Segment databases store N non-crossing but possibly touching segments in secondary storage. Efficient data structures have been proposed to determine all segments intersecting a vertical line (stabbing queries). In this paper, we consider a more general type of query for segment databases, determining intersections with respect to a generalized segment (a line, a ray, a segment) with a fixed angular coefficient. We propose two solutions to solve this problem. The first solution has optimal O(N/B) space complexity, where N is the database size and B is the page size, but the query time is far from optimal. The second solution requires O(N/B log₂ B) space, the query time is O(log_B N/B(log_B N/B+log₂ B+IL ^* (B))+T/B), which is very close to the optimal, and insertion amortized time is O(log_B N/B+log₂ B+1/Blog² _B N/B), where T is the size of the query result, and IL ^* (B) is a small constant, representing the number of times we must repeatedly apply the log^* function to B before the result becomes ≤ 2.