ANGULAR TREEMAPS - Information Visualisation: Techniques, Usability and Evaluation - page 86

to optimize rectangle aspect ratios of squares. Squarified Treemaps follow
the aspect ratio rule, and generate roughly a square layout [12]. Qualified
layouts were developed based on three assumptions: 1) The border of
nodes is reduced, as squares minimize rectangular perimeter; 2) Squares
are easier to select with a mouse cursor; 3) Similar aspect ratios closing to
one, ease area comparisons. The first and second assertions are both
supported by theoretical and empirical evidence (Fitts' law). However, the
algorithm is built on the aspect ratio aesthetics rule, which was not fully
studied in empirical perception of visualizations. The empirical perception
results [14] showed that square aspect ratios are not optimal for area
comparisons, which did not support the third assumption. Furthermore, the
other aspects of graph visualization were not taken into account by this
algorithm.
The layout algorithm of Cushion Treemaps is similar to standard
treemaps, but this technique uses intuitive shading to provide better
readability in the hierarchical structure. To maintain the orientation of
hierarchy, Ordered and Quantum Treemaps strengthen the visualization of
the structural hierarchy by preserving the order of the underlying data [13].
Although these further developments of treemap layouts significantly
improve readability, some algorithms can be too complicated to maintain
stability over time in the display of dynamically changing data.
Later developments, such as Space-Optimized Tree [15], Voronoi
Treemaps [16], Generalized Treemaps [17], and the work of Onak and
Sidiropoulos [18] have extended the implementation of treemaps to
polygonal partitioning techniques. Nguyen and Huang in 2003 created a
new tree map concept which starts partitioning from the centre of an area
and provides 360 degree freedom to divide sub-areas [15]. The new
partitioning algorithm generates polygon-shaped nodes other than
rectangles. The Space-Optimized Tree takes a different approach,
combining connection with enclosure visualization. Balzer and Deussen
proposed a polygonal treemap, which relaxes rectangular constraints by
using centroid Voronoi tessellations [19]. This method is widely-used for
energy minimizations in many application domains, for example data
compression, image processing, and resource planning etc. [20]. Similarly,
the circular partition approach proposed by Onak and Sidiropoulos [18]
also works on constructed polygonal structures and has achieved more
consistent aspect ratio results.
Rather than other complicated partitioning algorithms, new techniques
follow the rectangular treemap paradigm. Those algorithms mentioned
previously are either too difficult to implement in domain applications or