python 二维点与由起点和终点指定的线段之间的最短距离。

Posted 2021-05-09

"""
Shortest distance between a point and a line segment (using 2D-vectors)
=======================================================================
Ported to Python from javascript solution by @Grumdrig at http://bit.ly/1RW6etG
"""

from math import hypot
from collections import namedtuple

Point = namedtuple('Point', ['x', 'y'])


def distance(point1, point2):
    """
    calculate distance between two 2-dimensional points
    ---------------------------------------------------
    :param point1: Point(float, float)
    :param point2: Point(float, float)

    >>> distance(Point(1, 0), Point(0, 0))
    1.0
    >>> distance(Point(-30, 15), Point(20, 10))
    50.24937810560445
    """
    return hypot(point2.x - point1.x, point2.y - point1.y)


def dist_to_segment(point, start, end):
    """
    Calculate shortest distance between 2-dimensional point and line segment
    ------------------------------------------------------------------------
    :param point: Point(float, float) - point
    :param start: Point(float, float) - start of line
    :param end: Point(float, float) - end of line

    >>> dist_to_segment(Point(1, 0), Point(0, 0), Point(1, 1))
    0.7071067811865475
    >>> dist_to_segment(Point(5, 4), Point(0, 0), Point(20, 10))
    1.3416407864998738
    >>> dist_to_segment(Point(30, 15), Point(0, 0), Point(20, 10))
    11.180339887498949
    >>> dist_to_segment(Point(-30, 15), Point(0, 0), Point(20, 10))
    33.54101966249685
    >>> dist_to_segment(Point(5, 1), Point(0, 0), Point(10, 0))
    1.0
    >>> dist_to_segment(Point(1, 5), Point(0, 0), Point(0, 10))
    1.0
    """
    length = distance(start, end)
    if length == 0:
        return distance(point, start)
    pct = ((point.x - start.x) * (end.x - start.x) +
           (point.y - start.y) * (end.y - start.y)) / length ** 2
    if pct < 0:
        return distance(point, start)
    if pct > 1:
        return distance(point, end)
    return distance(point, Point(start.x + (end.x - start.x) * pct,
                                 start.y + (end.y - start.y) * pct))


if __name__ == '__main__':
    import doctest
    doctest.testmod()