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as a “spring force analogy.” Informally, we may intuitively picture each
data image in RadViz as being tethered to multiple springs, one for each
dimension, each of these springs attached to one of the dimensional
anchors. These springs then can be thought to “pull” the data image
towards the circumference of the circle. Fig. 13.2 illustrates this.
In RadViz the spring constants vary according to the data records'
coordinate values and thus create a characteristic “pull” towards certain
dimensions. To rigorously formulate the mapping, as done by Daniels
et
al.
[1], we start with the stretching forces (
F
) of
d
springs under Hooke's
law. At equilibrium we have:
&
&
d
1
d
1
¦
¦
(1)
F
0
vS
(
x
)
j
j
j
j
0
j
0
for
k
some spring constant and
x
is the stretched distance.
The stretched distance is the distance from the dimensional anchor to a
point in the two-dimensional image space. We substitute for
k
the data
record's value for the
j
-th dimension
where
F
kx
j
v
. For
x
we substitute the distance
&
between the dimensional anchor
S
on the unit circle and the data record's
j
image
x
and then solve for
x
&
.
&
d
1
¦
Sv
jj
&
j
0
x
(2)
d
1
¦
v
j
j
0
In two-dimensional RadViz we then have:
d
1
d
1
¦
¦
cos(
T
)
v
sin(
T
)
v
j
j
j
j
(3)
j
0
j
0
x
x
1
2
d
1
d
1
¦
¦
v
v
j
j
j
0
j
0
&
is decomposed into its components for the
x
and
x
positions of the dimensional anchor (respectively, in polar
coordinates, cos(
In the above expressions
S
j
T and sin(
)
T ). These expressions may be generalised
)
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