def isantipode_(phi1, lam1, phi2, lam2, eps=EPS):
'''Check whether two points are antipodal, on diametrically
opposite sides of the earth.
@arg phi1: Latitude of one point (C{radians}).
@arg lam1: Longitude of one point (C{radians}).
@arg phi2: Latitude of the other point (C{radians}).
@arg lam2: Longitude of the other point (C{radians}).
@kwarg eps: Tolerance for near-equality (C{radians}).
@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(wrapPI_2(phi1) + wrapPI_2(phi2)) < eps and \
abs(abs(wrapPI(lam1) - wrapPI(lam2)) % PI2 - PI) < eps
def antipode_(phi, lam):
'''Return the antipode, the point diametrically opposite
to a given point in C{radians}.
@arg phi: Latitude (C{radians}).
@arg lam: Longitude (C{radians}).
@return: A L{PhiLam2Tuple}C{(phi, lam)}.
@see: U{Geosphere<https://CRAN.R-Project.org/web/packages/geosphere/geosphere.pdf>}.
'''
return PhiLam2Tuple(-wrapPI_2(phi), wrapPI(lam + PI))
def _rhumb3(self, other):
'''(INTERNAL) Rhumb_ helper function.
@param other: The other point (spherical C{LatLon}).
'''
self.others(other)
a1, b1 = self.to2ab()
a2, b2 = other.to2ab()
# if |db| > 180 take shorter rhumb
# line across the anti-meridian
db = wrapPI(b2 - b1)
dp = log(tanPI_2_2(a2) / tanPI_2_2(a1))
return (a2 - a1), db, dp
def _xb(a1, b1, end, a, b, wrap):
# difference between the bearing to (a, b) and the given
# bearing is negative if both are in opposite directions
r = bearing_(a1, b1, radians(a), radians(b), wrap=wrap)
return PI_2 - abs(wrapPI(r - radians(end)))