segment_intersection.py

"""
Given two line segments, determine whether they intersect.

This is based on the algorithm described in Introduction to Algorithms
(CLRS), Chapter 33.

Reference:
 - https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
 - https://en.wikipedia.org/wiki/Orientation_(geometry)
"""

from __future__ import annotations

from typing import NamedTuple


class Point(NamedTuple):
 """A point in 2D space.

 >>> Point(0, 0)
 Point(x=0, y=0)
 >>> Point(1, -3)
 Point(x=1, y=-3)
 """

 x: float
 y: float


def direction(pivot: Point, target: Point, query: Point) -> float:
 """Return the cross product of vectors (pivot->query) and (pivot->target).

 The sign of the result encodes the orientation of the ordered triple
 (pivot, target, query):
 - Negative -> counter-clockwise (left turn)
 - Positive -> clockwise (right turn)
 - Zero -> collinear

 >>> direction(Point(0, 0), Point(1, 0), Point(0, 1))
 -1
 >>> direction(Point(0, 0), Point(0, 1), Point(1, 0))
 1
 >>> direction(Point(0, 0), Point(1, 1), Point(2, 2))
 0
 """
 return (query.x - pivot.x) * (target.y - pivot.y) - (target.x - pivot.x) * (
 query.y - pivot.y
 )


def on_segment(seg_start: Point, seg_end: Point, point: Point) -> bool:
 """Check whether *point*, known to be collinear with the segment, lies on it.

 >>> on_segment(Point(0, 0), Point(4, 4), Point(2, 2))
 True
 >>> on_segment(Point(0, 0), Point(4, 4), Point(5, 5))
 False
 >>> on_segment(Point(0, 0), Point(4, 0), Point(2, 0))
 True
 """
 return min(seg_start.x, seg_end.x) <= point.x <= max(
 seg_start.x, seg_end.x
 ) and min(seg_start.y, seg_end.y) <= point.y <= max(seg_start.y, seg_end.y)


def segments_intersect(p1: Point, p2: Point, p3: Point, p4: Point) -> bool:
 """Return True if line segment p1p2 intersects line segment p3p4.

 Uses the CLRS cross-product / orientation method. Handles both the
 general case (proper crossing) and degenerate cases where one endpoint
 lies exactly on the other segment.

 >>> segments_intersect(Point(0, 0), Point(2, 2), Point(0, 2), Point(2, 0))
 True
 >>> segments_intersect(Point(0, 0), Point(2, 2), Point(1, 1), Point(3, 3))
 True
 >>> segments_intersect(Point(0, 0), Point(1, 0), Point(2, 0), Point(3, 0))
 False
 >>> segments_intersect(Point(0, 0), Point(1, 1), Point(1, 0), Point(2, 1))
 False
 >>> segments_intersect(Point(0, 0), Point(1, 1), Point(0, 1), Point(0, 2))
 False
 >>> segments_intersect(Point(0, 0), Point(1, 0), Point(1, 0), Point(2, 0))
 True
 """
 d1 = direction(p3, p4, p1)
 d2 = direction(p3, p4, p2)
 d3 = direction(p1, p2, p3)
 d4 = direction(p1, p2, p4)

 if ((d1 < 0 < d2) or (d2 < 0 < d1)) and ((d3 < 0 < d4) or (d4 < 0 < d3)):
 return True

 if d1 == 0 and on_segment(p3, p4, p1):
 return True
 if d2 == 0 and on_segment(p3, p4, p2):
 return True
 if d3 == 0 and on_segment(p1, p2, p3):
 return True
 return d4 == 0 and on_segment(p1, p2, p4)


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 print("Enter four points as 'x y' pairs (one per line):")
 points = [Point(*map(float, input().split())) for _ in range(4)]
 p1, p2, p3, p4 = points
 result = segments_intersect(p1, p2, p3, p4)
 print(1 if result else 0)