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where v
j
xyz
denotes the value of the jth
field at the spatial position xyz. The distance
value is 0 for two identical
fields, and increases proportional to the differences
between the compared
fields.
The *-dimensional points are then projected to points in a 2D space while trying
to maintain the computed pairwise distances (Eq.
4
) as much as possible. We have
selected Sammon
s mapping (Sammon
1969
) as a projection technique. It starts
with random point coordinates in the 2D space and then iteratively moves the points
to minimize the error given by the equation:
'
2
X
½d
ij
d
ij
N
1
P
i
\
j
d
i
hi
E ¼
ð
5
Þ
;
d
ij
i
\
j
where d
ij
are the Euclidean distances of projected 2D points in the 2-dimensional
space, and d
ij
are the distances between original points in the multidimensional
space.
Finally, the results of the projection are visualized as a scatterplot. By de
nition,
this scatterplot has no inherent axes (i.e. it is only unique up to rotation), while the
distances between the 2D points indicate how similar the respective
fields are
(Figs.
1
,
4
and
5
). Colors are used to indicate the types of the
fields (original,
derivative or similarity
fields).
4 Interactive Visual Analysis
The
field similarity plot described above helps the scientist to identify informative
fields. The plot serves as an interaction widget, where individual
fields can be
clicked at and investigated using linked views (selected
fields are highlighted by
increased point size).
The linked views are (1) slice-based volume visualizations for the spatial
investigation of
field value distributions (Figs.
2
a,
3
a and
6
a) and (2) 1D histograms
of the normalized
field value distribution within
its range (Figs.
2
b,
3
b and
6
b). In the individual views, we decided to avoid using
the typically default rainbow colormap because of its misleading perceptual prop-
erties (e.g. it introduces arti
field values for understanding the
cial sharp contrasts at the color transitions) (Borland
and Taylor
2007
; Rogowitz and Treinish
1998
; Silva et al.
2007
). The selected
black body radiance colormap represents data without such issues.
The slice-based visualization renders axis-aligned slices through the volumetric
dataset. The position and the orientation of the cutting plane, as well as the ori-
entation and scaling of the 3D view, can be changed interactively. Multiple slice-
based visualizations for different data
fields are coordinated: all of them use the
same view on the volume data as well as the same cutting plane.
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