I asked this question on RaspberryPi Stack Exchange site, and @hildred had a beautiful solution for this:
Write these few lines to etc/sudoers
*:
Defaults env_reset
Defaults secure_path="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin"
Defaults env_keep += "DISPLAY"
Defaults env_keep += "XAUTHORITY"
And these few lines to ~/.bashrc
:
if [ -z "$XAUTHORITY" ]; then
if [ -e $HOME/.Xauthority ]; then
export XAUTHORITY=$HOME/.Xauthority;
fi;
fi
**On a Raspbian this will be etc/sudoers.d/README
for example*