Created geodesy section with one algorithm (TheAlgorithms#1757)

* implemented haversine

* updated docstring

Only calculate distance

* added type hints

* added type hints

* improved docstring and math usage

* f"{haversine_distance(*SAN_FRANCISCO, *YOSEMITE):0,.0f} meters"

Co-authored-by: Christian Clauss <[email protected]>

Author: eightysixth

geodesy/haversine_distance.py

@@ -0,0 +1,56 @@
+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()