Distance from a point to a line segment in 3d (Python)

问题

I am looking for Python function that would compute distance from a point in 3D (x_0,y_0,z_0) to a line segment defined by its endpoints (x_1,y_1,z_1) and (x_2,y_2,z_2).

I have only found solution for 2D for this problem.

There are solutions to finding a distance from a point to a line in 3d, but not to a line segment, like here:

(picture taken from Calculate distance point to line segment with special cases)

回答1:

This answer is adapted from here: Calculate the euclidian distance between an array of points to a line segment in Python without for loop.

Function lineseg_dist returns the distance the distance from point p to line segment [a,b]. p, a and b are np.arrays.

import numpy as np

def lineseg_dist(p, a, b):

    # normalized tangent vector
    d = np.divide(b - a, np.linalg.norm(b - a))

    # signed parallel distance components
    s = np.dot(a - p, d)
    t = np.dot(p - b, d)

    # clamped parallel distance
    h = np.maximum.reduce([s, t, 0])

    # perpendicular distance component
    c = np.cross(p - a, d)

    return np.hypot(h, np.linalg.norm(c))

来源：https://stackoverflow.com/questions/56463412/distance-from-a-point-to-a-line-segment-in-3d-python