Warning, within this answer, I only consider IPv4 (I believe that may be adapted to IPv6 with a few efforts)
Exactly what is a local interface exactly? What can be an Ip of the local interface?
It’s the Ip of the computer, in your LAN (on large amount of computers, something similar to 192.168.x.y).
Observe that for those who have several network interface cards (NIC), let us say one ethernet card, one wireless card, they ought to have differents adresses.