Running a script as sudo wihout terminal

The full path of the shell script including its name is in $0. You can extract the path by using ${0%/*}.

This doesn't solve other issues though:

Double-clicking the script will open Terminal which might confuse the user
sudo will only work as expected if the user is an Administrator (or if you changed /etc/sudoers but I assume you didn't)
They still need to enter their password in the Terminal window.

PS: The probably better way to approach this might be handling any access right issues from within the application.

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