has been difficult. but because
displaying the result has also been difficult.
- Multivariate - there may be 1 or many dependent
variables. Much hype from product brochures blurs the distinction
between the independent and dependent variables, resulting in
confusing claims such as "This system handles 4D data".
- Compound data - data could exist as a number of scalars at
each sampled point. However many problems respond better if the
internal structure of the data is respected. Thus data about flow and
gradients can be represented as vectors. Data aboul strain can be
represented as tensors. Electrical data can be represented as complex
numbers.
- Geometry - some systems assume that a Cartesian coordinate
space is being used. Many problems are defined on a curved space. Some
data can be defined on parameters such as (u,v) or (phi,theta), which
are themselves used to define a curve or surface. Earth based data is
a common example of this.
- How the data is structured - the simplest case is where
the data is sampled on a regular grid. However for experimental
reasons, data may only be accessible over a scattered grid, or for
computational reasons, unstructured data may be used. In the latter
case, the problem may be further complicated by the need to use
non-linear interpolation functions.
- Time-varying - there could be one or many timesteps - in
other words one of the independent variables may be time. This is not
necessarily the same as using time to present the result. A
time-varying phenomenon could be presented as multiple displays on one
frame and sometimes this is preferred if the investigator wishes to
make a controlled comparison. A static phenomenon can be presented as
a time sequence if there is too much complexity to be presented on one
frame - so a volume can be presented as an time-based sequence of
slices. Often though - and not surprisingly - time is the preferred
way to present a time-varying phenomenon and has been avoided by
investigators until now because of technological difficulties. Flow
phenomena such as turbulence, eddies and shifting boundaries are
perceived without conscious thought when presented using time.
- Application control - the simplest case is no control of the application, where data is postprocessed offline of the application. In the other extreme, the investigator needs to exercise full interactive control of the application, in response to events as they are visualized.
- Size of data set - many problems become complex, simply
through the sheer size of the data set being examined. Effective use
of present-day visualization systems often relies on being able to
make partly processed copies of the data at various stages. Large data
sets make this replication impossible. Vast data sets could be defined
as having such a size that they cannot be accomodated at all on the
investigator's local processing facilities and have their own special
problems.
For convenience, the characteristics are summarised in the following table.
Table - Characteristics of Investigator's Data
Characteristic | Simple | Hard |
Independent variables | 1 | Multidimensional |
Independent variables | 1 | Multivariate |
Data compounding | Scalars | Tensors |
Geometry | Cartesian | Curved |
Structure | Regular | Unstructured |
Time | Static phenomenon | Time-varying |
Application control | None - postprocess | Full interactive control steering |
| Small | Vast |
Visualization could be said to encompass problems of all types,
whether simple or hard.
In practice many traditional solutions (graphs, bar charts) exist
where the characteristics of a problem are simple in all respects or
where the problem is hard to a limited degree.
The purpose of much recent work in visualization is to investigate
the hard problems and bring them into the realm of the possible. In
practice the difficultics are interlinked. So, while it is possible to
display a field of scalars in 3D space by some suitable volume
rendering techniques, it is much harder if the data are vectors,
especially if there are many of them - it is easy to display them but
hard to perceive them.
As might be expected, there is a gradual adoption of solutions into
commercial systems.
Examples
Some examples may be useful at this point.
- a simple case - temperature distribution across a
flat surface, a single scalar variable defined in 2D
- simple 2Dflow problems - in the simple case, the data
exists as a field of veceors at regularly spaced positions in 2D space
- more complex 3D flow problems - the data is defined in 3D,
an unstructured grid has been used for computational reasons, the flow
is time-varying. (these examples are not intended to imply that 2D
problems always have a simple structure or that 3D problems are always
more complex).
- Multiple independent variables - chemical processes are a
source of problems, that are hard in most characteristics. The study
may involve studying the progress of a chemical reaction at various
points in a mixture at various times, depending on several variables,
such as pressure, temperature and initial fractions of the constituent
substances. In addition flow rates and the use of unstructured data
may be involved. In its full complexity, such a problem is still
extremely hard to be visualized.
For convenience, these examples are summarised.
Table - Examples
Characteristic | Temperature | Simple 2D flow | Complex 3D flow | Chemical process |
| | | | |
Independent variables | 2 | 2 | 3 | many |
Dependent variables | 1 | 1 | 1 | many |
Data compounding | scalar | vector | vector | vector |
Geometry | Cartesian | Cartesian | Cartesian | Cartesian |
Structure | regular | regular | unstructured | unstructured |
Time | static | static | time-varying | time-varying |
Some characteristics have not been presented in the table. For
instance the data set size can be small or large in any of the
problems just described.
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