Fix issue #11308 Haversine Distance Calculation to Use Raw Latitudes

geodesy/haversine_distance.py

@@ -1,54 +1,44 @@
-from math import asin, atan, cos, radians, sin, sqrt, tan
-
-AXIS_A = 6378137.0
-AXIS_B = 6356752.314245
-RADIUS = 6378137
+from math import asin, cos, radians, sin, sqrt
 
 
 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.
+    Calculate the great-circle distance between two points
+    on the Earth specified by latitude and longitude using
+    the Haversine formula.
 
     Args:
-        lat1, lon1: latitude and longitude of coordinate 1
-        lat2, lon2: latitude and longitude of coordinate 2
+        lat1, lon1: Latitude and longitude of point 1 in decimal degrees.
+        lat2, lon2: Latitude and longitude of point 2 in decimal degrees.
+
+
     Returns:
-        geographical distance between two points in metres
+        Distance between the two points in meters.
+
     >>> 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'
+    '254,033 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))
-    return 2 * RADIUS * asin(h_value)
+
+    radius = 6378137  # earth radius (meters)
+
+    lat1_rad = radians(lat1)
+    lat2_rad = radians(lat2)
+    delta_lat = radians(lat2 - lat1)
+    delta_lon = radians(lon2 - lon1)
+
+    # Haversine formula
+    a = (
+        sin(delta_lat / 2) ** 2
+        + cos(lat1_rad) * cos(lat2_rad) * sin(delta_lon / 2) ** 2
+    )
+    c = 2 * asin(sqrt(a))
+
+    # Great-Circle Distance
+    return radius * c
 
 
 if __name__ == "__main__":

geodesy/lamberts_ellipsoidal_distance.py

@@ -15,22 +15,21 @@ def lamberts_ellipsoidal_distance(
     two points on the surface of earth given longitudes and latitudes
     https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines
 
-    NOTE: This algorithm uses geodesy/haversine_distance.py to compute central angle,
-        sigma
-
+    NOTE: This algorithm uses geodesy/haversine_distance.py to compute the
+          central angle, sigma
     Representing the earth as an ellipsoid allows us to approximate distances between
     points on the surface much better than a sphere. Ellipsoidal formulas treat the
     Earth as an oblate ellipsoid which means accounting for the flattening that happens
-    at the North and South poles. Lambert's formulae provide accuracy on the order of
-    10 meteres over thousands of kilometeres. Other methods can provide
-    millimeter-level accuracy but this is a simpler method to calculate long range
+    at the North and South poles. Lambert's formulas provide accuracy on the order of
+    10 meters over thousands of kilometers. Other methods can provide
+    millimeter-level accuracy, but this is a simpler method to calculate long-range
     distances without increasing computational intensity.
 
     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
+        geographical distance between two points in meters
 
     >>> from collections import namedtuple
     >>> point_2d = namedtuple("point_2d", "lat lon")
@@ -39,39 +38,32 @@ def lamberts_ellipsoidal_distance(
     >>> NEW_YORK = point_2d(40.713019, -74.012647)
     >>> VENICE = point_2d(45.443012, 12.313071)
     >>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *YOSEMITE):0,.0f} meters"
-    '254,351 meters'
+    '254,032 meters'
     >>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *NEW_YORK):0,.0f} meters"
-    '4,138,992 meters'
+    '4,133,295 meters'
     >>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *VENICE):0,.0f} meters"
-    '9,737,326 meters'
+    '9,719,525 meters'
     """
 
     # CONSTANTS per WGS84 https://en.wikipedia.org/wiki/World_Geodetic_System
-    # Distance in metres(m)
-    # Equation Parameters
-    # https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines
     flattening = (AXIS_A - AXIS_B) / AXIS_A
     # Parametric latitudes
-    # https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude
     b_lat1 = atan((1 - flattening) * tan(radians(lat1)))
     b_lat2 = atan((1 - flattening) * tan(radians(lat2)))
 
-    # Compute central angle between two points
-    # using haversine theta. sigma =  haversine_distance / equatorial radius
+    # Compute the central angle between two points using the haversine function
     sigma = haversine_distance(lat1, lon1, lat2, lon2) / EQUATORIAL_RADIUS
 
     # Intermediate P and Q values
     p_value = (b_lat1 + b_lat2) / 2
     q_value = (b_lat2 - b_lat1) / 2
 
     # Intermediate X value
-    # X = (sigma - sin(sigma)) * sin^2Pcos^2Q / cos^2(sigma/2)
     x_numerator = (sin(p_value) ** 2) * (cos(q_value) ** 2)
-    x_demonimator = cos(sigma / 2) ** 2
-    x_value = (sigma - sin(sigma)) * (x_numerator / x_demonimator)
+    x_denominator = cos(sigma / 2) ** 2
+    x_value = (sigma - sin(sigma)) * (x_numerator / x_denominator)
 
     # Intermediate Y value
-    # Y = (sigma + sin(sigma)) * cos^2Psin^2Q / sin^2(sigma/2)
     y_numerator = (cos(p_value) ** 2) * (sin(q_value) ** 2)
     y_denominator = sin(sigma / 2) ** 2
     y_value = (sigma + sin(sigma)) * (y_numerator / y_denominator)

geodesy/temp_code_runner_file.py

@@ -0,0 +1,3 @@
+# if __name__ == "__main__":
+#     import doctest
+#     doctest.testmod()