import numpy as np
[docs]def vincenty(lon0, lat0, a1, s):
"""
Returns the coordinates of a new point that is a given angular distance s away from a starting point (lon0, lat0) at bearing (angle from north) a1), to within a given precision
Note that this calculation is a simplified version of the full vincenty problem, which solves for the coordinates on the surface on an arbitrary ellipsoid. Here we only care about the surface of a sphere.
Note: All parameters are assumed to be given in DEGREES
:param lon0: float, longitude of starting point
:param lat0: float, latitude of starting point
:param a1: float, bearing to second point, i.e. angle between due north and line connecting 2 points
:param s: float, angular distance between the two points
:return: coordinates of second point in degrees
"""
lon0 = np.deg2rad(lon0)
lat0 = np.deg2rad(lat0)
a1 = np.deg2rad(a1)
s = np.deg2rad(s)
sina = np.cos(lat0) * np.sin(a1)
num1 = np.sin(lat0)*np.cos(s) + np.cos(lat0)*np.sin(s)*np.cos(a1)
den1 = np.sqrt(sina**2 + (np.sin(lat0)*np.sin(s) - np.cos(lat0)*np.cos(a1))**2)
lat = np.rad2deg(np.arctan2(num1, den1))
num2 = np.sin(s)*np.sin(a1)
den2 = np.cos(lat0)*np.cos(s) - np.sin(lat0)*np.sin(s)*np.cos(a1)
L = np.arctan2(num2, den2)
lon = np.rad2deg(lon0 + L)
return lon, lat