def toWm(latlon, lon=None, radius=R_MA, Wm=Wm, name=''):
'''Convert a lat-/longitude point to a WM coordinate.
@param latlon: Latitude (C{degrees}) or an (ellipsoidal or
spherical) geodetic C{LatLon} point.
@keyword lon: Optional longitude (C{degrees} or C{None}).
@keyword radius: Optional earth radius (C{meter}).
@keyword Wm: Optional (sub-)class for the WM coordinate
(L{Wm}) or C{None}.
@keyword name: Optional name (C{str}).
@return: The WM coordinate (L{Wm}) or 3-tuple (easting,
northing, radius) if I{Wm} is C{None}.
@raise ValueError: If I{lon} value is missing, if I{latlon}
is not scalar, if I{latlon} is beyond the
valid WM range and L{rangerrors} is set
to C{True} or if I{radius} is invalid.
@example:
>>> p = LatLon(48.8582, 2.2945) # 448251.8 5411932.7
>>> w = toWm(p) # 448252 5411933
>>> p = LatLon(13.4125, 103.8667) # 377302.4 1483034.8
>>> w = toWm(p) # 377302 1483035
'''
r, e = radius, None
try:
lat, lon = latlon.lat, latlon.lon
if isinstance(latlon, _ELLB):
r = latlon.datum.ellipsoid.a
e = latlon.datum.ellipsoid.e
if not name: # use latlon.name
name = _nameof(latlon) or name # PYCHOK no effect
lat = clipDMS(lat, _LatLimit)
except AttributeError:
lat, lon = parseDMS2(latlon, lon, clipLat=_LatLimit)
s = sin(radians(lat))
y = atanh(s) # == log(tan((90 + lat) / 2)) == log(tanPI_2_2(radians(lat)))
if e:
y -= e * atanh(e * s)
e, n = r * radians(lon), r * y
return (e, n, r) if Wm is None else _xnamed(Wm(e, n, radius=r), name)
def toCss(latlon, cs0=_CassiniSoldner0, height=None, Css=Css, name=''):
'''Convert an (ellipsoidal) geodetic point to a Cassini-Soldner location.
@param latlon: Ellipsoidal point (C{LatLon}).
@keyword cs0: Optional, the Cassini-Soldner projection to use
(L{CassiniSoldner}).
@keyword height: Optional height for the point, overriding
the default height (C{meter}).
@keyword Css: Optional (sub-)class to return the location
(L{Css}) or C{None}.
@keyword name: Optional I{Css} name (C{str}).
@return: The Cassini-Soldner location (L{Css}) or 3-tuple
(C{easting, northing, height}) if I{Css} is C{None}.
@raise ImportError: Package U{GeographicLib<http://PyPI.org/
project/geographiclib>} missing.
@raise TypeError: If I{latlon} is not ellipsoidal.
'''
if not isinstance(latlon, _LLEB):
raise TypeError('%s not %s: %r' % ('latlon', 'ellipsoidal', latlon))
cs = _CassiniSoldner(cs0)
C, E = cs.datum.ellipsoid, latlon.datum.ellipsoid
if C.a != E.a or C.f != E.f:
raise ValueError('%s mistmatch %r vs %r' % ('ellipsoidal', C, E))
e, n, z, rk = cs.forward4(latlon.lat, latlon.lon)
h = latlon.height if height is None else height
if Css is None:
r = e, n, h
else:
r = _xnamed(Css(e, n, h=h, cs0=cs), name or _nameof(latlon))
r._latlon = latlon.lat, latlon.lon
r._azi, r._rk = z, rk
return r
def toOsgr(latlon, lon=None, datum=Datums.WGS84, Osgr=Osgr, name=''):
'''Convert a lat-/longitude point to an OSGR coordinate.
@param latlon: Latitude (C{degrees}) or an (ellipsoidal)
geodetic C{LatLon} point.
@keyword lon: Optional longitude in degrees (scalar or C{None}).
@keyword datum: Optional datum to convert (C{Datum}).
@keyword Osgr: Optional (sub-)class to return the OSGR
coordinate (L{Osgr}) or C{None}.
@keyword name: Optional I{Osgr} name (C{str}).
@return: The OSGR coordinate (L{Osgr}) or 2-tuple (easting,
northing) if I{Osgr} is C{None}.
@raise TypeError: Non-ellipsoidal I{latlon} or I{datum}
conversion failed.
@raise ValueError: Invalid I{latlon} or I{lon}.
@example:
>>> p = LatLon(52.65798, 1.71605)
>>> r = toOsgr(p) # TG 51409 13177
>>> # for conversion of (historical) OSGB36 lat-/longitude:
>>> r = toOsgr(52.65757, 1.71791, datum=Datums.OSGB36)
'''
if not isinstance(latlon, _LLEB):
# XXX fix failing _LLEB.convertDatum()
latlon = _LLEB(*parseDMS2(latlon, lon), datum=datum)
elif lon is not None:
raise ValueError('%s not %s: %r' % ('lon', None, lon))
elif not name: # use latlon.name
name = _nameof(latlon) or name # PYCHOK no effect
E = _OSGB36.ellipsoid
ll = _ll2datum(latlon, _OSGB36, 'latlon')
a, b = map1(radians, ll.lat, ll.lon)
sa, ca = sincos2(a)
s = E.e2s2(sa)
v = E.a * _F0 / sqrt(s) # nu
r = s / E.e12 # nu / rho == v / (v * E.e12 / s)
x2 = r - 1 # η2
ta = tan(a)
ca3, ca5 = fpowers(ca, 5, 3) # PYCHOK false!
ta2, ta4 = fpowers(ta, 4, 2) # PYCHOK false!
vsa = v * sa
I4 = (E.b * _F0 * _M(E.Mabcd, a) + _N0, (vsa / 2) * ca,
(vsa / 24) * ca3 * fsum_(5, -ta2, 9 * x2),
(vsa / 720) * ca5 * fsum_(61, ta4, -58 * ta2))
V4 = (_E0, (v * ca), (v / 6) * ca3 * (r - ta2), (v / 120) * ca5 * fdot(
(-18, 1, 14, -58), ta2, 5 + ta4, x2, ta2 * x2))
d, d2, d3, d4, d5, d6 = fpowers(b - _B0, 6) # PYCHOK false!
n = fdot(I4, 1, d2, d4, d6)
e = fdot(V4, 1, d, d3, d5)
return (e, n) if Osgr is None else _xnamed(Osgr(e, n), name)
def toUtm(latlon, lon=None, datum=None, Utm=Utm, name='', cmoff=True):
'''Convert a lat-/longitude point to a UTM coordinate.
@param latlon: Latitude (C{degrees}) or an (ellipsoidal)
geodetic C{LatLon} point.
@keyword lon: Optional longitude (C{degrees} or C{None}).
@keyword datum: Optional datum for this UTM coordinate,
overriding I{latlon}'s datum (C{Datum}).
@keyword Utm: Optional (sub-)class to use for the UTM
coordinate (L{Utm}) or C{None}.
@keyword name: Optional I{Utm} name (C{str}).
@keyword cmoff: Offset longitude from zone's central meridian,
apply false easting and false northing (C{bool}).
@return: The UTM coordinate (L{Utm}) or a 6-tuple (zone, easting,
northing, band, convergence, scale) if I{Utm} is C{None}
or I{cmoff} is C{False}.
@raise TypeError: If I{latlon} is not ellipsoidal.
@raise RangeError: If I{lat} is outside the valid UTM bands or if
I{lat} or I{lon} outside the valid range and
I{rangerrrors} set to C{True}.
@raise ValueError: If I{lon} value is missing or if I{latlon}
is invalid.
@note: Implements Karney’s method, using 8-th order Krüger series,
giving results accurate to 5 nm (or better) for distances
up to 3900 km from the central meridian.
@example:
>>> p = LatLon(48.8582, 2.2945) # 31 N 448251.8 5411932.7
>>> u = toUtm(p) # 31 N 448252 5411933
>>> p = LatLon(13.4125, 103.8667) # 48 N 377302.4 1483034.8
>>> u = toUtm(p) # 48 N 377302 1483035
'''
try:
lat, lon = latlon.lat, latlon.lon
if not isinstance(latlon, _LLEB):
raise TypeError('%s not %s: %r' %
('latlon', 'ellipsoidal', latlon))
if not name: # use latlon.name
name = _nameof(latlon) or name # PYCHOK no effect
d = datum or latlon.datum
except AttributeError:
lat, lon = parseDMS2(latlon, lon)
d = datum or Datums.WGS84
E = d.ellipsoid
z, B, a, b = _toZBab4(lat, lon, cmoff)
# easting, northing: Karney 2011 Eq 7-14, 29, 35
cb, sb, tb = cos(b), sin(b), tan(b)
T = tan(a)
T12 = hypot1(T)
S = sinh(E.e * atanh(E.e * T / T12))
T_ = T * hypot1(S) - S * T12
H = hypot(T_, cb)
y = atan2(T_, cb) # ξ' ksi
x = asinh(sb / H) # η' eta
A0 = _K0 * E.A
Ks = _Kseries(E.AlphaKs, x, y) # Krüger series
y = Ks.ys(y) * A0 # ξ
x = Ks.xs(x) * A0 # η
if cmoff:
# C.F.F. Karney, "Test data for the transverse Mercator projection (2009)",
# <http://GeographicLib.SourceForge.io/html/transversemercator.html> and
# <http://Zenodo.org/record/32470#.W4LEJS2ZON8>
x += _FalseEasting # make x relative to false easting
if y < 0:
y += _FalseNorthing # y relative to false northing in S
# convergence: Karney 2011 Eq 23, 24
p_ = Ks.ps(1)
q_ = Ks.qs(0)
c = degrees(atan(T_ / hypot1(T_) * tb) + atan2(q_, p_))
# scale: Karney 2011 Eq 25
s = E.e2s(sin(a)) * T12 / H * (A0 / E.a * hypot(p_, q_))
if cmoff and Utm is not None:
h = 'S' if a < 0 else 'N' # hemisphere
return _xnamed(
Utm(z, h, x, y, band=B, datum=d, convergence=c, scale=s), name)
else: # zone, easting, northing, band, convergence and scale
return z, x, y, B, c, s