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Here are a few animated data visualization projects that have some relevance to this discussion, which you may want to explore further:
Many researchers begin playing with zooming and panning as basic operations in a visualization with Pad++, a zoomable architecture for laying out data in large spaces (Bederson and Hollan 1994).
Scatterdice (Elmqvist, Dragicevic, and Fekete 2008) explores a way to transition between scatterplots by rotating through the third dimension.
Visualizations of tree data structures include ConeTrees (Card, Robertson, and Mackinlay 1991), CandidTree (Lee et al. 2007), and Polyarchy (Robertson et al. 2002). Researchers have explored animation with treemaps by zooming (distorting) the treemap (Blanch and Lecolinet 2007) and moving through 3D space (Bladh, Carr, and Kljun 2005).