I want to write an extension that does the opposite of the "focus-follows mouse" setting in GNOME Shell: I want to make my pointer move to the center of the currently focused window.
Can this be done in a GNOME Shell extension? I see some GNOME code that wraps xfixes cursor, but I can't find any references to programmatic pointer updates in either the core Javascript or any existing extensions. (Am I just bad at Google?)
Valid answers include (1) example code that does it or (2) citation of a canonical source that says it can't be done.