The main idea of the Bentley–Ottmann algorithm is to use a sweep line approach, in which a vertical line L moves from left to right (or, e.g., from top to bottom) across the plane, intersecting the input line segments in sequence as it moves. In the description of the algorithm in , the sweep line is horizontal and moves vertically; this change entails swapping the use of x- and y-coordinates consistently throughout the algorithm, but is not otherwise of great significance for the description or analysis of the algorithm. The algorithm is described most easily in its general position, meaning:
