Graph Visualization For Geography - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 95

pixel in the graph visualization. This value is then used to map pixel colors to a
user-defined gradient color scale after the minimum and maximum values of the
overdraw have been computed. Lambert et al. ( 2010 ) introduce an “edge splatting”
technique that allows the viewer to perceive bundle density while preserving edge
colors. In a similar manner, the GraphSplatting technique introduced by Liere
and Leeuw ( 2003 ), a splat field is computed to encode continuous variations in
the density of the merged edges. To obtain the splat field, the first step is to
compute the number of edges crossing each pixel in the drawing. A GPU-based
method ( Holten & Wijk , 2009 ) is used to perform that task. Then, the splat field
is generated by convoluting the discrete density values (associated with each pixel)
with a Gaussian kernel. The larger the kernel radius and the standard deviation,
the more the splat field is smoothed. This splat field can be rendered on a screen
in a various ways. After computing the minimum and maximum values of the
splat field, one can perform a simple color mapping, for instance. To preserve edge
colors, Lambert et al. use a bump mapping technique. Bump mapping is a computer
graphics technique that allows a rendered surface to appear more realistic without
modifying its geometry. Bump mapping adds a per-pixel shading that makes the
surface appears bumpy, by changing the surface normals. The color and brightness
of each pixel are then altered with respect to these normals by using an illumination
algorithm. The final color of a pixel is computed from the light properties and a
color map. This color map can correspond to a splat field color mapping or to the
original edge colors. By mapping the splatting values to the heights, bundles with
high density edges appear taller than others and visually emerge from the layout.
Results of this rendering technique can be found in Fig. 6.11 .

6.5 Conclusion

In this chapter, we presented the main methods for the automatic drawing of
networks for geographic data visualization. Among these methods, one of the
most popular approaches is the force-directed method, which produces visually
pleasant and structurally significant results. In that method, nodes are considered as
particles and edges represent attractions between these particles. To overcome the
computational cost problem of such methods, fast algorithms have been designed to
make a trade-off between computation time and aesthetic criteria.
We also presented the compound graph visualization that displays an abstraction
of the network. This is achieved by first producing a partition of the nodes using a
clustering algorithm. Then, each cluster is collapsed into a single node to build the
abstraction. In the case of large and complex data, compound graph visualization
allows the reduction of visual clutter in the representation while preserving the
rendering speed and, therefore, supporting interactive exploration.
Finally, we reviewed the main flow map layout techniques. In this approach,
node positions must be preserved because they can provide information. The main
problem is that it thereby creates many edge crossings that clutter the representation.