mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +00:00
57 lines
2.3 KiB
Python
57 lines
2.3 KiB
Python
|
from math import asin, atan, cos, radians, sin, sqrt, tan
|
||
|
|
|
||
|
|
|
||
|
|
def haversine_distance(lat1: float, lon1: float, lat2: float, lon2: float) -> float:
|
||
|
|
"""
|
||
|
|
Calculate great circle distance between two points in a sphere,
|
||
|
|
given longitudes and latitudes https://en.wikipedia.org/wiki/Haversine_formula
|
||
|
|
|
||
|
|
We know that the globe is "sort of" spherical, so a path between two points
|
||
|
|
isn't exactly a straight line. We need to account for the Earth's curvature
|
||
|
|
when calculating distance from point A to B. This effect is negligible for
|
||
|
|
small distances but adds up as distance increases. The Haversine method treats
|
||
|
|
the earth as a sphere which allows us to "project" the two points A and B
|
||
|
|
onto the surface of that sphere and approximate the spherical distance between
|
||
|
|
them. Since the Earth is not a perfect sphere, other methods which model the
|
||
|
|
Earth's ellipsoidal nature are more accurate but a quick and modifiable
|
||
|
|
computation like Haversine can be handy for shorter range distances.
|
||
|
|
|
||
|
|
Args:
|
||
|
|
lat1, lon1: latitude and longitude of coordinate 1
|
||
|
|
lat2, lon2: latitude and longitude of coordinate 2
|
||
|
|
Returns:
|
||
|
|
geographical distance between two points in metres
|
||
|
|
>>> from collections import namedtuple
|
||
|
|
>>> point_2d = namedtuple("point_2d", "lat lon")
|
||
|
|
>>> SAN_FRANCISCO = point_2d(37.774856, -122.424227)
|
||
|
|
>>> YOSEMITE = point_2d(37.864742, -119.537521)
|
||
|
|
>>> f"{haversine_distance(*SAN_FRANCISCO, *YOSEMITE):0,.0f} meters"
|
||
|
|
'254,352 meters'
|
||
|
|
"""
|
||
|
|
# CONSTANTS per WGS84 https://en.wikipedia.org/wiki/World_Geodetic_System
|
||
|
|
# Distance in metres(m)
|
||
|
|
AXIS_A = 6378137.0
|
||
|
|
AXIS_B = 6356752.314245
|
||
|
|
RADIUS = 6378137
|
||
|
|
# Equation parameters
|
||
|
|
# Equation https://en.wikipedia.org/wiki/Haversine_formula#Formulation
|
||
|
|
flattening = (AXIS_A - AXIS_B) / AXIS_A
|
||
|
|
phi_1 = atan((1 - flattening) * tan(radians(lat1)))
|
||
|
|
phi_2 = atan((1 - flattening) * tan(radians(lat2)))
|
||
|
|
lambda_1 = radians(lon1)
|
||
|
|
lambda_2 = radians(lon2)
|
||
|
|
# Equation
|
||
|
|
sin_sq_phi = sin((phi_2 - phi_1) / 2)
|
||
|
|
sin_sq_lambda = sin((lambda_2 - lambda_1) / 2)
|
||
|
|
# Square both values
|
||
|
|
sin_sq_phi *= sin_sq_phi
|
||
|
|
sin_sq_lambda *= sin_sq_lambda
|
||
|
|
h_value = sqrt(sin_sq_phi + (cos(phi_1) * cos(phi_2) * sin_sq_lambda))
|
||
|
|
return 2 * RADIUS * asin(h_value)
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == "__main__":
|
||
|
|
import doctest
|
||
|
|
|
||
|
|
doctest.testmod()
|