feat: add Segment Intersection algorithm

geometry/segment_intersection.py

@@ -0,0 +1,112 @@
+"""
+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)