Calculate the distance between two segments identified by a pair of extremity 2D points

distance_segments.py

# this script is meant to be run inside Blender
import math
from mathutils import Vector, geometry

def distance_point_to_segment(p, p0, p1):
    """
    Project point p on line passing through points p0 and p1
    Returns Distance between point p & its projection, if the latter belongs to segment p0-p1,
            Infinity otherwise
    """
    # percentage gives the dist from the 1st line point to the proj. point => in [0, 1] if in segment
    p_proj, percentage = geometry.intersect_point_line(p, p0, p1)
    dist = (p_proj - p).length
    
    print('### p:', p)
    print('proj:', p_proj)
    print('percentage:', percentage)
    print('dist:', dist)
    print()
    
    return dist if 0 <= percentage <= 1 else math.inf
    

if __name__ == '__main__':
    # 1st line: y = x
    p0 = Vector((0, 0))
    p1 = Vector((2, 2))

    # 2nd line: y = 2x
    p2 = Vector((1, 2)) # for when proj. inside segments!
    p3 = Vector((2, 4))
    # p2 = Vector((2, 4)) # for when proj. outside segments!
    # p3 = Vector((3, 6))

    # project of points p0/p1 (from 1st line) on 2nd line
    dist0 = distance_point_to_segment(p0, p2, p3)
    dist1 = distance_point_to_segment(p1, p2, p3)

    # project of p2/p3 (from 2nd line) on 1st line line
    dist2 = distance_point_to_segment(p2, p0, p1)
    dist3 = distance_point_to_segment(p3, p0, p1)

    # dist = inf if all proj. points outside segments
    dists = [ dist0, dist1, dist2, dist3 ]
    dist = min(dists)

    # in this case dist = min dist. between segments extremities
    if dist == math.inf:
        print('All projected points outside segments')
        dists = [
            (p0 - p2).length,
            (p0 - p3).length,
            (p1 - p2).length,
            (p1 - p3).length,
        ]
        dist = min(dists)

    print('Dist:', dist)