haversine_distance.py

frommathimportasin, atan, cos, radians, sin, sqrt, tan

AXIS_A=6378137.0
AXIS_B=6356752.314245
RADIUS=6378137


defhaversine_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)
# 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))
return2*RADIUS*asin(h_value)


if__name__=="__main__":
importdoctest

doctest.testmod()