Constructing sensor barriers to detect intruders crossing a randomly-deployed sensor network is an important problem. Early results have shown how to construct sensor barriers to detect intruders moving along restricted crossing paths in rectangular areas. We present a complete solution to this problem for sensors that are distributed according to a Poisson point process. In particular, we present an efficient distributed algorithm to construct sensor barriers on long strip areas of irregular shape without any constraint on crossing paths. Our approach is as follows: We first show that in a rectangular area of width w and length with w = (log ), if the sensor density reaches a certain value, then there exist, with high probability, multiple disjoint sensor barriers across the entire length of the area such that intruders cannot cross the area undetected. On the other hand, if w = o(log ), then with high probability there is a crossing path not covered by any sensor regardless of the s...