[LinaLauneBaer]

You could infer the heading by "simply" telling the user:

"Move in the way you look for about 50 meters."

If you walk a straight line and the Laptop knows where it is at any given time it can infer the heading.

[ryannevius]

A compass isn't a heading indicator though...it's an orientation indicator.

[LinaLauneBaer]

If you have the heading and a few locations then you can also infer where north/south/east/west is. Or am I wrong?

[moron4hire]

If it's based on GPS, you could get a rough idea of where north was for the user, on average, while they were moving. It would be very static and wouldn't lend well to this sort of interface.

If all you have is WiFi- or cell-tower-based location, then you're not going to be able to get enough precision to make the value meaningful.