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The overriden function is public override void DrawDynamicLayer(esriDynamicDrawPhase DynamicDrawPhase, IDisplay Display, IDynamicDisplay dynamicDisplay)

What's the difference between dynamicDisplay and Display? They both have similar functions like "DrawPolygon" and "DrawText"

and then how about if I cast my map to an ActiveView and access ScreenDisplay, how are all of these display types different? How should I know which one to use?

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up vote 3 down vote accepted

Use the DynamicDisplay when you want to animation or do real-time tracking in a map. About dynamic display

See also About Dynamic Display in 10.0.

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