line_segment_and_circle.py

import math


def get_distance_in_meters(lat1, lon1, lat2, lon2):
    earth_radius = 6371007.2  # meters
    lat1, lon1, lat2, lon2 = map(math.radians, (lat1, lon1, lat2, lon2))
    dlon = lon2 - lon1
    dlat = lat2 - lat1
    a = math.sin(dlat / 2) ** 2 + math.cos(lat1) * math.cos(lat2) * math.sin(dlon / 2) ** 2
    c = 2 * math.atan2(math.sqrt(a), math.sqrt(1 - a))
    return earth_radius * c


def is_line_segment_intersecting_circle(ax, ay, bx, by, cx, cy, r_in_meters):
    """
    https://gis.stackexchange.com/questions/36841/line-intersection-with-circle-on-a-sphere-globe-or-earth
    """

    earth_radius = 6371007.2  # meters

    def make_projection(x, y):
        return math.radians(x) * earth_radius, math.radians(y) * earth_radius * math.cos(math.radians(cx))

    Ax, Ay = make_projection(ax, ay)
    Bx, By = make_projection(bx, by)
    Cx, Cy = make_projection(cx, cy)

    # Compute coefficients of the quadratic equation
    vx, vy = Ax - Cx, Ay - Cy
    ux, uy = Bx - Ax, By - Ay
    alpha = ux ** 2 + uy ** 2
    beta = ux * vx + uy * vy
    gamma = vx ** 2 + vy ** 2 - r_in_meters ** 2

    # Solve the equation.
    d = beta ** 2 - alpha * gamma
    if d < 0:
        return False
    t1 = (-beta + math.sqrt(d)) / alpha
    t2 = (-beta - math.sqrt(d)) / alpha
    return 0 <= t1 <= 1 or 0 <= t2 <= 1


def is_line_segment_intersecting_circle_or_inside_circle(ax, ay, bx, by, cx, cy, r_in_meters):
    return (get_distance_in_meters(ax, ay, cx, cy) <= r_in_meters or
            get_distance_in_meters(bx, by, cx, cy) <= r_in_meters or
            is_line_segment_intersecting_circle(ax, ay, bx, by, cx, cy, r_in_meters))


# in dnipro, must be true
is_line_segment_intersecting_circle(48.3884145, 35.497376, 48.5301052, 34.6690791, 48.4658508, 35.0759286, 10_000)
# large radius - must be false, segment is inside circle
is_line_segment_intersecting_circle(48.3884145, 35.497376, 48.5301052, 34.6690791, 48.4658508, 35.0759286, 200_000)
# large radius - must be true, segment is inside circle
is_line_segment_intersecting_circle_or_inside_circle(48.3884145, 35.497376, 48.5301052, 34.6690791, 48.4658508,
                                                     35.0759286, 200_000)

# line segment in kiev, circle in iran, must be false
is_line_segment_intersecting_circle(50.4498503, 30.5238646, 50.452297, 30.5271611, 35.046183, 48.464717, 50_000)
is_line_segment_intersecting_circle_or_inside_circle(50.4498503, 30.5238646, 50.452297, 30.5271611, 35.046183,
                                                     48.464717, 500_000)

# from example on stackexchange, must be true
is_line_segment_intersecting_circle(48.139115, 11.578081, 48.146303, 11.593102, 48.137024, 11.575249, 1000)
# with bigger radius must be false, segment is inside circle
is_line_segment_intersecting_circle(48.139115, 11.578081, 48.146303, 11.593102, 48.137024, 11.575249, 10_000)
# same parameters, different function - must be true, segment is inside circle
is_line_segment_intersecting_circle_or_inside_circle(48.139115, 11.578081, 48.146303, 11.593102, 48.137024, 11.575249,
                                                     10_000)