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I am pondering the possibility of somehow reprojecting tiles for display in my Flex application using Pixel Bender or something equivalent. The tile cache in question here is not owned/maintained by me, so I have no control over its output. I know I could use ArcGISDynamicMapServiceLayer to reproject to the desired coordinate system, but that will be very slow.

Hopefully the following use case explains the need to do so: I have a Flex app that is using ESRI ArcGIS Online basemaps in the standard Web Mercator projection. I use a service that returns polygons around and over the polar regions. Displaying in the Web Mercator projection looks like crap.

So, I guess my questions are: 1. Does anyone know of any good examples/tutorials...etc showing how this can be done? 2. Will this overwhelm the processing power of the client browser?

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While possible, I think you would be better off using a basemap that supports the polar regions. Either an "un-projected geographic" that at least cover the poles (as supposed to web mercator). Or one projection focused on the north pole and another on the south pole.

Some example "un-projected" services are:

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