Information Technology Reference
In-Depth Information
y
The widths of leaf rectangles are equalized.
y
The height of a leaf rectangle is proportional to the weight of a leaf
node.
y
The filling rate and aspect ratio are as close to 1 as possible.
Here, the filling rate is the sum of the areas of all leaf rectangles
divided by the area of the whole Treemap. The aspect ratio is the length of
the short side of the rectangle divided by the length of the long side of the
rectangle. These are formulated as follows.
Let
T
be a rooted tree in which each root is expressed by
r
and a set of
leaf nodes is
L
. The area of node
l
is expressed by
a
(
l
)
. The width of a
rectangle is
w
(
l
)
, and the height of a rectangle is
h
(
l
)
.
The filling rate
f
is given by equation (1). The output is a positive number
less than or equal to 1.
1
f
a
(
l
)
a
(
r
)
l
L
(1)
The aspect ratio
g
(
l
)
of node
l
is expressed
b
y equation (2), a
nd
the
average aspect ratio of all leaf rectangles is
g
. Both
g
(
l
)
and
g
are
positive numbers less than or equal to 1.
§
·
h
(
l
)
w
(
l
)
g
(
l
)
min
¨
,
¸
w
(
l
)
h
(
l
)
©
¹
(2)
1
g
g
(
l
)
L
l
L
(3)
To balance the average filling rate and the aspect ratio, we aim to
increase
s
, defin
e
d in equation (4). Here,
w
1
and
w
2
represent the weights
applied to
f
and
g
, respectively. It is possible to adjust the balance of the
filling rate and aspect ratio by changing
w
1
and
w
2
.
s
w
f
w
g
(4)
1
2
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