Line Segment Intersection

In computational geometry, the line segment intersection problem supplies a list of line segments in the plane and asks whether any two of them intersect, or cross.

Naive algorithms examine each pair of segments, but for a high number of possibly intersecting segments this becomes increasingly inefficient since most pairs of segments are not close to one another in a typical input sequence.

The most common, more efficient way to solve this problem for a high number of segments is to use a sweep line algorithm, where we imagine a line sliding across the line segments and we track which line segments it intersects at each point in time using a dynamic data structure based on binary search trees. The Shamos–Hoey algorithm applies this principle to solve the line segment intersection detection problem, as stated above, of determining whether or not a set of line segments has an intersection; the Bentley–Ottmann algorithm works by the same principle to list all intersections in logarithmic time per intersection.