2D version for finding the shortest distance between a point and line segments. Based on https://stackoverflow.com/a/51240898 and http://www.fundza.com/vectors/point2line/index.html.

point_to_line.py

import math


def dot(v, w):
    x, y = v
    X, Y = w
    return x * X + y * Y


def length(v):
    x, y = v
    return math.sqrt(x * x + y * y)


def vector(b, e):
    x, y = b
    X, Y = e
    return X - x, Y - y


def unit(v):
    x, y = v
    mag = length(v)
    return x / mag, y / mag


def distance(p0, p1):
    return length(vector(p0, p1))


def scale(v, sc):
    x, y = v
    return x * sc, y * sc


def add(v, w):
    x, y = v
    X, Y = w
    return x + X, y + Y


def pnt2line(pnt, start, end):
    line_vec = vector(start, end)
    pnt_vec = vector(start, pnt)
    line_len = length(line_vec)
    line_unit_vec = unit(line_vec)
    pnt_vec_scaled = scale(pnt_vec, 1.0 / line_len)
    t = dot(line_unit_vec, pnt_vec_scaled)
    if t < 0.0:
        t = 0.0
    elif t > 1.0:
        t = 1.0
    nearest = scale(line_vec, t)
    dist = distance(nearest, pnt_vec)
    nearest = add(nearest, start)
    return dist, nearest