A computer implemented method includes obtaining a navigation mesh representing a multi-level structure. The navigation mesh has multiple polygons defined by vertices and segments extending between vertices. Some of the polygons overlap. A first status data structure is created in response to a sweep line first encountering a first vertex corresponding to a first contiguous interval of polygons, wherein the first data structure includes at least two segments having the vertex in common. A second status data structure is created in response to the sweep line encountering a second vertex having two different segments in common corresponding to a second contiguous interval of polygons. The method continues to sweep the mesh with the sweep line while keeping the first and second statuses isolated for each contiguous interval of polygons.