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properties, navigation features, and a case study. Fig. 5.1 demonstrates that
Angular Treemaps can employ an angular polygonal algorithm with
multiple partition angles, to emphasis data structure. When the level of
visualization goes deeper, the rotation angle decreases, which creates a
sense of levels changing for structure tracking.
Basic properties
In a tree
T
rooted
r
, let
(
P
,
Q
)
be a directed edge in
T
. If
T
contains vertex Q,
then the sub-tree
T (
Q
)
rooted at Q is the sub-graph induced by all vertices
on paths originating fromQ. If
v
i
has sub vertices, then
v
i
=
{v
i,1
,…,v
i,2
,…,v
i,n
}
; if
v
i
has no sub-vertices, then
v
i
is called a leaf vertex.
T
is transferred into treemaps as a constrained polygonal area. Each
v
i
is
presented as a bounded polygon. Let
P
be a constrained polygon, which
contains sub-polygons, i.e.
P = {P(v
1
),…, P(v
i
),…, P(v
n
)}
. The area of each
polygon
P (v
i
)
is based on the weight
w(v
i
)
of vertex
v
i
, i.e.
,
where
a
is a constant representing the proportional ratio between the total
display size and the total weight of vertices. In the implementation, the
weight of a vertex
w (v
i
)
can be defined by a specific property of the
vertices, such as file size in the visualization of file systems (see Fig. 5.9).
For the illustrations in this section, it is simply calculated proportionally
using the total of vertices contained in
Sub-hierarchie
s
if a vertex weight
is not specified.
Area
(
P
(
v
))
a
u
w
(
v
)
i
i
Weighted angular Treemaps tessellation
In the geometric space,
R
2
represents a two-dimensional plane in
Euclidean geometry, and
S
2
represents a subset of Euclidean space.
R
2
is
compact if and only if it is closed and bounded. Angular tessellation
maximises an m-dimensional space
S
2
for partitioning, without generating
holes or overlapping. For root
r
, the local region
P(r) is defined
as the
entire polygonal container. The partitioning of a sub-tree
T(v
i
)
is restricted
within the area of
P(v
i
)
. A drawing of polygon
P(v
i
)
rooted at
v
i
is
calculated based on the properties of
v
i
and its local area. A series of side
vertices {
s
i,1,…,
s
i,i,…,
s
i,m
}
is bounded by a polygon
P(v
i
)
in the coordinates
(x
1
,y
1
),…,(x
i
,y
i
),…, (x
m
,y
m
).
Unlike a point-based rendering paradigm [22], we still follow the
polygonal partitioning approach in the algorithm. The tessellation
produces nested polygons whose sizes are proportional to the weight of
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