def Deg2Rad(x): "Degrees to radians." return x * (math.pi/180) def CalcRad(lat): "Radius of curvature in meters at specified latitude." a = 6378.137 e2 = 0.081082 * 0.081082 # the radius of curvature of an ellipsoidal Earth in the plane of a # meridian of latitude is given by # # R' = a * (1 - e^2) / (1 - e^2 * (sin(lat))^2)^(3/2) # # where a is the equatorial radius, # b is the polar radius, and # e is the eccentricity of the ellipsoid = sqrt(1 - b^2/a^2) # # a = 6378 km (3963 mi) Equatorial radius (surface to center distance) # b = 6356.752 km (3950 mi) Polar radius (surface to center distance) # e = 0.081082 Eccentricity sc = math.sin(Deg2Rad(lat)) x = a * (1.0 - e2) z = 1.0 - e2 * sc * sc y = pow(z, 1.5) r = x / y r = r * 1000.0 # Convert to meters return r def EarthDistance((lat1, lon1), (lat2, lon2)): "Distance in meters between two points specified in degrees." x1 = CalcRad(lat1) * math.cos(Deg2Rad(lon1)) * math.sin(Deg2Rad(90-lat1)) x2 = CalcRad(lat2) * math.cos(Deg2Rad(lon2)) * math.sin(Deg2Rad(90-lat2)) y1 = CalcRad(lat1) * math.sin(Deg2Rad(lon1)) * math.sin(Deg2Rad(90-lat1)) y2 = CalcRad(lat2) * math.sin(Deg2Rad(lon2)) * math.sin(Deg2Rad(90-lat2)) z1 = CalcRad(lat1) * math.cos(Deg2Rad(90-lat1)) z2 = CalcRad(lat2) * math.cos(Deg2Rad(90-lat2)) a = (x1*x2 + y1*y2 + z1*z2)/pow(CalcRad((lat1+lat2)/2), 2) # a should be in [1, -1] but can sometimes fall outside it by # a very small amount due to rounding errors in the preceding # calculations (this is prone to happen when the argument points # are very close together). Thus we constrain it here. if abs(a) > 1: a = 1 elif a < -1: a = -1 return CalcRad((lat1+lat2) / 2) * math.acos(a)