def latlon(self, latlonh):
'''Set the lat- and longitude and optionally the height.
@param latlonh: New lat-, longitude and height (2- or
3-tuple of C{degrees} and C{meter}).
@raise TypeError: Height of I{latlonh} not C{scalar} or
I{latlonh} not C{list} or C{tuple}.
@raise ValueError: Invalid I{latlonh} or M{len(latlonh)}.
@see: Function L{parse3llh} to parse a I{latlonh} string
into a 3-tuple (lat, lon, h).
'''
if not isinstance(latlonh, (list, tuple)):
raise TypeError('%s invalid: %r' % ('latlonh', latlonh))
if len(latlonh) == 3:
h = scalar(latlonh[2], None, name='latlonh')
elif len(latlonh) != 2:
raise ValueError('%s invalid: %r' % ('latlonh', latlonh))
else:
h = self._height
lat, lon = parseDMS2(latlonh[0], latlonh[1])
self._update(lat != self._lat or
lon != self._lon or h != self._height)
self._lat, self._lon, self._height = lat, lon, h
def upsZoneBand5(lat, lon, strict=True):
'''Return the UTM/UPS zone number, (polar) Band letter, pole and
clipped lat- and longitude for a given location.
@param lat: Latitude in degrees (C{scalar} or C{str}).
@param lon: Longitude in degrees (C{scalar} or C{str}).
@keyword strict: Restrict B{C{lat}} to UPS ranges (C{bool}).
@return: A L{UtmUpsLatLon5Tuple}C{(zone, band, hemipole,
lat, lon)} where C{hemipole} is the C{'N'|'S'} pole,
the UPS projection top/center.
@raise RangeError: If B{C{strict}} and B{C{lat}} in the UTM
and not the UPS range or if B{C{lat}} or
B{C{lon}} outside the valid range and
L{rangerrors} set to C{True}.
@raise ValueError: Invalid B{C{lat}} or B{C{lon}}.
'''
z, lat, lon = _to3zll(*parseDMS2(lat, lon))
if lat < _UPS_LAT_MIN: # includes 30' overlap
z, B, p = _UPS_ZONE, _Band(lat, lon), 'S'
elif lat > _UPS_LAT_MAX: # includes 30' overlap
z, B, p = _UPS_ZONE, _Band(lat, lon), 'N'
elif strict:
x = '%s [%s, %s]' % ('range', _UPS_LAT_MIN, _UPS_LAT_MAX)
raise RangeError('%s inside UTM %s: %s' % ('lat', x, degDMS(lat)))
else:
B, p = '', _hemi(lat)
return UtmUpsLatLon5Tuple(z, B, p, lat, lon)
def __init__(self, lat, lon, height=0, name=''):
'''New C{LatLon}.
@param lat: Latitude (C{degrees} or DMS C{str} with N or S suffix).
@param lon: Longitude (C{degrees} or DMS C{str} with E or W suffix).
@keyword height: Optional height (C{meter} above or below the earth surface).
@keyword name: Optional name (C{str}).
@return: New instance (C{LatLon}).
@raise RangeError: Value of I{lat} or I{lon} outside the valid
range and I{rangerrrors} set to C{True}.
@raise ValueError: Invalid I{lat} or I{lon}.
@example:
>>> p = LatLon(50.06632, -5.71475)
>>> q = LatLon('50°03′59″N', """005°42'53"W""")
'''
self._lat, self._lon = parseDMS2(lat, lon)
if height: # elevation
self._height = scalar(height, None, name='height')
if name:
self.name = name
def upsZoneBand5(lat, lon, strict=True):
'''Return the UTM/UPS zone number, (polar) Band letter, pole and
clipped lat- and longitude for a given location.
@param lat: Latitude in degrees (C{scalar} or C{str}).
@param lon: Longitude in degrees (C{scalar} or C{str}).
@keyword strict: Restrict I{lat} to UPS ranges (C{bool}).
@return: 5-Tuple (C{zone, Band, hemisphere, lat, lon}) as
(C{int, str, 'N'|'S', degrees90, degrees180}) where
C{zone} is always C{0} for UPS and polar C{Band} is
C{""} or C{'A'|'B'|'Y'|'Z'}.
@raise RangeError: If I{strict} and I{lat} in UTM and not UPS
range or if I{lat} or I{lon} outside the valid
range and I{rangerrrors} set to C{True}.
@raise ValueError: Invalid I{lat} or I{lon}.
'''
z, lat, lon = _to3zll(*parseDMS2(lat, lon))
if lat < _UPS_LAT_MIN: # includes 30' overlap
return _UPS_ZONE, _Band(lat, lon), 'S', lat, lon
elif lat > _UPS_LAT_MAX: # includes 30' overlap
return _UPS_ZONE, _Band(lat, lon), 'N', lat, lon
elif strict:
x = '%s [%s, %s]' % ('range', _UPS_LAT_MIN, _UPS_LAT_MAX)
raise RangeError('%s inside UTM %s: %s' % ('lat', x, degDMS(lat)))
return z, '', _hemi(lat), lat, lon
def toOsgr(latlon, lon=None, datum=Datums.WGS84, Osgr=Osgr):
'''Convert a lat-/longitude point to an OSGR coordinate.
@param latlon: Latitude (degrees) or an (ellipsoidal)
geodetic I{LatLon} point.
@keyword lon: Optional longitude in degrees (scalar or None).
@keyword datum: Optional datum to convert (I{Datum}).
@keyword Osgr: Optional Osgr class to use for the
OSGR coordinate (L{Osgr}).
@return: The OSGR coordinate (L{Osgr}).
@raise TypeError: If I{latlon} is not ellipsoidal or if
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, _eLLb):
# XXX fix failing _eLLb.convertDatum()
latlon = _eLLb(*parseDMS2(latlon, lon), datum=datum)
elif lon is not None:
raise ValueError('%s not %s: %r' % ('lon', None, lon))
E = _OSGB36.ellipsoid
ll = _ll2datum(latlon, _OSGB36, 'latlon')
a, b = map1(radians, ll.lat, ll.lon)
ca, sa, ta = cos(a), sin(a), tan(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
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 Osgr(e, n)
def _to4lldn(latlon, lon, datum, name):
'''(INTERNAL) Return 4-tuple (C{lat, lon, datum, name}).
'''
try:
# if lon is not None:
# raise AttributeError
lat, lon = latlon.lat, latlon.lon
if not isinstance(latlon, _LLEB):
raise TypeError('%s not %s: %r' %
('latlon', 'ellipsoidal', latlon))
d = datum or latlon.datum
except AttributeError:
lat, lon = parseDMS2(latlon, lon)
d = datum or Datums.WGS84
return lat, lon, d, (name or nameof(latlon))
def utmZoneBand2(lat, lon):
'''Return the UTM zone number and UTM Band letter for a location.
@param lat: Latitude (C{degrees}) or string.
@param lon: Longitude (C{degrees}) or string.
@return: 2-Tuple (zone, Band) as (int, string).
@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: Invalid I{lat} or I{lon}.
'''
return _toZBab4(*parseDMS2(lat, lon))[:2]
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 to return the WM coordinate
(L{Wm}) or C{None}.
@keyword name: Optional name (C{str}).
@return: The WM coordinate (B{C{Wm}}) or an
L{EasNorRadius3Tuple}C{(easting, northing, radius)}
if B{C{Wm}} is C{None}.
@raise ValueError: If B{C{lon}} value is missing, if B{C{latlon}}
is not scalar, if B{C{latlon}} is beyond the
valid WM range and L{rangerrors} is set
to C{True} or if B{C{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, _LLEB):
r = latlon.datum.ellipsoid.a
e = latlon.datum.ellipsoid.e
if not name: # use latlon.name
name = nameof(latlon)
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
r = EasNorRadius3Tuple(e, n, r) if Wm is None else \
Wm(e, n, radius=r)
return _xnamed(r, name)
def toWm(latlon, lon=None, radius=R_MA, Wm=Wm):
'''Convert a lat-/longitude point to a WM coordinate.
@param latlon: Latitude (degrees) or an (ellipsoidal or
spherical) geodetic I{LatLon} point.
@keyword lon: Optional longitude (degrees or None).
@keyword radius: Optional earth radius (meter).
@keyword Wm: Optional Wm class for the WM coordinate (L{Wm}).
@return: The WM coordinate (L{Wm}).
@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 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
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)
return Wm(r * radians(lon), r * y, radius=r)
def utmZoneBand5(lat, lon, cmoff=False):
'''Return the UTM zone number, Band letter, hemisphere and
(clipped) lat- and longitude for a given location.
@param lat: Latitude in degrees (C{scalar} or C{str}).
@param lon: Longitude in degrees (C{scalar} or C{str}).
@keyword cmoff: Offset longitude from the zone's central
meridian (C{bool}).
@return: A L{UtmUpsLatLon5Tuple}C{(zone, band, hemipole,
lat, lon)} where C{hemipole} is the C{'N'|'S'}
UTM hemisphere.
@raise RangeError: If B{C{lat}} outside the valid UTM bands
or if B{C{lat}} or B{C{lon}} outside the
valid range and L{rangerrors} set to
C{True}.
@raise ValueError: Invalid B{C{lat}} or B{C{lon}}.
'''
lat, lon = parseDMS2(lat, lon)
z, B, lat, lon = _to3zBll(lat, lon, cmoff=cmoff)
return UtmUpsLatLon5Tuple(z, B, _hemi(lat), lat, lon)
def utmZoneBand5(lat, lon, cmoff=False):
'''Return the UTM zone number, Band letter, hemisphere and
clipped lat- and longitude for a given location.
@param lat: Latitude in degrees (C{scalar} or C{str}).
@param lon: Longitude in degrees (C{scalar} or C{str}).
@keyword cmoff: Offset longitude from zone's central meridian
(C{bool}).
@return: 5-Tuple (C{zone, Band, hemisphere, lat, lon}) as
(C{int, str, 'N'|'S', degrees90, degrees180}) where
C{zone} is C{1..60} and C{Band} is C{'C'|'D'..'W'|'X'}
for UTM.
@raise RangeError: If I{lat} 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: Invalid I{lat} or I{lon}.
'''
lat, lon = parseDMS2(lat, lon)
z, B, lat, lon = _to3zBll(lat, lon, cmoff=cmoff)
return z, B, _hemi(lat), lat, lon
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
def _2fll(lat, lon, *unused):
'''(INTERNAL) Convert lat, lon to 2-tuple of floats.
'''
return parseDMS2(lat, lon)
def _2fll(lat, lon, *unused):
'''(INTERNAL) Convert lat, lon.
'''
return parseDMS2(lat, lon)
def _2fllh(lat, lon, height=None):
'''(INTERNAL) Convert lat, lon, height.
'''
return parseDMS2(lat, lon) + (height,)
def toUtm(latlon, lon=None, datum=None, Utm=Utm):
'''Convert a lat-/longitude point to a UTM coordinate.
@note: Implements Karney’s method, using 6-th order Krüger
series, giving results accurate to 5 nm for distances up to
3900 km from the central meridian.
@param latlon: Latitude (degrees) or an (ellipsoidal)
geodetic I{LatLon} point.
@keyword lon: Optional longitude (degrees or None).
@keyword datum: Optional datum for this UTM coordinate,
overriding latlon's datum (I{Datum}).
@keyword Utm: Optional I{Utm} class to usefor the UTM
coordinate (L{Utm}).
@return: The UTM coordinate (L{Utm}).
@raise TypeError: If I{latlon} is not ellipsoidal.
@raise ValueError: If I{lon} value is missing, if I{latlon}
is not scalar or I{latlon} is outside
the valid UTM bands.
@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, _eLLb):
raise TypeError('%s not %s: %r' %
('latlon', 'ellipsoidal', latlon))
d = datum or latlon.datum
except AttributeError:
lat, lon = parseDMS2(latlon, lon)
d = datum or Datums.WGS84
E = d.ellipsoid
z, B, a, b = _toZBll(lat, lon)
h = 'S' if a < 0 else 'N' # hemisphere
# 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
A6 = _K6s(E.Alpha6, x, y) # 6th-order Krüger series, 1-origin
y = A6.ys(y) * A0 # ξ
x = A6.xs(x) * A0 # η
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_ = A6.ps(1)
q_ = A6.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_))
return Utm(z, h, x, y, band=B, datum=d, convergence=c, scale=s)
