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Thumbnail generation is up to the developer of the file system provider.
In case you don't want to develop your own thumbnail generation procedure, you can use a service like http://rethumb.com/ to create a thumbnail URL. For other options, see this Google search.
thumbnailfield is optional, so if you don't want a thumbnail for your file, do not pass the field and BEE will show you a generic icon based on the mime type you passed.
The thumbnail image must be contained in a 200px by 200px virtual square (see pictures below).