def destination(self, point, bearing, distance=None):
point = Point(point)
lat1 = units.radians(degrees=point.latitude)
lng1 = units.radians(degrees=point.longitude)
bearing = units.radians(degrees=bearing)
if distance is None:
distance = self
if isinstance(distance, Distance):
distance = distance.kilometers
d_div_r = float(distance) / self.RADIUS
lat2 = asin(
sin(lat1) * cos(d_div_r) +
cos(lat1) * sin(d_div_r) * cos(bearing)
)
lng2 = lng1 + atan2(
sin(bearing) * sin(d_div_r) * cos(lat1),
cos(d_div_r) - sin(lat1) * sin(lat2)
)
return Point(units.degrees(radians=lat2), units.degrees(radians=lng2))
def parse_degrees(cls, degrees, arcminutes, arcseconds, direction=None):
negative = degrees < 0 or degrees.startswith('-')
degrees = float(degrees or 0)
arcminutes = float(arcminutes or 0)
arcseconds = float(arcseconds or 0)
if arcminutes or arcseconds:
more = units.degrees(arcminutes=arcminutes, arcseconds=arcseconds)
if negative:
degrees -= more
else:
degrees += more
if direction in [None, 'N', 'E']:
return degrees
elif direction in ['S', 'W']:
return -degrees
else:
raise ValueError("Invalid direction! Should be one of [NSEW].")
def destination(self, point, bearing, distance=None):
point = Point(point)
lat1 = units.radians(degrees=point.latitude)
lng1 = units.radians(degrees=point.longitude)
bearing = units.radians(degrees=bearing)
if distance is None:
distance = self
if isinstance(distance, Distance):
distance = distance.kilometers
ellipsoid = self.ELLIPSOID
if isinstance(ellipsoid, basestring):
ellipsoid = ELLIPSOIDS[ellipsoid]
major, minor, f = ellipsoid
tan_reduced1 = (1 - f) * tan(lat1)
cos_reduced1 = 1 / sqrt(1 + tan_reduced1 ** 2)
sin_reduced1 = tan_reduced1 * cos_reduced1
sin_bearing, cos_bearing = sin(bearing), cos(bearing)
sigma1 = atan2(tan_reduced1, cos_bearing)
sin_alpha = cos_reduced1 * sin_bearing
cos_sq_alpha = 1 - sin_alpha ** 2
u_sq = cos_sq_alpha * (major ** 2 - minor ** 2) / minor ** 2
A = 1 + u_sq / 16384. * (
4096 + u_sq * (-768 + u_sq * (320 - 175 * u_sq))
)
B = u_sq / 1024. * (256 + u_sq * (-128 + u_sq * (74 - 47 * u_sq)))
sigma = distance / (minor * A)
sigma_prime = 2 * pi
while abs(sigma - sigma_prime) > 10e-12:
cos2_sigma_m = cos(2 * sigma1 + sigma)
sin_sigma, cos_sigma = sin(sigma), cos(sigma)
delta_sigma = B * sin_sigma * (
cos2_sigma_m + B / 4. * (
cos_sigma * (
-1 + 2 * cos2_sigma_m
) - B / 6. * cos2_sigma_m * (
-3 + 4 * sin_sigma ** 2) * (
-3 + 4 * cos2_sigma_m ** 2
)
)
)
sigma_prime = sigma
sigma = distance / (minor * A) + delta_sigma
sin_sigma, cos_sigma = sin(sigma), cos(sigma)
lat2 = atan2(
sin_reduced1 * cos_sigma + cos_reduced1 * sin_sigma * cos_bearing,
(1 - f) * sqrt(
sin_alpha ** 2 + (
sin_reduced1 * sin_sigma -
cos_reduced1 * cos_sigma * cos_bearing
) ** 2
)
)
lambda_lng = atan2(
sin_sigma * sin_bearing,
cos_reduced1 * cos_sigma - sin_reduced1 * sin_sigma * cos_bearing
)
C = f / 16. * cos_sq_alpha * (4 + f * (4 - 3 * cos_sq_alpha))
delta_lng = (
lambda_lng - (1 - C) * f * sin_alpha * (
sigma + C * sin_sigma * (
cos2_sigma_m + C * cos_sigma * (
-1 + 2 * cos2_sigma_m ** 2
)
)
)
)
final_bearing = atan2(
sin_alpha,
cos_reduced1 * cos_sigma * cos_bearing - sin_reduced1 * sin_sigma
)
lng2 = lng1 + delta_lng
return Point(units.degrees(radians=lat2), units.degrees(radians=lng2))
