A system that facilitates a geofencing operation is disclosed. The system obtains polygons that define a set of geographic regions. Then, the system projects rays from endpoints of the line segments that define the polygons onto a reference line to form intersection points. For each interval between pairs of consecutive intersection points on the reference line, the system keeps track of open line segments that project onto the interval. For each data point in a set of data points, the system identifies a relevant interval on the reference line that the data point projects onto, and performs a crossing number operation to identify polygons that the data point falls into, and the system increments a count for each polygon that the data point falls into. Finally, the system performs a geofencing operation for the location-aware device based on the identified polygons that the data point falls into.