Does cartodb implements a wms service?
If not, is there a way to contribute to the project to implement it?
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CartoDB does not implement a WMS service, but the team has talked about it internally.
Contributions are definitely welcome though, as CartoDB is open source. And doing this would be an awesome contribution, I think many others would appreciate it.
Probably the easiest way to implement it would be to integrate with http://mapproxy.org/ I believe CartoDB uses MapProxy the other way, to connect to existing WMS services to consume it.
But MapProxy could be backed by CartoDB Tiles, and then expose those through WMS (and WMTS, Super-overlays, etc).
For contributing, can make pull requests on github, or can get in touch at https://groups.google.com/forum/#!forum/cartodb
A blog posting titled CartoDB makes it easy to add the perfect basemap to your data visualization says (with my bolding):
using the CartoDB interface, you can easily add MapBox, XYZ, or WMS tiles by just dropping in a URL.
This indicates that CartoDB can consume a WMS.
However, I have not uncovered anything to suggest that CartoDB provide a WMS service. From Wikipedia I have learned that CartoDB includes:
a Maps API that acts as a dynamic tile service, rendering and serving new tiles based on client request
To me this suggests that it would be more likely to provide a WMTS than a WMS.
I recommend that you try to contact the CartoDB development team to see what opportunities there may be for you to contribute but from searching its home page just now I could not locate any obvious contact details for you to do that.