def rescale0(self, lat, scale0=_K0):
'''Set the central scale factor for this UPS projection.
@param lat: Northern latitude (C{degrees}).
@param scale0: UPS k0 scale at B{C{lat}} latitude (C{scalar}).
@raise RangeError: If B{C{lat}} outside the valid range
and L{rangerrors} set to C{True}.
@raise ValueError: Invalid B{C{scale}}.
'''
try:
s0 = float(scale0)
if not 0 < s0: # <= 1.003 or 1.0016?
raise ValueError
except (TypeError, ValueError):
raise ValueError('%s invalid: %r' % ('scale', scale0))
lat = clipDMS(lat, 90) # clip and force N
u = toUps8(abs(lat), 0, datum=self.datum, Ups=_UpsK1)
k = s0 / u.scale
if self.scale0 != k:
self._band = '' # force re-compute
self._latlon = self._epsg = self._mgrs = self._utm = None
self._scale0 = k
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 degrees2m(deg, radius=R_M, lat=0):
'''Convert angle to distance along the equator or along a
parallel at an other latitude.
@param deg: Angle (C{degrees}).
@keyword radius: Mean earth radius (C{meter}).
@keyword lat: Parallel latitude (C{degrees90}).
@return: Distance (C{meter}, same units as B{C{radius}}).
@raise RangeError: Latitude B{C{lat}} outside valid range
and L{rangerrors} set to C{True}.
'''
m = radians(deg) * radius
if lat:
from pygeodesy.dms import clipDMS
m *= cos(radians(clipDMS(lat, 90)))
return m