def isantipode(lat1, lon1, lat2, lon2, eps=EPS):
'''Check whether two points are antipodal, on diametrically
opposite sides of the earth.
@arg lat1: Latitude of one point (C{degrees}).
@arg lon1: Longitude of one point (C{degrees}).
@arg lat2: Latitude of the other point (C{degrees}).
@arg lon2: Longitude of the other point (C{degrees}).
@kwarg eps: Tolerance for near-equality (C{degrees}).
@return: C{True} if points are antipodal within the
B{C{eps}} tolerance, C{False} otherwise.
@see: U{Geosphere<https://CRAN.R-Project.org/web/packages/geosphere/geosphere.pdf>}.
'''
return abs(wrap90(lat1) + wrap90(lat2)) < eps and \
abs(abs(wrap180(lon1) - wrap180(lon2)) % 360 - 180) < eps
def antipode(lat, lon):
'''Return the antipode, the point diametrically opposite
to a given point in C{degrees}.
@arg lat: Latitude (C{degrees}).
@arg lon: Longitude (C{degrees}).
@return: A L{LatLon2Tuple}C{(lat, lon)}.
@see: U{Geosphere<https://CRAN.R-Project.org/web/packages/geosphere/geosphere.pdf>}.
'''
return LatLon2Tuple(-wrap90(lat), wrap180(lon + 180))
def _to3zll(lat, lon): # imported by .ups, .utm
'''Wrap lat- and longitude and determine UTM zone.
@arg lat: Latitude (C{degrees}).
@arg lon: Longitude (C{degrees}).
@return: 3-Tuple (C{zone, lat, lon}) as (C{int}, C{degrees90},
C{degrees180}) where C{zone} is C{1..60} for UTM.
'''
x = wrap360(lon + 180) # use wrap360 to get ...
z = int(x) // 6 + 1 # ... longitudinal UTM zone [1, 60] and ...
lon = x - 180.0 # ... lon [-180, 180) i.e. -180 <= lon < 180
return Zone(z), wrap90(lat), lon
def _direct(self, distance, bearing, llr, height=None):
'''(INTERNAL) Direct Karney method.
'''
g = self.datum.ellipsoid.geodesic
m = g.AZIMUTH
if llr:
m |= g.LATITUDE | g.LONGITUDE
r = g.Direct(self.lat, self.lon, bearing, distance, m)
t = wrap360(r['azi2'])
if llr:
a, b = wrap90(r['lat2']), wrap180(r['lon2'])
h = self.height if height is None else height
t = self.classof(a, b, height=h, datum=self.datum), t
return t
def _direct(self, distance, bearing, LL, height):
'''(INTERNAL) Karney's C{Direct} method.
@return: A L{Destination2Tuple}C{(destination, final)} or
a L{Destination3Tuple}C{(lat, lon, final)} if
B{C{LL}} is C{None}.
'''
g = self.datum.ellipsoid.geodesic
r = g.Direct3(self.lat, self.lon, bearing, distance)
if LL:
h = self.height if height is None else height
d = LL(wrap90(r.lat), wrap180(r.lon), height=h, datum=self.datum)
r = Destination2Tuple(self._xnamed(d), wrap360(r.final))
return r
