# Coverage for pygeodesy/albers.py : 95%

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Classes L{AlbersEqualArea}, L{AlbersEqualArea2}, L{AlbersEqualArea4}, L{AlbersEqualAreaCylindrical}, L{AlbersEqualAreaNorth}, L{AlbersEqualAreaSouth} and L{AlbersError}, transcoded from I{Charles Karney}'s C++ class U{AlbersEqualArea <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1AlbersEqualArea.html>}. See also I{Albers Equal-Area Conic Projection} in U{John P. Snyder, "Map Projections -- A Working Manual", 1987<https://Pubs.USGS.gov/pp/1395/report.pdf>}, pp 98-106 and the Albers Conical Equal-Area examples on pp 291-294. ''' # make sure int/int division yields float quotient, see .basics from __future__ import division as _; del _ # PYCHOK semicolon from pygeodesy.basics import copysign0, neg from pygeodesy.datums import _ellipsoidal_datum, _WGS84 from pygeodesy.errors import _ValueError, _xkwds from pygeodesy.fmath import Fsum, fsum_, hypot, hypot1, sqrt3 from pygeodesy.interns import EPS0, EPS02, NN, _EPSqrt as _TOL, _datum_, \ _gamma_, _lat_, _lat1_, _lat2_, _lon_, _no_, \ _scale_, _x_, _y_, _0_0, _0_5, _1_0, _N_1_0, \ _2_0, _N_2_0, _3_0, _90_0, _N_90_0 from pygeodesy.karney import _diff182, _norm180 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY from pygeodesy.named import _NamedBase, _NamedTuple, _Pass from pygeodesy.props import deprecated_Property_RO, Property_RO, \ property_RO from pygeodesy.streprs import Fmt from pygeodesy.units import Bearing, Float_, Lat, Lat_, Lon, Lon_, \ Meter, Scalar_ from pygeodesy.utily import atand, atan2d, degrees360, sincos2, \ sincos2d, sincos2d_ from math import atan, atan2, atanh, degrees, radians, sqrt __all__ = _ALL_LAZY.albers __version__ = '21.11.30' _NUMIT = 8 # XXX 4? _NUMIT0 = 41 # XXX 21? _TERMS = 21 # XXX 9? _TOL0 = sqrt3(_TOL) class AlbersError(_ValueError): '''An L{AlbersEqualArea}, L{AlbersEqualArea2}, L{AlbersEqualArea4}, L{AlbersEqualAreaCylindrical}, L{AlbersEqualAreaNorth}, L{AlbersEqualAreaSouth} or L{Albers7Tuple} issue. ''' pass def _Dsn(x, y, sx, sy): '''(INTERNAL) Divided differences, defined as M{Df(x, y) = (f(x) - f(y)) / (x - y)} with M{sn(x) = x / sqrt(1 + x^2)}: M{Dsn(x, y) = (x + y) / ((sn(x) + sn(y)) * (1 + x^2) * (1 + y^2))}. @see: U{W. M. Kahan and R. J. Fateman, "Sympbolic Computation of Divided Differences"<https://People.EECS.Berkeley.EDU/~fateman/papers/divdiff.pdf>}, U{ACM SIGSAM Bulletin 33(2), 7-28 (1999)<https://DOI.org/10.1145/334714.334716>} and U{AlbersEqualArea.hpp <https://GeographicLib.SourceForge.io/html/AlbersEqualArea_8hpp_source.html>}. ''' # sx = x / hypot1(x) d, t = _1_0, (x * y) if t > 0: s = sx + sy if s: d = (x + y) * ((sx * sy) / t)**2 / s else: t = x - y if t: d = (sx - sy) / t return d def _Ks(**name_k): '''(INTERNAL) Scale C{B{k} >= EPS0}. ''' return Scalar_(Error=AlbersError, low=EPS0, **name_k) # > 0 def _Lat(*lat, **Error_name_lat): '''(INTERNAL) Latitude C{-90 <= B{lat} <= 90}. ''' kwds = _xkwds(Error_name_lat, Error=AlbersError) return Lat_(*lat, **kwds) def _Lon(*lon, **Error_name_lon): '''(INTERNAL) Longitude C{-180 <= B{lon} <= 180}. ''' kwds = _xkwds(Error_name_lon, Error=AlbersError) return Lon_(*lon, **kwds) def _tol(tol, x): '''(INTERNAL) Converge tolerance. ''' return tol * max(_1_0, abs(x)) class _AlbersBase(_NamedBase): '''(INTERNAL) Base class for C{AlbersEqualArea...} projections. @see: I{Karney}'s C++ class U{AlbersEqualArea<https://GeographicLib.SourceForge.io/ html/classGeographicLib_1_1AlbersEqualArea.html>}, method C{Init}. ''' _datum = _WGS84 _iteration = None _k0 = None # scale _k0n0 = None # (INTERNAL) k0 * no _k02 = None # (INTERNAL) k0**2 _k02n0 = None # (INTERNAL) k02 * n0 _lat0 = None # lat origin _lat1 = None # let 1st parallel _lat2 = None # lat 2nd parallel _m0 = _0_0 # if polar else sqrt(m02) _m02 = None # (INTERNAL) cached _n0 = None # (INTERNAL) cached _nrho0 = _0_0 # if polar else m0 * E.a _polar = False _qx = None # (INTERNAL) cached _qZ = None # (INTERNAL) cached _qZa2 = None # (INTERNAL) qZ * E.a**2 _scxi0 = None # (INTERNAL) sec(xi) _sign = +1 _sxi0 = None # (INTERNAL) sin(xi) _txi0 = None # (INTERNAL) tan(xi) def __init__(self, sa1, ca1, sa2, ca2, k, datum, name): '''(INTERNAL) New C{AlbersEqualArea...} instance. ''' if datum not in (None, self._datum): self._datum = _ellipsoidal_datum(datum, name=name) if name: self.name = name E = self.datum.ellipsoid b_a = E.b_a # fm = 1 - E.f e2 = E.e2 e12 = E.e12 # e2m = 1 - E.e2 self._qZ = qZ = _1_0 + e12 * self._atanhee(1) self._qZa2 = qZ * E.a2 self._qx = qZ / (_2_0 * e12) c = min(ca1, ca2) if c < 0: raise AlbersError(clat1=ca1, clat2=ca2) polar = c < EPS0 # == 0 # determine hemisphere of tangent latitude if sa1 < 0: # and sa2 < 0: self._sign = -1 # internally, tangent latitude positive sa1, sa2 = -sa1, neg(sa2) if sa1 > sa2: # make phi1 < phi2 sa1, sa2 = sa2, sa1 ca1, ca2 = ca2, ca1 if sa1 < 0: # or sa2 < 0: raise AlbersError(slat1=sa1, slat2=sa2) # avoid singularities at poles ca1, ca2 = max(EPS0, ca1), max(EPS0, ca2) ta1, ta2 = sa1 / ca1, sa2 / ca2 par1 = abs(ta1 - ta2) < EPS02 # ta1 == ta2 if par1 or polar: C, ta0 = _1_0, ta2 else: s1_qZ, C = self._s1_qZ_C2(ca1, sa1, ta1, ca2, sa2, ta2) ta0 = (ta2 + ta1) * _0_5 Ta0 = Fsum(ta0) tol = _tol(_TOL0, ta0) for self._iteration in range(1, _NUMIT0): ta02 = ta0**2 sca02 = ta02 + _1_0 sca0 = sqrt(sca02) sa0 = ta0 / sca0 sa01 = sa0 + _1_0 sa02 = sa0**2 # sa0m = 1 - sa0 = 1 / (sec(a0) * (tan(a0) + sec(a0))) sa0m = _1_0 / (sca0 * (ta0 + sca0)) # scb0^2 * sa0 g = (_1_0 + (b_a * ta0)**2) * sa0 dg = e12 * sca02 * (_1_0 + 2 * ta02) + e2 D = sa0m * (_1_0 - e2 * (_1_0 + sa01 * 2 * sa0)) / (e12 * sa01) # dD/dsa0 dD = -2 * (_1_0 - e2 * sa02 * (_3_0 + 2 * sa0)) / (e12 * sa01**2) sa02_ = _1_0 - e2 * sa02 sa0m_ = sa0m / (_1_0 - e2 * sa0) BA = sa0m_ * (self._atanhx1(e2 * sa0m_**2) * e12 - e2 * sa0m) \ - sa0m**2 * e2 * (2 + (_1_0 + e2) * sa0) / (e12 * sa02_) # == B + A dAB = 2 * e2 * (2 - e2 * (_1_0 + sa02)) / (e12 * sa02_**2 * sca02) u_du = fsum_(s1_qZ * g, -D, g * BA) \ / fsum_(s1_qZ * dg, -dD, dg * BA, g * dAB) # == u/du ta0, d = Ta0.fsum2_(-u_du * (sca0 * sca02)) if abs(d) < tol: break else: raise AlbersError(iteration=_NUMIT0, txt=_no_(Fmt.convergence(tol))) self._txi0 = txi0 = self._txif(ta0) self._scxi0 = hypot1(txi0) self._sxi0 = sxi0 = txi0 / self._scxi0 self._m02 = m02 = _1_0 / (_1_0 + (b_a * ta0)**2) self._n0 = n0 = ta0 / hypot1(ta0) if polar: self._polar = True self._nrho0 = self._m0 = _0_0 else: self._m0 = sqrt(m02) # == nrho0 / E.a self._nrho0 = E.a * self._m0 # == E.a * sqrt(m02) self._k0_(_1_0 if par1 else (k * sqrt(C / (m02 + n0 * qZ * sxi0)))) self._lat0 = _Lat(lat0=self._sign * atand(ta0)) def _s1_qZ_C2(self, ca1, sa1, ta1, ca2, sa2, ta2): '''(INTERNAL) Compute C{sm1 / (s / qZ)} and C{C} for .__init__. ''' E = self.datum.ellipsoid b_a = E.b_a e2 = E.e2 tb1 = b_a * ta1 tb2 = b_a * ta2 dtb12 = b_a * (tb1 + tb2) scb12 = _1_0 + tb1**2 scb22 = _1_0 + tb2**2 esa1_2 = (_1_0 - e2 * sa1**2) \ * (_1_0 - e2 * sa2**2) esa12 = _1_0 + e2 * sa1 * sa2 dsn = _Dsn(ta2, ta1, sa2, sa1) axi, bxi, sxi = self._a_b_sxi3((ca1, sa1, ta1, scb12), (ca2, sa2, ta2, scb22)) dsxi = (esa12 / esa1_2 + self._Datanhee(sa2, sa1)) * dsn / (_2_0 * self._qx) C = fsum_(sxi * dtb12 / dsxi, scb22, scb12) / (_2_0 * scb22 * scb12) sa12 = fsum_(sa1, sa2, sa1 * sa2) axi *= (_1_0 + e2 * sa12) / (_1_0 + sa12) bxi *= e2 * fsum_(sa1, sa2, esa12) / esa1_2 + E.e12 * self._D2atanhee(sa1, sa2) s1_qZ = dsn * (axi * self._qZ - bxi) / (_2_0 * dtb12) return s1_qZ, C def _a_b_sxi3(self, *ca_sa_ta_scb_4s): '''(INTERNAL) Sum of C{sm1} terms and C{sin(xi)}s for ._s1_qZ_C2. ''' a = b = s = _0_0 for ca, sa, ta, scb in ca_sa_ta_scb_4s: cxi, sxi, _ = self._cstxif3(ta) if sa > 0: sa += _1_0 a += (cxi / ca)**2 * sa / (_1_0 + sxi) b += scb * ca**2 / sa else: sa = _1_0 - sa a += (_1_0 - sxi) / sa b += scb * sa s += sxi return a, b, s @Property_RO def datum(self): '''Get the datum (L{Datum}). ''' return self._datum @Property_RO def equatoradius(self): '''Get the geodesic's equatorial radius, semi-axis (C{meter}). ''' return self.datum.ellipsoid.a @property_RO def iteration(self): '''Get the iteration number (C{int}) or C{None} if not available/applicable. ''' return self._iteration @Property_RO def flattening(self): '''Get the geodesic's flattening (C{float}). ''' return self.datum.ellipsoid.f def forward(self, lat, lon, lon0=0, name=NN): '''Convert a geodetic location to east- and northing. @arg lat: Latitude of the location (C{degrees}). @arg lon: Longitude of the location (C{degrees}). @kwarg lon0: Optional central meridian longitude (C{degrees}). @kwarg name: Optional name for the location (C{str}). @return: An L{Albers7Tuple}C{(x, y, lat, lon, gamma, scale, datum)}. @note: The origin latitude is returned by C{property lat0}. No false easting or northing is added. The value of B{C{lat}} should be in the range C{[-90..90] degrees}. The returned values C{x} and C{y} will be large but finite for points projecting to infinity, i.e. one or both of the poles. ''' E = self.datum.ellipsoid s = self._sign k0 = self._k0 n0 = self._n0 nrho0 = self._nrho0 txi0 = self._txi0 sa, ca = sincos2d(_Lat(lat=lat) * s) ca = max(EPS0, ca) ta = sa / ca _, sxi, txi = self._cstxif3(ta) dq = self._qZ * _Dsn(txi, txi0, sxi, self._sxi0) * (txi - txi0) drho = -E.a * dq / (sqrt(self._m02 - n0 * dq) + self._m0) lon, _ = _diff182(lon0, lon) b = radians(lon) th = self._k02n0 * b sth, cth = sincos2(th) # XXX sin, cos if n0: x = sth / n0 y = ((_1_0 - cth) if cth < 0 else (sth**2 / (_1_0 + cth))) * nrho0 / n0 else: x = self._k02 * b y = _0_0 t = nrho0 + n0 * drho x = t * x / k0 y = s * (y - drho * cth) / k0 g = degrees360(s * th) if t: k0 = self._azik(t, ta) return Albers7Tuple(x, y, lat, lon, g, k0, self.datum, name=name or self.name) @Property_RO def ispolar(self): '''Is this projection polar (C{bool})? ''' return self._polar isPolar = ispolar # synonym @Property_RO def lat0(self): '''Get the latitude of the projection origin (C{degrees}). This is the latitude of minimum azimuthal scale and equals the B{C{lat}} in the 1-parallel L{AlbersEqualArea} and lies between B{C{lat1}} and B{C{lat2}} for the 2-parallel L{AlbersEqualArea2} and L{AlbersEqualArea4} projections. ''' return self._lat0 @Property_RO def lat1(self): '''Get the latitude of the first parallel (C{degrees}). ''' return self._lat1 @Property_RO def lat2(self): '''Get the latitude of the second parallel (C{degrees}). @note: The second and first parallel latitudes are the same instance for 1-parallel C{AlbersEqualArea*} projections. ''' return self._lat2 @deprecated_Property_RO def majoradius(self): # PYCHOK no cover '''DEPRECATED, use property C{equatoradius}.''' return self.equatoradius def rescale0(self, lat, k=1): '''Set the azimuthal scale for this projection. @arg lat: Northern latitude (C{degrees}). @arg k: Azimuthal scale at latitude B{C{lat}} (C{scalar}). @raise AlbersError: Invalid B{C{lat}} or B{C{k}}. @note: This allows a I{latitude of conformality} to be specified. ''' k0 = _Ks(k=k) / self.forward(lat, _0_0).scale self._update(k0 != self._k0) self._k0_(k0) def reverse(self, x, y, lon0=0, name=NN, LatLon=None, **LatLon_kwds): '''Convert an east- and northing location to geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @kwarg lon0: Optional central meridian longitude (C{degrees}). @kwarg name: Optional name for the location (C{str}). @kwarg LatLon: Class to use (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Albers7Tuple}C{(x, y, lat, lon, gamma, scale, datum)}. @note: The origin latitude is returned by C{property lat0}. No false easting or northing is added. The returned value of C{lon} is in the range C{[-180..180] degrees} and C{lat} is in the range C{[-90..90] degrees}. If the given B{C{x}} or B{C{y}} point is outside the valid projected space the nearest pole is returned. ''' x = Meter(x=x) y = Meter(y=y) k0 = self._k0 n0 = self._n0 k0n0 = self._k0n0 nrho0 = self._nrho0 txi0 = self._txi0 y_ = self._sign * y nx = k0n0 * x ny = k0n0 * y_ y1 = nrho0 - ny drho = den = nrho0 + hypot(nx, y1) # 0 implies origin with polar aspect if den: drho = fsum_(x * nx, _N_2_0 * y_ * nrho0, y_ * ny) * k0 / den # dsxia = scxi0 * dsxi dsxia = -self._scxi0 * (_2_0 * nrho0 + n0 * drho) * drho / self._qZa2 t = _1_0 - dsxia * (_2_0 * txi0 + dsxia) txi = (txi0 + dsxia) / (sqrt(t) if t > EPS02 else EPS0) ta = self._tanf(txi) lat = atand(ta * self._sign) th = atan2(nx, y1) lon = degrees(th / self._k02n0 if n0 else x / (y1 * k0)) if lon0: lon += _norm180(lon0) lon = _norm180(lon) if LatLon is None: g = degrees360(self._sign * th) if den: k0 = self._azik(nrho0 + n0 * drho, ta) r = Albers7Tuple(x, y, lat, lon, g, k0, self.datum, name=name or self.name) else: kwds = _xkwds(LatLon_kwds, datum=self.datum) r = self._xnamed(LatLon(lat, lon, **kwds), name=name) return r @Property_RO def scale0(self): '''Get the central scale for the projection (C{float}). This is the azimuthal scale on the latitude of origin of the projection, see C{property lat0}. ''' return self._k0 def _atanhee(self, x): '''(INTERNAL) Function M{atanhee(x)}, defined as ... atanh( E.e * x) / E.e if f > 0 # oblate atan (sqrt(-E.e2) * x) / sqrt(-E.e2) if f < 0 # prolate x if f = 0. ''' E = self.datum.ellipsoid if E.isOblate: x = atanh(x * E.e) / E.e elif E.isProlate: x = atan2(abs(x) * E.e, copysign0(_1_0, x)) / E.e return x def _atanhx1(self, x): '''(INTERNAL) Function M{atanh(sqrt(x)) / sqrt(x) - 1}. ''' s = abs(x) if s < _0_5: # for typical ... # x < E.e^2 = 2 * E.f use ... # x / 3 + x^2 / 5 + x^3 / 7 + ... y, k = x, 3 S = Fsum(y / k) for _ in range(_TERMS): y *= x # x**n k += 2 # 2*n + 1 s, d = S.fsum2_(y / k) if not d: break else: s = sqrt(s) s = (atanh(s) if x > 0 else atan(s)) / s - _1_0 return s def _azik(self, t, ta): '''(INTERNAL) Compute the azimuthal scale C{_Ks(k0=k0)}. ''' E = self.datum.ellipsoid return _Ks(k=self._k0 * t * hypot1(E.b_a * ta) / E.a) def _cstxif3(self, ta): '''(INTERNAL) Get 3-tuple C{(cos, sin, tan)} of M{xi(ta)}. ''' t = self._txif(ta) c = _1_0 / hypot1(t) s = c * t return c, s, t def _Datanhee(self, x, y): '''(INTERNAL) Function M{Datanhee(x, y)}, defined as M{atanhee((x - y) / (1 - E.e^2 * x * y)) / (x - y)}. ''' e2 = self.datum.ellipsoid.e2 d = _1_0 - e2 * x * y if d: d = _1_0 / d t = x - y if t: d = self._atanhee(t * d) / t else: raise AlbersError(x=x, y=y, txt=_AlbersBase._Datanhee.__name__) return d def _D2atanhee(self, x, y): '''(INTERNAL) Function M{D2atanhee(x, y)}, defined as M{(Datanhee(1, y) - Datanhee(1, x)) / (y - x)}. ''' e2 = self.datum.ellipsoid.e2 if (abs(x) + abs(y)) * e2 < _0_5: e = z = _1_0 k = 1 C = Fsum() S = Fsum() T = Fsum() # Taylor expansion for _ in range(_TERMS): T *= y; p = T.fsum_(z); z *= x # PYCHOK ; T *= y; t = T.fsum_(z); z *= x # PYCHOK ; e *= e2 k += 2 s, d = S.fsum2_(e * C.fsum_(p, t) / k) if not d: break elif (_1_0 - x): s = (self._Datanhee(_1_0, y) - self._Datanhee(x, y)) / (_1_0 - x) else: raise AlbersError(x=x, y=y, txt=_AlbersBase._D2atanhee.__name__) return s def _k0_(self, k): '''(INTERNAL) Set C{._k0}, C{._k02}, etc. ''' self._k0 = k = _Ks(k0=k) self._k02 = k2 = k**2 self._k0n0 = k * self._n0 self._k02n0 = k2 * self._n0 def _tanf(self, txi): # called by .Ellipsoid.auxAuthalic '''(INTERNAL) Function M{tan-phi from tan-xi}. ''' tol = _tol(_TOL, txi) e2 = self.datum.ellipsoid.e2 qx = self._qx ta = txi Ta = Fsum(ta) for self._iteration in range(1, _NUMIT): # max 2, mean 1.99 # dtxi/dta = (scxi / sca)^3 * 2 * (1 - e^2) / (qZ * (1 - e^2 * sa^2)^2) ta2 = ta**2 sca2 = ta2 + _1_0 txia = self._txif(ta) s3qx = sqrt3(sca2 / (_1_0 + txia**2)) * qx ta, d = Ta.fsum2_((txi - txia) * s3qx * (_1_0 - e2 * ta2 / sca2)**2) if abs(d) < tol: return ta raise AlbersError(iteration=_NUMIT, txt=_no_(Fmt.convergence(tol))) def _txif(self, ta): # called from .Ellipsoid.auxAuthalic '''(INTERNAL) Function M{tan-xi from tan-phi}. ''' E = self.datum.ellipsoid ca2 = _1_0 / (_1_0 + ta**2) sa = sqrt(ca2) * abs(ta) # enforce odd parity es1 = E.e2 * sa es2m1 = _1_0 - sa * es1 sp1 = _1_0 + sa es1p1 = sp1 / (_1_0 + es1) es1m1 = sp1 * (_1_0 - es1) es2m1a = es2m1 * E.e12 # e2m s = sqrt((ca2 / (es1p1 * es2m1a) + self._atanhee(ca2 / es1m1)) * (es1m1 / es2m1a + self._atanhee(es1p1))) t = (sa / es2m1 + self._atanhee(sa)) / s if ta < 0: t = neg(t) return t class AlbersEqualArea(_AlbersBase): '''An Albers equal-area (authalic) projection with a single standard parallel. @see: L{AlbersEqualArea2} and L{AlbersEqualArea4}. ''' def __init__(self, lat, k0=1, datum=_WGS84, name=NN): '''New L{AlbersEqualArea} projection. @arg lat: Standard parallel (C{degrees}). @kwarg k0: Azimuthal scale on the standard parallel (C{scalar}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg name: Optional name for the projection (C{str}). @raise AlbertError: Invalid B{C{lat}}, B{C{k0}} or no convergence. ''' self._lat1 = self._lat2 = lat = _Lat(lat1=lat) args = tuple(sincos2d(lat)) * 2 + (_Ks(k0=k0), datum, name) _AlbersBase.__init__(self, *args) class AlbersEqualArea2(_AlbersBase): '''An Albers equal-area (authalic) projection with two standard parallels. @see: L{AlbersEqualArea} and L{AlbersEqualArea4}. ''' def __init__(self, lat1, lat2, k1=1, datum=_WGS84, name=NN): '''New L{AlbersEqualArea2} projection. @arg lat1: First standard parallel (C{degrees}). @arg lat2: Second standard parallel (C{degrees}). @kwarg k1: Azimuthal scale on the standard parallels (C{scalar}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg name: Optional name for the projection (C{str}). @raise AlbertError: Invalid B{C{lat1}}m B{C{lat2}}, B{C{k1}} or no convergence. ''' self._lat1, self._lat2 = lats = _Lat(lat1=lat1), _Lat(lat2=lat2) args = tuple(sincos2d_(*lats)) + (_Ks(k1=k1), datum, name) _AlbersBase.__init__(self, *args) class AlbersEqualArea4(_AlbersBase): '''An Albers equal-area (authalic) projection specified by the C{sin} and C{cos} of both standard parallels. @see: L{AlbersEqualArea} and L{AlbersEqualArea2}. ''' def __init__(self, slat1, clat1, slat2, clat2, k1=1, datum=_WGS84, name=NN): '''New L{AlbersEqualArea4} projection. @arg slat1: Sine of first standard parallel (C{scalar}). @arg clat1: Cosine of first standard parallel (non-negative C{scalar}). @arg slat2: Sine of second standard parallel (C{scalar}). @arg clat2: Cosine of second standard parallel (non-negative C{scalar}). @kwarg k1: Azimuthal scale on the standard parallels (C{scalar}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg name: Optional name for the projection (C{str}). @raise AlbertError: Negative B{C{clat1}} or B{C{clat2}}, B{C{slat1}} and B{C{slat2}} have opposite signs (hemispheres), invalid B{C{k1}} or no convergence. ''' def _Lat_s_c3(name, s, c): L = Lat_(atan2d(s, c), name=name, Error=AlbersError) r = _1_0 / Float_(hypot(s, c), name=name, Error=AlbersError) return L, s * r, c * r self._lat1, sa1, ca1 = _Lat_s_c3(_lat1_, slat1, clat1) self._lat2, sa2, ca2 = _Lat_s_c3(_lat2_, slat2, clat2) _AlbersBase.__init__(self, sa1, ca1, sa2, ca2, _Ks(k1=k1), datum, name) class AlbersEqualAreaCylindrical(_AlbersBase): '''An L{AlbersEqualArea} projection at C{lat=0} and C{k0=1} degenerating to the cylindrical-equal-area projection. ''' _lat1 = _lat2 = _Lat(lat1=_0_0) def __init__(self, datum=_WGS84, name=NN): '''New L{AlbersEqualAreaCylindrical} projection. @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg name: Optional name for the projection (C{str}). ''' _AlbersBase.__init__(self, _0_0, _1_0, _0_0, _1_0, _1_0, datum, name) class AlbersEqualAreaNorth(_AlbersBase): '''An azimuthal L{AlbersEqualArea} projection at C{lat=90} and C{k0=1} degenerating to the L{azimuthal} L{LambertEqualArea} projection. ''' _lat1 = _lat2 = _Lat(lat1=_90_0) def __init__(self, datum=_WGS84, name=NN): '''New L{AlbersEqualAreaNorth} projection. @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg name: Optional name for the projection (C{str}). ''' _AlbersBase.__init__(self, _1_0, _0_0, _1_0, _0_0, _1_0, datum, name) class AlbersEqualAreaSouth(_AlbersBase): '''An azimuthal L{AlbersEqualArea} projection at C{lat=-90} and C{k0=1} degenerating to the L{azimuthal} L{LambertEqualArea} projection. ''' _lat1 = _lat2 = _Lat(lat1=_N_90_0) def __init__(self, datum=_WGS84, name=NN): '''New L{AlbersEqualAreaSouth} projection. @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg name: Optional name for the projection (C{str}). ''' _AlbersBase.__init__(self, _N_1_0, _0_0, _N_1_0, _0_0, _1_0, datum, name) class Albers7Tuple(_NamedTuple): '''7-Tuple C{(x, y, lat, lon, gamma, scale, datum)}, in C{meter}, C{meter}, C{degrees90}, C{degrees180}, C{degrees360}, C{scalar} and C{Datum} where C{(x, y)} is the projected, C{(lat, lon)} the geodetic location, C{gamma} the meridian convergence at point, the bearing of the y-axis measured clockwise from true North and C{scale} is the azimuthal scale of the projection at point. The radial scale is the reciprocal C{1 / scale}. ''' _Names_ = (_x_, _y_, _lat_, _lon_, _gamma_, _scale_, _datum_) _Units_ = ( Meter, Meter, Lat, Lon, Bearing, _Pass, _Pass) __all__ += _ALL_DOCS(_AlbersBase) # **) MIT License # # Copyright (C) 2016-2022 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.