"""
Functions for computing navigational information. Can be used to add
navigational information to DataFrames.
"""
from math import acos, asin, atan2, cos, sin, degrees, radians, sqrt
def gcd_slc(
lon0: float,
lat0: float,
lon1: float,
lat1: float,
) -> float:
"""
Compute great circle distance on earth surface between two locations.
Parameters
----------
lon0 : float
Longitude of position 0
lat0 : float
Latitude of position 0
lon1 : float
Longitude of position 1
lat1 : float
Latitude of position 1
Returns
-------
dist : float
Great circle distance between position 0 and position 1.
"""
if abs(lat0 - lat1) <= 1e-6 and abs(lon0 - lon1) <= 1e-6:
return 0
r_earth = 6371
# Convert to radians
lat0, lat1, lon0, lon1 = map(radians, [lat0, lat1, lon0, lon1])
return r_earth * acos(
sin(lat0) * sin(lat1) + cos(lat0) * cos(lat1) * cos(lon1 - lon0)
)
def haversine(
lon0: float,
lat0: float,
lon1: float,
lat1: float,
) -> float:
"""
Compute Haversine distance between two points.
Parameters
----------
lon0 : float
Longitude of position 0
lat0 : float
Latitude of position 0
lon1 : float
Longitude of position 1
lat1 : float
Latitude of position 1
Returns
-------
dist : float
Haversine distance between position 0 and position 1.
"""
lat0, lat1, dlon, dlat = map(
radians, [lat0, lat1, lon1 - lon0, lat1 - lat0]
)
if abs(dlon) < 1e-6 and abs(dlat) < 1e-6:
return 0
r_earth = 6371
a = sin(dlat / 2) ** 2 + cos(lat0) * cos(lat1) * sin(dlon / 2) ** 2
c = 2 * asin(sqrt(a))
return c * r_earth
def bearing(
lon0: float,
lat0: float,
lon1: float,
lat1: float,
) -> float:
"""
Compute the bearing of a track from (lon0, lat0) to (lon1, lat1).
Duplicated from geo-py
Parameters
----------
lon0 : float,
Longitude of start point
lat0 : float,
Latitude of start point
lon1 : float,
Longitude of target point
lat1 : float,
Latitude of target point
Returns
-------
bearing : float
The bearing from point (lon0, lat0) to point (lon1, lat1) in degrees.
"""
lon0, lat0, lon1, lat1 = map(radians, [lon0, lat0, lon1, lat1])
dlon = lon1 - lon0
numerator = sin(dlon) * cos(lat1)
denominator = cos(lat0) * sin(lat1) - (sin(lat0) * cos(lat1) * cos(dlon))
theta = atan2(numerator, denominator)
theta_deg = (degrees(theta) + 360) % 360
return theta_deg
def destination(
lon: float, lat: float, bearing: float, distance: float
) -> tuple[float, float]:
"""
Compute destination of a great circle path.
Compute the destination of a track started from 'lon', 'lat', with
'bearing'. Distance is in units of km.
Duplicated from geo-py
Parameters
----------
lon : float
Longitude of initial position
lat : float
Latitude of initial position
bearing : float
Direction of track
distance : float
Distance to travel
Returns
-------
destination : tuple[float, float]
Longitude and Latitude of final position
"""
lon, lat = radians(lon), radians(lat)
radians_bearing = radians(bearing)
r_earth = 6371
delta = distance / r_earth
lat2 = asin(
sin(lat) * cos(delta) + cos(lat) * sin(delta) * cos(radians_bearing)
)
numerator = sin(radians_bearing) * sin(delta) * cos(lat)
denominator = cos(delta) - sin(lat) * sin(lat2)
lon2 = lon + atan2(numerator, denominator)
lon2_deg = (degrees(lon2) + 540) % 360 - 180
lat2_deg = degrees(lat2)
return lon2_deg, lat2_deg
def midpoint(
lon0: float,
lat0: float,
lon1: float,
lat1: float,
) -> tuple[float, float]:
"""
Compute the midpoint of a great circle track
Parameters
----------
lon0 : float
Longitude of position 0
lat0 : float
Latitude of position 0
lon1 : float
Longitude of position 1
lat1 : float
Latitude of position 1
Returns
-------
lon, lat
Positions of midpoint between position 0 and position 1
"""
bear = bearing(lon0, lat0, lon1, lat1)
dist = haversine(lon0, lat0, lon1, lat1)
return destination(lon0, lat0, bear, dist / 2)