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.
Famous quotes containing the words line and/or intersection:
“A line will take us hours maybe;
Yet if it does not seem a moment’s thought,
Our stitching and unstitching has been naught.”
—William Butler Yeats (1865–1939)
“You can always tell a Midwestern couple in Europe because they will be standing in the middle of a busy intersection looking at a wind-blown map and arguing over which way is west. European cities, with their wandering streets and undisciplined alleys, drive Midwesterners practically insane.”
—Bill Bryson (b. 1951)