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I'm working with the ArcGIS Flex API. For example, ArcGISDynamicMapLayers do reproject their data in order to make it in the same projection as the map. Do FeatureLayers have the same behaviour?

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Just a small clarification: The ArcGISDynamicMapLayers are not projected in the client's Flash player. The Images themselves are requested in the appropriate projection. It is ArcGIS server which does the reprojection. –  Devdatta Tengshe May 1 '13 at 6:49
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Here's an article I wrote about this. Might be helpful... particularly the performance considerations for mixed spatial references... spatialexception.org/posts/arcgis-server-spatial-reference-faqs –  awesomo May 1 '13 at 17:21
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The answer is Yes.

Have a look at this sample: Generalized Data.

If you have a look at the Original Services, the Feature service is wkid:4267, while the map and the tiled map service are in wkid:3857/102100.

If you have a look at the service call using Firebug, you will see that the data is requested in wkid 102100:

enter image description here

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Ok. But it seems that the reprojection is not correctly made in the case of the feature service I'm using ?! I have a map projected in wkid=102100. A feature service calls some data projected in wkid=2154. The data from the feature service doesn't appear exactly where it should appear. It's moved by ~20 meters. I made some research and the answer may be that ArcGIS needs the "grid of correction" between the projections Web Mercator and Lambert93. Is that the answer? If yes, how can I do it? –  yo_haha May 1 '13 at 21:16
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This is because wkid=2154 is in a different datum. When you try to project from one datum to another, you need to use a transformation. ArcGIS server by default, uses the default transformation, which might not be the best for your Area. AFAIK, there is no way to ask ArcGIS server to use a particular datum transformation. Your best bet is to publish the original service in WGS84 datum, so as to get proper projection. –  Devdatta Tengshe May 2 '13 at 4:34
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If a default transformation is known. In the case of AGD66/WGS94 or AGD66/GDA94 unless a transformation is supplied the features will be 200m (approx) displaced. I'm sure more cases like this exist, this is just one I've come across. It is always best to keep your features in the same projection if possible and datum if not; the performance cost for project-on-the-fly is less than it used to be but it could still 'cost' in the views-per-second. –  Michael Miles-Stimson Oct 17 '13 at 2:57
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