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The service provider set up the GetCapabilities response for the WMS service. This defines which projections are supported by the WMS service and these are also the projections that can be requested.

I am wondering about the resources that are used when a large set of projections is made available.

  1. I guess the map is stored with one projections and the GIS software on the server knows the formulas to re-project the data ?
  2. But when is the image re-projected exactly in the process ?
  3. And does this have any influence on performances and caching ?
  4. What is the influence of the number of available projections on performances?

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I've never looked at QGISserver but for GeoServer and MapServer the following:

  1. Yes.
  2. Usually when it is rendered to the image being returned.
  3. Each projection will usually be cached separately. You will note most caches don't offer so many projections. There is of course a small performance hit with any reprojection.
  4. Ease of coding, By default GeoServer for instance lists all possible projections even if they make no sense for that particular data set but can be modified to show only those the provider wants to offer. MapServer only lists the ones that the user has specified for the map layer (or file).
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