"Distorted graphic" maps do exist in geovisualization. They are called
graduated symbol maps. The size of symbol is based on a certain attribute.
For example, larger the value(e.g. distance/travel time), the bigger the
circle. Graduated symbol maps are quite good in giving a perspective view of
the variations.
However, in case you want to make all-point to all-point map, the only
possible way I could think of is to make an "interactive map", which
involves some form of brushing effect. In other words, as you move your
mouse over a place, you would see a graduated symbol map according to that
place as an origin but if you move your mouse to another, you would see a
new map based on the new place as the origin. Its fairly easy to make such a
map in high level scripting languages such as Tcl/Tk that allow this type of
dynamic mapping.
Sanjay.
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