Find the shortest distance between a point and line segments (not line)

Question

I have set of line segments (not lines), (A1, B1), (A2, B2), (A3, B3), where A,B are ending points of the line segment. Each A and B has (x,y) coordinates.

QUESTION: I need to know the shortest distance between point O and line segments as shown in the shown figure implemented in line of codes. The code I can really understand is either pseudo-code or Python.

CODE: I tried to solve the problem with this code, unfortunately, it does not work properly.

def dist(A, B, O):
    A_ = complex(*A)
    B_ = complex(*B)
    O_= complex(*O)
    OA = O_ - A_
    OB = O_ - B_
    return min(OA, OB)
# coordinates are given
A1, B1 = [1, 8], [6,4]
A2, B2 = [3,1], [5,2]
A3, B3 = [2,3], [2, 1]
O = [2, 5]
A = [A1, A2, A3]
B = [B1, B2, B3]
print [ dist(i, j, O)  for i, j in zip(A, B)]

Thanks in advance.

Answer 1

Rather than using a for loop, you can vectorize these operations and get much better performance. Here is my solution that allows you to compute the distance from a single point to multiple line segments with vectorized computation.

def lineseg_dists(p, a, b):
    """Cartesian distance from point to line segment

    Edited to support arguments as series, from:
    https://stackoverflow.com/a/54442561/11208892

    Args:
        - p: np.array of single point, shape (2,) or 2D array, shape (x, 2)
        - a: np.array of shape (x, 2)
        - b: np.array of shape (x, 2)
    """
    # normalized tangent vectors
    d_ba = b - a
    d = np.divide(d_ba, (np.hypot(d_ba[:, 0], d_ba[:, 1])
                           .reshape(-1, 1)))

    # signed parallel distance components
    # rowwise dot products of 2D vectors
    s = np.multiply(a - p, d).sum(axis=1)
    t = np.multiply(p - b, d).sum(axis=1)

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

    # perpendicular distance component
    # rowwise cross products of 2D vectors  
    d_pa = p - a
    c = d_pa[:, 0] * d[:, 1] - d_pa[:, 1] * d[:, 0]

    return np.hypot(h, c)

And some tests:

p = np.array([0, 0])
a = np.array([[ 1,  1],
              [-1,  0],
              [-1, -1]])
b = np.array([[ 2,  2],
              [ 1,  0],
              [ 1, -1]])

print(lineseg_dists(p, a, b))

p = np.array([[0, 0],
              [1, 1],
              [0, 2]])

print(lineseg_dists(p, a, b))

>>> [1.41421356 0.         1.        ]
    [1.41421356 1.         3.        ]