Here are a few examples of transmogrifiers in a variety of scenarios.
Please be aware that this is still under construction.
Scenario: Using transmogrifiers to straighten or compare length
An example of using transmogrifiers to compare the length of rivers (modelled after the Hanging Rivers infographic recently mentioned by Tufte in Envisioning Information).
Straightening a path to create a route map.
Scenario: Transmogrifiers for detail + context
A simple focus+context style lens created by drawing a triangle.
A transmogrifier used to create a Melange style lens.
Scenario: Swapping visualizations between polar and rectilinear coordinates
Transmogrifying a rose pie chart to a bar chart and then back to a rose pie (with the gray entries removed).
Transmogrifying a standard parallel coordinates vis into a circular representation
Transmogrifying a sunburst tree (left) to an icicle plot (right).
Transmogrifying a radial tree to a cladogram
. . . more to come.