Does someone passing in front of me invalidate my prayer, and if I must prevent it, how do I do that, and is it permissible for me to estimate an imaginary distance as a limit for passing in front of me?

The majority of jurists—from the Maliki, Hanafi, and Shafi'i schools, and it is also the view of the Hanbalis except concerning a woman, a black dog, and a donkey—are of the opinion that the passing of anything in front of a praying person does not invalidate the prayer. This is based on the saying of the Prophet, peace and blessings be upon him: "Nothing cuts off the prayer, so ward off [passers-by] as much as you can." As for compensating for a sutrah (barrier) by drawing a line in one's mind, this was not reported from the Prophet, peace and blessings be upon him, nor was it ever stated by any scholar. Rather, what has been reported is the permissibility of using a line drawn on the ground as a sutrah if one cannot find an actual barrier.