def greatCircle(self, bearing):
'''Compute the n-vector normal to great circle obtained by
heading on given compass bearing from this point as its
n-vector.
Direction of vector is such that initial bearing vector
b = c × p.
@param bearing: Initial compass bearing (C{degrees}).
@return: N-vector representing great circle (L{Nvector}).
@raise Valuerror: Polar coincidence.
@example:
>>> n = LatLon(53.3206, -1.7297).toNvector()
>>> gc = n.greatCircle(96.0) # [-0.794, 0.129, 0.594]
'''
s, c = sincos2d(bearing)
e = NorthPole.cross(self, raiser='pole') # easting
n = self.cross(e, raiser='point') # northing
e = e.times(c / e.length)
n = n.times(s / n.length)
return n.minus(e)
def _gc(p, b):
n = p.toNvector()
de = NorthPole.cross(n, raiser='pole').unit() # east vector @ n
dn = n.cross(de) # north vector @ n
s, c = sincos2d(b)
dest = de.times(s)
dnct = dn.times(c)
d = dnct.plus(dest) # direction vector @ n
return n.cross(d) # great circle point + bearing
def fEd(self, deg):
'''The incomplete integral of the second kind with
the argument given in degrees.
@param deg: Angle (C{degrees}).
@return: E(π deg/180, k).
'''
n = ceil(deg / 360.0 - 0.5)
sn, cn = sincos2d(deg - n * 360.0)
return self.fE(sn, cn, self.fDelta(sn, cn)) + 4 * self.cE * n
def rhumbDestination(self, distance, bearing, radius=R_M, height=None):
'''Return the destination point having travelled along a rhumb
(loxodrome) line from this point the given distance on the
given bearing.
@param distance: Distance travelled (C{meter}, same units as
I{radius}).
@param bearing: Bearing from this point (compass C{degrees360}).
@keyword radius: Optional, mean earth radius (C{meter}).
@keyword height: Optional height, overriding the default
height (C{meter}, same unit as I{radius}).
@return: The destination point (spherical C{LatLon}).
@example:
>>> p = LatLon(51.127, 1.338)
>>> q = p.rhumbDestination(40300, 116.7) # 50.9642°N, 001.8530°E
@JSname: I{rhumbDestinationPoint}
'''
a1, b1 = self.to2ab()
r = float(distance) / float(radius) # angular distance in radians
sb, cb = sincos2d(bearing)
da = r * cb
a2 = a1 + da
# normalize latitude if past pole
if a2 > PI_2:
a2 = PI - a2
elif a2 < -PI_2:
a2 = -PI - a2
dp = log(tanPI_2_2(a2) / tanPI_2_2(a1))
# E-W course becomes ill-conditioned with 0/0
q = (da / dp) if abs(dp) > EPS else cos(a1)
b2 = (b1 + r * sb / q) if abs(q) > EPS else b1
h = self.height if height is None else height
return self.classof(degrees90(a2), degrees180(b2), height=h)
def destination(self, distance, bearing, radius=R_M, height=None):
'''Locate the destination from this point after having
travelled the given distance on the given bearing.
@param distance: Distance travelled (C{meter}, same units
as B{C{radius}}).
@param bearing: Bearing from this point (compass C{degrees360}).
@keyword radius: Optional, mean earth radius (C{meter}).
@keyword height: Optional height at destination, overriding
the default height (C{meter}, same units as
B{C{radius}}).
@return: Destination point (L{LatLon}).
@raise Valuerror: Polar coincidence.
@example:
>>> p = LatLon(51.4778, -0.0015)
>>> q = p.destination(7794, 300.7)
>>> q.toStr() # 51.513546°N, 000.098345°W
@JSname: I{destinationPoint}.
'''
p = self.toNvector()
e = NorthPole.cross(p, raiser='pole').unit() # east vector at p
n = p.cross(e) # north vector at p
s, c = sincos2d(bearing)
q = n.times(c).plus(e.times(s)) # direction vector @ p
s, c = sincos2(float(distance) /
float(radius)) # angular distance in radians
n = p.times(c).plus(q.times(s))
return n.toLatLon(
height=height,
LatLon=self.classof) # Nvector(n.x, n.y, n.z).toLatLon(...)
def toUps8(latlon, lon=None, datum=None, Ups=Ups, pole='',
falsed=True, strict=True, name=''):
'''Convert a lat-/longitude point to a UPS coordinate.
@param latlon: Latitude (C{degrees}) or an (ellipsoidal)
geodetic C{LatLon} point.
@keyword lon: Optional longitude (C{degrees}) or C{None}
if I{latlon} is a C{LatLon}.
@keyword datum: Optional datum for this UPS coordinate,
overriding I{latlon}'s datum (C{Datum}).
@keyword Ups: Optional (sub-)class to return the UPS
coordinate (L{Ups}) or C{None}.
@keyword pole: Optional top/center of (stereographic) projection
(C{str}, C{'N[orth]'} or C{'S[outh]'}).
@keyword falsed: False both easting and northing (C{bool}).
@keyword strict: Restrict I{lat} to UPS ranges (C{bool}).
@keyword name: Optional I{Ups} name (C{str}).
@return: The UPS coordinate (L{Ups}) or a 8-tuple (zone, hemisphere,
easting, northing, band, datum, convergence, scale) if
I{Ups} is C{None}.
@raise RangeError: If I{strict} and I{lat} outside the valid UPS
bands or if I{lat} or I{lon} outside the valid
range and I{rangerrrors} set to C{True}.
@raise TypeError: If I{latlon} is not ellipsoidal.
@raise ValueError: If I{lon} value is missing or if I{latlon}
is invalid.
@see: Karney's C++ class U{UPS
<http://GeographicLib.SourceForge.io/html/classGeographicLib_1_1UPS.html>}.
'''
lat, lon, d, name = _to4lldn(latlon, lon, datum, name)
z, B, p, lat, lon = upsZoneBand5(lat, lon, strict=strict)
p = str(pole or p)[:1]
N = p in 'Nn'
E = d.ellipsoid
A = abs(lat - 90) < _TOL
t = tan(radians(lat if N else -lat))
T = E.es_taupf(t)
r = hypot1(T) + abs(T)
if T >= 0:
r = 0 if A else 1 / r
k0 = getattr(Ups, '_scale0', _K0) # Ups is class or None
r *= 2 * k0 * E.a / E.es_c
k = k0 if A else _scale(E, r, t)
c = lon # [-180, 180) from .upsZoneBand5
x, y = sincos2d(c)
x *= r
y *= r
if N:
y = -y
else:
c = -c
if falsed:
x += _Falsing
y += _Falsing
if Ups is None:
r = z, p, x, y, B, d, c, k
else:
if z != _UPS_ZONE and not strict:
z = _UPS_ZONE # ignore UTM zone
r = _xnamed(Ups(z, p, x, y, band=B, datum=d,
convergence=c, scale=k,
falsed=falsed), name)
if hasattr(Ups, '_hemisphere'):
r._hemisphere = _hemi(lat)
return r
def toUps8(latlon,
lon=None,
datum=None,
Ups=Ups,
pole='',
falsed=True,
strict=True,
name=''):
'''Convert a lat-/longitude point to a UPS coordinate.
@param latlon: Latitude (C{degrees}) or an (ellipsoidal)
geodetic C{LatLon} point.
@keyword lon: Optional longitude (C{degrees}) or C{None}
if B{C{latlon}} is a C{LatLon}.
@keyword datum: Optional datum for this UPS coordinate,
overriding B{C{latlon}}'s datum (C{Datum}).
@keyword Ups: Optional (sub-)class to return the UPS
coordinate (L{Ups}) or C{None}.
@keyword pole: Optional top/center of (stereographic) projection
(C{str}, C{'N[orth]'} or C{'S[outh]'}).
@keyword falsed: False both easting and northing (C{bool}).
@keyword strict: Restrict B{C{lat}} to UPS ranges (C{bool}).
@keyword name: Optional B{C{Ups}} name (C{str}).
@return: The UPS coordinate (B{C{Ups}}) or a
L{UtmUps8Tuple}C{(zone, hemipole, easting, northing,
band, datum, convergence, scale)} if B{C{Ups}} is
C{None}. The C{hemipole} is the C{'N'|'S'} pole,
the UPS projection top/center.
@raise RangeError: If B{C{strict}} and B{C{lat}} outside the
valid UPS bands or if B{C{lat}} or B{C{lon}}
outside the valid range and L{rangerrors}
set to C{True}.
@raise TypeError: If B{C{latlon}} is not ellipsoidal.
@raise ValueError: If B{C{lon}} value is missing or if B{C{latlon}}
is invalid.
@see: Karney's C++ class U{UPS
<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1UPS.html>}.
'''
lat, lon, d, name = _to4lldn(latlon, lon, datum, name)
z, B, p, lat, lon = upsZoneBand5(
lat, lon, strict=strict) # PYCHOK UtmUpsLatLon5Tuple
E = d.ellipsoid
p = str(pole or p)[:1].upper()
N = p == 'N' # is north
a = lat if N else -lat
A = abs(a - 90) < _TOL # at pole
t = tan(radians(a))
T = E.es_taupf(t)
r = hypot1(T) + abs(T)
if T >= 0:
r = 0 if A else 1 / r
k0 = getattr(Ups, '_scale0', _K0) # Ups is class or None
r *= 2 * k0 * E.a / E.es_c
k = k0 if A else _scale(E, r, t)
c = lon # [-180, 180) from .upsZoneBand5
x, y = sincos2d(c)
x *= r
y *= r
if N:
y = -y
else:
c = -c
if falsed:
x += _Falsing
y += _Falsing
if Ups is None:
r = UtmUps8Tuple(z, p, x, y, B, d, c, k)
else:
if z != _UPS_ZONE and not strict:
z = _UPS_ZONE # ignore UTM zone
r = Ups(z,
p,
x,
y,
band=B,
datum=d,
falsed=falsed,
convergence=c,
scale=k)
r._hemisphere = _hemi(lat)
if isinstance(latlon, _LLEB) and d is latlon.datum:
r._latlon_to(latlon, falsed) # XXX weakref(latlon)?
return _xnamed(r, name)
