def distance(start, end, options=None):
"""
Calculates the distance between two Points in degrees, radians, miles, or kilometers.
This uses the [Haversine formula](http://en.wikipedia.org/wiki/Haversine_formula) to account for global curvature.
:param start: starting point [lng, lat] or Point feature
:param end: ending point [lng, lat] or Point feature
:param options: dictionary with units as an attribute. Can be degrees, radians, miles, or kilometers
:return: distance between the 2 points
"""
kwargs = {}
if isinstance(options, dict) and "units" in options:
kwargs.update(options)
coordinates1 = get_coords_from_features(start, ["Point"])
coordinates2 = get_coords_from_features(end, ["Point"])
d_lat = degrees_to_radians(coordinates2[1] - coordinates1[1])
d_lon = degrees_to_radians(coordinates2[0] - coordinates1[0])
lat1 = degrees_to_radians(coordinates1[1])
lat2 = degrees_to_radians(coordinates2[1])
distance_rad = calculate_radians_distance(d_lon, d_lat, lat1, lat2)
return radians_to_length(distance_rad, **kwargs)
def __init__(self, lon: float, lat: float, decimals=6):
self.lon = lon
self.lat = lat
self.x = degrees_to_radians(lon)
self.y = degrees_to_radians(lat)
self.decimals = decimals
def bearing(start, end, options=None):
"""
Takes two points and finds the geographic bearing between them,
i.e. the angle measured in degrees from the north line (0 degrees)
:param start: starting point [lng, lat] or Point feature
:param end: ending point [lng, lat] or Point feature
:param options: dictionary with options:
[options["final"]] - calculates the final bearing if true
:return: bearing in decimal degrees, between -180 and 180 (positive clockwise)
"""
if not options:
options = {}
if isinstance(options, dict) and "final" in options:
return calculate_final_bearing(start, end)
start = get_coords_from_features(start, ["Point"])
end = get_coords_from_features(end, ["Point"])
lon1 = degrees_to_radians(start[0])
lon2 = degrees_to_radians(end[0])
lat1 = degrees_to_radians(start[1])
lat2 = degrees_to_radians(end[1])
a = np.sin(lon2 - lon1) * np.cos(lat2)
b = np.cos(lat1) * np.sin(lat2) - np.sin(lat1) * np.cos(lat2) * np.cos(lon2 - lon1)
return radians_to_degrees(np.arctan2(a, b))
def calculate_rhumb_destination(origin: Sequence,
distance_in_meters: float,
bearing: float,
radius: float = None) -> List:
"""
Calculates the destination point having travelled along a rhumb line
from origin point the given distance on the given bearing.
Adapted from Geodesy:
http://www.movable-type.co.uk/scripts/latlong.html#rhumblines
param origin: point coordinates in [lng, lat] form
param distance: - Distance travelled, in same units as earth radius (default: metres).
param bearing: - Bearing in degrees from north.
param radius: - (Mean) radius of earth
returns destination: point.
"""
if not radius:
radius = earth_radius
# angular distance in radians
delta = distance_in_meters / radius
# to radians, but without normalize to pi
lambda_1 = origin[0] * pi / 180
phi_1 = degrees_to_radians(origin[1])
theta = degrees_to_radians(bearing)
delta_phi = delta * cos(theta)
phi_2 = phi_1 + delta_phi
# check for some points going past the pole, normalise latitude if so
if abs(phi_2) > (pi / 2) and (phi_2 > 0):
phi_2 = pi - phi_2
if abs(phi_2) > (pi / 2) and (phi_2 < 0):
phi_2 = pi - phi_2
delta_psi = log(tan(phi_2 / 2 + pi / 4) / tan(phi_1 / 2 + pi / 4))
# E-W course becomes ill-conditioned with 0/0
if abs(delta_psi) > 10e-12:
q_1 = delta_phi / delta_psi
else:
q_1 = cos(phi_1)
delta_lambda = delta * sin(theta) / q_1
lambda_2 = lambda_1 + delta_lambda
# normalise to −180..+180°
destination = [
fmod(((lambda_2 * 180 / pi) + 540), 360) - 180,
(phi_2 * 180 / pi),
]
return destination
def calculate_rhumb_distance(origin: List,
destination: List,
radius: float = None) -> float:
"""
Calculates the rhumb distance between two Points.
# https://en.wikipedia.org/wiki/Rhumb_line
:param origin: starting point [lng, lat]
:param destination: ending point [lng, lat]
:param radius: radius of the earth
:return: distance between the 2 points in meters
"""
if not radius:
radius = earth_radius
phi_1 = degrees_to_radians(origin[1])
phi_2 = degrees_to_radians(destination[1])
delta_phi = phi_2 - phi_1
delta_lambda = degrees_to_radians(abs(destination[0] - origin[0]))
# if dLon over 180° take shorter rhumb line across the anti-meridian:
if delta_lambda > np.pi:
delta_lambda -= 2 * np.pi
# on Mercator projection, longitude distances shrink by latitude; q is the 'stretch factor'
# q becomes ill-conditioned along E-W line (0/0); use empirical tolerance to avoid it
delta_psi = np.log(
np.tan(phi_2 / 2 + np.pi / 4) / np.tan(phi_1 / 2 + np.pi / 4))
if abs(delta_psi) > 10e-12:
q_1 = delta_phi / delta_psi
else:
q_1 = np.cos(phi_1)
# distance is pythagoras on 'stretched' Mercator projection
delta = np.sqrt(delta_phi * delta_phi +
q_1 * q_1 * delta_lambda * delta_lambda)
# angular distance in radians
distance = delta * radius
return distance
def destination(origin, distance, bearing, options=None):
"""
Takes a Point and calculates the location of a destination point given a distance in
degrees, radians, miles, or kilometers; and bearing in degrees.
This uses the [Haversine formula](http://en.wikipedia.org/wiki/Haversine_formula) to account for global curvature.
:param origin: starting point
:param distance: distance from the origin point
:param bearing: bearing ranging from -180 to 180
:param options: optional parameters
[options["units"]='kilometers'] miles, kilometers, degrees, or radians
[options["properties"]={}] Translate properties to Point
:return: destination GeoJSON Point feature
"""
if not options:
options = {}
kwargs = {}
if "units" in options:
kwargs["units"] = options.get("units")
coords = get_coords_from_features(origin, ["Point"])
longitude1 = degrees_to_radians(coords[0])
latitude1 = degrees_to_radians(coords[1])
bearing_rads = degrees_to_radians(bearing)
radians = length_to_radians(distance, **kwargs)
latitude2 = asin(
sin(latitude1) * cos(radians) +
cos(latitude1) * sin(radians) * cos(bearing_rads))
longitude2 = longitude1 + atan2(
sin(bearing_rads) * sin(radians) * cos(latitude1),
cos(radians) - sin(latitude1) * sin(latitude2),
)
lng = truncate(radians_to_degrees(longitude2), 6)
lat = truncate(radians_to_degrees(latitude2), 6)
return point([lng, lat], options.get("properties", None))
def calculate_rhumb_bearing(origin: Sequence, destination: Sequence) -> float:
"""
Calculates the bearing from origin to destination point along a rhumb line.
http://www.edwilliams.org/avform.htm#Rhumb
"""
phi_1 = degrees_to_radians(origin[1])
phi_2 = degrees_to_radians(destination[1])
delta_lambda = degrees_to_radians(destination[0] - origin[0])
# if delta_lambda over 180° take shorter rhumb line across the anti-meridian:
if abs(delta_lambda) > pi:
if delta_lambda > 0:
delta_lambda = -(2 * pi - delta_lambda)
if delta_lambda < 0:
delta_lambda = 2 * pi + delta_lambda
delta_psi = log(tan(phi_2 / 2 + pi / 4) / tan(phi_1 / 2 + pi / 4))
theta = atan2(delta_lambda, delta_psi)
return fmod(radians_to_degrees(theta) + 360, 360)
def test_degrees_to_radians(value, result):
assert degrees_to_radians(value) == result