Bad Advice

So, if being nice and ignoring them do not work, what does? You scope them. Scoping is not glaring or sneering, which will antagonize. Scoping is a look that says, "I see you. I know your game and I can handle it." Then you look away. If you look down to break eye contact, you lose. Slide your eyes sideways and scope the rest of the room.

After you scope the antagonist and decide that he or she does not look that bad, then either leave or hang around and keep him or her in your peripheral vision. Watch without looking. Martial artists call it "looking at nothing and to see everything." By using a soft focus, you can increase your peripheral (sideways) vision up to about 200 degrees. In the movie Little Big Man, while Dustin Hoffman's sister is teaching him to be a gunfighter she tells him to make snake eyes. This is a way to soft focus and gain peripheral acuity because peripheral vision processes movement quickly. 

If the antagonist leaves just as you are getting up to leave, either wait until you are sure he or she is gone or leave by another exit or be prepared when leaving. Acting unaware may bring an attack and paying too much attention may draw too much attention you.