EDGE-EQUALIZED TREEMAPS - Information Visualisation: Techniques, Usability and Evaluation - page 117

5 Determination of the layout
If we equalize the widths of the rectangles in each level of the hierarchy,
the top-down division of space can be used, as in many other variations of
the Treemap. However, one of our constraints states that we must equalize
the widths of all leaf nodes, regardless of the level. In addition, we only
wish to equalize the widths of leaf nodes; we do not want to equalize the
widths of branch nodes. Therefore, we consider the top-down partitioning
of space to be unsuited to the achievement of our goal.
5.1 Rough flow of the process
We examine bottom-up methods of positioning the rectangles, as described
in the following. First, we prepare rectangles corresponding to leaf nodes
with equal widths. The height of the rectangle is proportional to the weight
of the leaf node. When the rectangles of all child nodes have been
determined, we place them into as narrow a rectangular area as possible.
We repeat this process bottom-up, from the leaf nodes to the root node.
Using this method, we cannot know in advance the width and height of
the rectangles. Therefore, after the rectangle corresponding to the root
node is determined, we adjust the horizontal and vertical scale to fit the
drawing area.
5.2 Flow of the process including trial and error and evaluation
In the process described in Section 5.1, there are two degrees of freedom.
(1) How do we determine the height of the rectangle corresponding to
the leaf node of a certain width?
(2) How do we fit child nodes into the rectangular area of each branch
node?
In fact, (1) does not influence the resulting layout by adjusting the
scale to fit the drawing area. We want to find a good layout based on the
aesthetic criteria that we set previously (aspect ratio and filling rate).
However, based directly on the aesthetic criteria, it is difficult to determine
the rectangle into which we should place the child rectangles. There are
two reasons behind this statement. If the rectangle of the root node is not
determined, we cannot calculate the filling rate. In addition, if the scale of
the Treemap is not adjusted to the drawing area, we cannot evaluate the
aspect ratio. Because of this, we parameterize the filling of the rectangle