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Pure Python implementation of UTM / WGS-84 conversion functions using an ellipsoidal earth model, transcribed from JavaScript originals by I{(C) Chris Veness 2011-2016} published under the same MIT Licence**, see U{UTM<https://www.Movable-Type.co.UK/scripts/latlong-utm-mgrs.html>} and U{Module utm<https://www.Movable-Type.co.UK/scripts/geodesy/docs/module-utm.html>}. The U{UTM<https://WikiPedia.org/wiki/Universal_Transverse_Mercator_coordinate_system>} system is a 2-dimensional Cartesian coordinate system providing another way to identify locations on the surface of the earth. UTM is a set of 60 transverse Mercator projections, normally based on the WGS-84 ellipsoid. Within each zone, coordinates are represented as B{C{easting}}s and B{C{northing}}s, measured in metres. This module includes some of Charles Karney's U{'Transverse Mercator with an accuracy of a few nanometers'<https://Arxiv.org/pdf/1002.1417v3.pdf>}, 2011 (building on Krüger's U{'Konforme Abbildung des Erdellipsoids in der Ebene' <https://bib.GFZ-Potsdam.DE/pub/digi/krueger2.pdf>}, 1912) and C++ class U{TransverseMercator <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1TransverseMercator.html>}. Some other references are U{Universal Transverse Mercator coordinate system <https://WikiPedia.org/wiki/Universal_Transverse_Mercator_coordinate_system>}, U{Transverse Mercator Projection<https://GeographicLib.SourceForge.io/tm.html>} and Henrik Seidel U{'Die Mathematik der Gauß-Krueger-Abbildung' <https://Henrik-Seidel.GMXhome.DE/gausskrueger.pdf>}, 2006. @newfield example: Example, Examples ''' from pygeodesy.datum import Datums from pygeodesy.dms import degDMS, parseDMS2, _parseUTMUPS, RangeError from pygeodesy.fmath import EPS, fdot3, Fsum, hypot, hypot1, len2, map2 from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import EasNor2Tuple, UtmUps5Tuple, UtmUps8Tuple, \ UtmUpsLatLon5Tuple, _xnamed from pygeodesy.utily import degrees90, degrees180, property_RO, sincos2 # splice from pygeodesy.utmupsBase import _LLEB, _hemi, _to4lldn, _to3zBhp, _to3zll, \ _UTM_LAT_MAX, _UTM_LAT_MIN, \ _UTM_ZONE_MIN, _UTM_ZONE_MAX, \ _UTM_ZONE_OFF_MAX, UtmUpsBase from math import asinh, atan, atanh, atan2, cos, cosh, \ degrees, radians, sin, sinh, tan, tanh from operator import mul # all public contants, classes and functions __all__ = _ALL_LAZY.utm __version__ = '20.02.22' # Latitude bands C..X of 8° each, covering 80°S to 84°N with X repeated # for 80-84°N _Bands = 'CDEFGHJKLMNPQRSTUVWXX' #: (INTERNAL) Latitude bands. _FalseEasting = 500e3 #: (INTERNAL) False (C{meter}). _FalseNorthing = 10000e3 #: (INTERNAL) False (C{meter}). _K0 = 0.9996 #: (INTERNAL) UTM scale central meridian. class UTMError(ValueError): '''Universal Transverse Mercator (UTM parse or other L{Utm} issue. ''' pass class _Kseries(object): '''(INTERNAL) Alpha or Beta Krüger series. Krüger series summations for B{C{eta}}, B{C{ksi}}, B{C{p}} and B{C{q}}, caching the C{cos}, C{cosh}, C{sin} and C{sinh} values for the given B{C{eta}} and B{C{ksi}} angles (in C{radians}). ''' def __init__(self, AB, x, y): '''(INTERNAL) New Alpha or Beta Krüger series @param AB: Krüger Alpha or Beta series coefficients (C{4-, 6- or 8-tuple}). @param x: Eta angle (C{radians}). @param y: Ksi angle (C{radians}). ''' n, j2 = len2(range(2, len(AB) * 2 + 1, 2)) self._ab = AB self._pq = map2(mul, j2, self._ab) # assert len(self._ab) == len(self._pq) == n x2 = map2(mul, j2, (x,) * n) self._chx = map2(cosh, x2) self._shx = map2(sinh, x2) # assert len(x2) == len(self._chx) == len(self._shx) == n y2 = map2(mul, j2, (y,) * n) self._cy = map2(cos, y2) self._sy = map2(sin, y2) # self._sy, self._cy = splice(sincos2(*y2)) # PYCHOK false # assert len(y2) == len(self._cy) == len(self._sy) == n def xs(self, x0): '''(INTERNAL) Eta summation (C{float}). ''' return fdot3(self._ab, self._cy, self._shx, start=x0) def ys(self, y0): '''(INTERNAL) Ksi summation (C{float}). ''' return fdot3(self._ab, self._sy, self._chx, start=y0) def ps(self, p0): '''(INTERNAL) P summation (C{float}). ''' return fdot3(self._pq, self._cy, self._chx, start=p0) def qs(self, q0): '''(INTERNAL) Q summation (C{float}). ''' return fdot3(self._pq, self._sy, self._shx, start=q0) def _cmlon(zone): '''(INTERNAL) Central meridian longitude (C{degrees180}). ''' return (zone * 6) - 183 def _false2(e, n, h): '''(INTERNAL) False easting and northing. ''' # Karney, "Test data for the transverse Mercator projection (2009)" # <https://GeographicLib.SourceForge.io/html/transversemercator.html> # and <https://Zenodo.org/record/32470#.W4LEJS2ZON8> e += _FalseEasting # make e relative to central meridian if h == 'S': n += _FalseNorthing # make n relative to equator return e, n def _to3zBlat(zone, band, Error=UTMError): # imported by .mgrs.py '''(INTERNAL) Check and return zone, Band and band latitude. @param zone: Zone number or string. @param band: Band letter. @param Error: Exception to raise (L{UTMError}). @return: 3-Tuple (zone, Band, latitude). ''' try: z, B, _ = _to3zBhp(zone, band=band) # in .ellipsoidalBase if _UTM_ZONE_MIN > z or z > _UTM_ZONE_MAX: raise ValueError except ValueError: raise Error('%s invalid: %r' % ('zone', zone)) b = None if B: b = _Bands.find(B) if b < 0: raise Error('%s invalid: %r' % ('band', band or B)) b = (b << 3) - 80 elif Error is not UTMError: raise Error('%s missing: %r' % ('band', band)) return z, B, b def _to3zBll(lat, lon, cmoff=True): '''(INTERNAL) Return zone, Band and lat- and (central) longitude in degrees. @param lat: Latitude (C{degrees}). @param lon: Longitude (C{degrees}). @keyword cmoff: Offset B{C{lon}} from zone's central meridian. @return: 4-Tuple (zone, Band, lat, lon). ''' z, lat, lon = _to3zll(lat, lon) # in .ellipsoidalBase if _UTM_LAT_MIN > lat or lat >= _UTM_LAT_MAX: # [-80, 84) x = '%s [%s, %s)' % ('range', _UTM_LAT_MIN, _UTM_LAT_MAX) raise RangeError('%s outside UTM %s: %s' % ('lat', x, degDMS(lat))) B = _Bands[int(lat + 80) >> 3] x = lon - _cmlon(z) # z before Norway/Svaldbard if abs(x) > _UTM_ZONE_OFF_MAX: x = '%s %d by %s' % ('zone', z, degDMS(x, prec=6)) raise RangeError('%s outside UTM %s: %s' % ('lon', x, degDMS(lon))) if B == 'X': # and 0 <= int(lon) < 42: z = int(lon + 183) // 6 + 1 x = {32: 9, 34: 21, 36: 33}.get(z, None) if x: # Svalbard z += 1 if lon >= x else -1 elif B == 'V' and z == 31 and lon >= 3: z += 1 # SouthWestern Norway if cmoff: # lon off central meridian lon -= _cmlon(z) # z after Norway/Svaldbard return z, B, lat, lon def _to7zBlldfn(latlon, lon, datum, falsed, name, zone, Error, **cmoff): '''(INTERNAL) Determine 7-tuple (zone, band, lat, lon, datum, falsed, name) for L{toEtm8} and L{toUtm8}. ''' f = falsed and cmoff.get('cmoff', True) # DEPRECATED lat, lon, d, name = _to4lldn(latlon, lon, datum, name) z, B, lat, lon = _to3zBll(lat, lon, cmoff=f) if zone: # re-zone for ETM/UTM r, _, _ = _to3zBhp(zone, band=B) if r != z: if not _UTM_ZONE_MIN <= r <= _UTM_ZONE_MAX: raise Error('%s invalid: %r' % ('zone', zone)) if f: # re-offset from central meridian lon += _cmlon(z) - _cmlon(r) z = r return z, B, lat, lon, d, f, name class Utm(UtmUpsBase): '''Universal Transverse Mercator (UTM) coordinate. ''' _band = '' #: (INTERNAL) Latitude band letter ('C..X'). _Error = UTMError # or etm.ETMError _latlon_args = () #: (INTERNAL) (eps, unfalse) from _latlon (C{float}, C{bool}). _scale = None #: (INTERNAL) Grid scale factor (C{scalar}) or C{None}. _scale0 = _K0 #: (INTERNAL) Central scale factor (C{scalar}). _zone = 0 #: (INTERNAL) Longitudinal zone (C{int} 1..60). def __init__(self, zone, hemisphere, easting, northing, band='', # PYCHOK expected datum=Datums.WGS84, falsed=True, convergence=None, scale=None, name=''): '''New L{Utm} UTM coordinate. @param zone: Longitudinal UTM zone (C{int}, 1..60) or zone with/-out (latitudinal) Band letter (C{str}, '01C'..'60X'). @param hemisphere: Northern or southern hemisphere (C{str}, C{'N[orth]'} or C{'S[outh]'}). @param easting: Easting, see B{C{falsed}} (C{meter}). @param northing: Northing, see B{C{falsed}} (C{meter}). @keyword band: Optional, (latitudinal) band (C{str}, 'C'..'X'). @keyword datum: Optional, this coordinate's datum (L{Datum}). @keyword falsed: Both B{C{easting}} and B{C{northing}} are falsed (C{bool}). @keyword convergence: Optional meridian convergence, bearing off grid North, clockwise from true North (C{degrees}) or C{None}. @keyword scale: Optional grid scale factor (C{scalar}) or C{None}. @keyword name: Optional name (C{str}). @raise UTMError: Invalid B{C{zone}}, B{C{hemishere}} or B{C{band}}. @example: >>> import pygeodesy >>> u = pygeodesy.Utm(31, 'N', 448251, 5411932) ''' if name: self.name = name self._zone, B, _ = _to3zBlat(zone, band) h = str(hemisphere)[:1].upper() if h not in ('N', 'S'): raise self._Error('%s invalid: %r' % ('hemisphere', hemisphere)) e, n = float(easting), float(northing) # if not falsed: # e, n = _false2(e, n, h) # # check easting/northing (with 40km overlap # # between zones) - is this worthwhile? # @raise RangeError: If B{C{easting}} or B{C{northing}} outside # the valid UTM range. # if 120e3 > e or e > 880e3: # raise RangeError('%s invalid: %r' % ('easting', easting)) # if 0 > n or n > _FalseNorthing: # raise RangeError('%s invalid: %r' % ('northing', northing)) self._band = B self._convergence = convergence self._datum = datum self._easting = e self._falsed = falsed self._hemisphere = h self._northing = n self._scale = scale def __eq__(self, other): return isinstance(other, Utm) and other.zone == self.zone \ and other.hemisphere == self.hemisphere \ and other.easting == self.easting \ and other.northing == self.northing \ and other.band == self.band \ and other.datum == self.datum def __repr__(self): return self.toStr2(B=True) def __str__(self): return self.toStr() def _xcopy2(self, Xtm): '''(INTERNAL) Make copy as an B{C{Xtm}} instance. @param Xtm: Class to return the copy (C{Xtm=Etm}, C{Xtm=Utm} or C{self.classof}). ''' return Xtm(self.zone, self.hemisphere, self.easting, self.northing, band=self.band, datum=self.datum, falsed=self.falsed, scale=self.scale, convergence=self.convergence) @property_RO def band(self): '''Get the (latitudinal) band (C{str}, 'C'..'X' or ''). ''' return self._band @property_RO def falsed2(self): '''Get the easting and northing falsing (L{EasNor2Tuple}C{(easting, northing)}). ''' e = n = 0 if self.falsed: e = _FalseEasting # relative to central meridian if self.hemisphere == 'S': # relative to equator n = _FalseNorthing return EasNor2Tuple(e, n) def parseUTM(self, strUTM): '''Parse a string to a UTM coordinate. @return: The coordinate (L{Utm}). @see: Function L{parseUTM5} in this module L{utm}. ''' return parseUTM5(strUTM, datum=self.datum, Utm=self.classof) @property_RO def pole(self): '''Get the top center of (stereographic) projection, C{""} always. ''' return '' # n/a for UTM def toEtm(self): '''Copy this UTM to an ETM coordinate. @return: The ETM coordinate (L{Etm}). ''' from pygeodesy.etm import Etm # PYCHOK recursive import return self._xnamed(self._xcopy2(Etm)) def toLatLon(self, LatLon=None, eps=EPS, unfalse=True): '''Convert this UTM coordinate to an (ellipsoidal) geodetic point. @keyword LatLon: Optional, ellipsoidal (sub-)class to return the point (C{LatLon}) or C{None}. @keyword eps: Optional convergence limit, L{EPS} or above (C{float}). @keyword unfalse: Unfalse B{C{easting}} and B{C{northing}} if falsed (C{bool}). @return: This UTM coordinate as (B{C{LatLon}}) or a L{LatLonDatum5Tuple}C{(lat, lon, datum, convergence, scale)} if B{C{LatLon}} is C{None}. @raise TypeError: If B{C{LatLon}} is not ellipsoidal. @raise UTMError: Invalid meridional radius or H-value. @example: >>> u = Utm(31, 'N', 448251.795, 5411932.678) >>> from pygeodesy import ellipsoidalVincenty as eV >>> ll = u.toLatLon(eV.LatLon) # 48°51′29.52″N, 002°17′40.20″E ''' if eps < EPS: eps = EPS # less doesn't converge if self._latlon and self._latlon_args == (eps, unfalse): return self._latlon5(LatLon) E = self.datum.ellipsoid # XXX vs LatLon.datum.ellipsoid x, y = self.to2en(falsed=not unfalse) # from Karney 2011 Eq 15-22, 36 A0 = self.scale0 * E.A if A0 < EPS: raise self._Error('%s invalid: %r' % ('meridional', E.A)) x /= A0 # η eta y /= A0 # ξ ksi K = _Kseries(E.BetaKs, x, y) # Krüger series y = -K.ys(-y) # ξ' x = -K.xs(-x) # η' shx = sinh(x) sy, cy = sincos2(y) H = hypot(shx, cy) if H < EPS: raise self._Error('%s invalid: %r' % ('H', H)) T = t0 = sy / H # τʹ S = Fsum(T) q = 1.0 / E.e12 P = 7 # -/+ toggle trips d = 1.0 + eps while abs(d) > eps and P > 0: p = -d # previous d, toggled h = hypot1(T) s = sinh(E.e * atanh(E.e * T / h)) t = T * hypot1(s) - s * h d = (t0 - t) / hypot1(t) * ((q + T**2) / h) T, d = S.fsum2_(d) # τi, (τi - τi-1) if d == p: # catch -/+ toggling of d P -= 1 # else: # P = 0 a = atan(T) # lat b = atan2(shx, cy) if unfalse and self.falsed: b += radians(_cmlon(self.zone)) ll = _LLEB(degrees90(a), degrees180(b), datum=self.datum, name=self.name) # convergence: Karney 2011 Eq 26, 27 p = -K.ps(-1) q = K.qs(0) ll._convergence = degrees(atan(tan(y) * tanh(x)) + atan2(q, p)) # scale: Karney 2011 Eq 28 ll._scale = E.e2s(sin(a)) * hypot1(T) * H * (A0 / E.a / hypot(p, q)) self._latlon_to(ll, eps, unfalse) return self._latlon5(LatLon) def _latlon_to(self, ll, eps, unfalse): '''(INTERNAL) See C{.toLatLon}, C{toUtm8}, C{_toXtm8}. ''' self._latlon, self._latlon_args = ll, (eps, unfalse) def toMgrs(self): '''Convert this UTM coordinate to an MGRS grid reference. See function L{toMgrs} in module L{mgrs} for more details. @return: The MGRS grid reference (L{Mgrs}). ''' if self._mgrs is None: from pygeodesy.mgrs import toMgrs # PYCHOK recursive import self._mgrs = toMgrs(self, name=self.name) return self._mgrs def toStr(self, prec=0, sep=' ', B=False, cs=False): # PYCHOK expected '''Return a string representation of this UTM coordinate. To distinguish from MGRS grid zone designators, a space is left between the zone and the hemisphere. Note that UTM coordinates are rounded, not truncated (unlike MGRS grid references). @keyword prec: Optional number of decimals, unstripped (C{int}). @keyword sep: Optional separator to join (C{str}). @keyword B: Optionally, include latitudinal band (C{bool}). @keyword cs: Optionally, include meridian convergence and grid scale factor (C{bool}). @return: This UTM as a string with C{zone[band], hemisphere, easting, northing, [convergence, scale]} in C{"00 N|S meter meter"} plus C{" degrees float"} if B{C{cs}} is C{True} (C{str}). @example: >>> u = Utm(3, 'N', 448251, 5411932.0001) >>> u.toStr(4) # 03 N 448251.0 5411932.0001 >>> u.toStr(sep=', ') # 03 N, 448251, 5411932 ''' return self._toStr4_6(self.hemisphere, B, cs, prec, sep) def toStr2(self, prec=0, fmt='[%s]', sep=', ', B=False, cs=False): # PYCHOK expected '''Return a string representation of this UTM coordinate. Note that UTM coordinates are rounded, not truncated (unlike MGRS grid references). @keyword prec: Optional number of decimals, unstripped (C{int}). @keyword fmt: Optional, enclosing backets format (C{str}). @keyword sep: Optional separator between name:value pairs (C{str}). @keyword B: Optionally, include latitudinal band (C{bool}). @keyword cs: Optionally, include meridian convergence and grid scale factor (C{bool}). @return: This UTM as a string C{"[Z:09[band], H:N|S, E:meter, N:meter]"} plus C{", C:degrees, S:float"} if B{C{cs}} is C{True} (C{str}). ''' return self._toStr2(prec=prec, fmt=fmt, sep=sep, B=B, cs=cs) def toUps(self, pole='', eps=EPS, falsed=True, **unused): '''Convert this UTM coordinate to a UPS coordinate. @keyword pole: Optional top/center of the UPS projection, (C{str}, 'N[orth]'|'S[outh]'). @keyword eps: Optional convergence limit, L{EPS} or above (C{float}), see method L{Utm.toLatLon}. @keyword falsed: False both easting and northing (C{bool}). @return: The UPS coordinate (L{Ups}). ''' u = self._ups if u is None or u.pole != (pole or u.pole) or falsed != bool(u.falsed): from pygeodesy.ups import toUps8, Ups # PYCHOK recursive import ll = self.toLatLon(LatLon=_LLEB, eps=eps, unfalse=True) self._ups = u = toUps8(ll, Ups=Ups, falsed=falsed, pole=pole, strict=False) return u def toUtm(self, zone, eps=EPS, falsed=True, **unused): '''Convert this UTM coordinate to a different zone. @param zone: New UTM zone (C{int}). @keyword eps: Optional convergence limit, L{EPS} or above (C{float}), see method L{Utm.toLatLon}. @keyword falsed: False both easting and northing (C{bool}). @return: The UTM coordinate (L{Utm}). ''' if zone == self.zone and falsed == self.falsed: return self.copy() elif zone: u = self._utm if u is None or u.zone != zone or falsed != u.falsed: ll = self.toLatLon(LatLon=_LLEB, eps=eps, unfalse=True) self._utm = u = toUtm8(ll, Utm=self.classof, falsed=falsed, name=self.name, zone=zone) return u raise self._Error('%s invalid: %r' % ('zone', zone)) @property_RO def zone(self): '''Get the (longitudinal) zone (C{int}, 1..60). ''' return self._zone def _parseUTM5(strUTM, Error): '''(INTERNAL) Parse a string representing a UTM coordinate, consisting of C{"zone[band] hemisphere easting northing"}, see L{parseETM5} and L{parseUTM5}. ''' try: z, h, e, n, B = _parseUTMUPS(strUTM) if _UTM_ZONE_MIN <= z <= _UTM_ZONE_MAX and \ (B in _Bands or not B): return UtmUps5Tuple(z, h, e, n, B) except ValueError: pass raise Error('%s invalid: %r' % ('strUTM', strUTM)) def parseUTM5(strUTM, datum=Datums.WGS84, Utm=Utm, falsed=True, name=''): '''Parse a string representing a UTM coordinate, consisting of C{"zone[band] hemisphere easting northing"}. @param strUTM: A UTM coordinate (C{str}). @keyword datum: Optional datum to use (L{Datum}). @keyword Utm: Optional (sub-)class to return the UTM coordinate (L{Utm}) or C{None}. @keyword falsed: Both easting and northing are falsed (C{bool}). @keyword name: Optional B{C{Utm}} name (C{str}). @return: The UTM coordinate (B{C{Utm}}) or a L{UtmUps5Tuple}C{(zone, hemipole, easting, northing, band)} if B{C{Utm}} is C{None}. The C{hemipole} is the C{'N'|'S'} hemisphere. @raise UTMError: Invalid B{C{strUTM}}. @example: >>> u = parseUTM5('31 N 448251 5411932') >>> u.toStr2() # [Z:31, H:N, E:448251, N:5411932] >>> u = parseUTM5('31 N 448251.8 5411932.7') >>> u.toStr() # 31 N 448252 5411933 ''' r = _parseUTM5(strUTM, UTMError) if Utm is not None: z, h, e, n, B = r r = Utm(z, h, e, n, band=B, datum=datum, falsed=falsed) return _xnamed(r, name) def toUtm8(latlon, lon=None, datum=None, Utm=Utm, falsed=True, name='', zone=None, **cmoff): '''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 B{C{latlon}}'s datum (C{Datum}). @keyword Utm: Optional (sub-)class to return the UTM coordinate (L{Utm}) or C{None}. @keyword falsed: False both easting and northing (C{bool}). @keyword name: Optional B{C{Utm}} name (C{str}). @keyword zone: Optional UTM zone to enforce (C{int} or C{str}). @keyword cmoff: DEPRECATED, use B{C{falsed}}. Offset longitude from the zone's central meridian (C{bool}). @return: The UTM coordinate (B{C{Utm}}) or a L{UtmUps8Tuple}C{(zone, hemipole, easting, northing, band, datum, convergence, scale)} if B{C{Utm}} is C{None} or not B{C{falsed}}. The C{hemipole} is the C{'N'|'S'} hemisphere. @raise TypeError: If B{C{latlon}} is not ellipsoidal. @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 UTMError: Invalid B{C{zone}}. @raise ValueError: If B{C{lon}} value is missing or if B{C{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 ''' z, B, lat, lon, d, f, name = _to7zBlldfn(latlon, lon, datum, falsed, name, zone, UTMError, **cmoff) E = d.ellipsoid a, b = radians(lat), radians(lon) # easting, northing: Karney 2011 Eq 7-14, 29, 35 sb, cb = sincos2(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 = E.A * getattr(Utm, '_scale0', _K0) # Utm is class or None K = _Kseries(E.AlphaKs, x, y) # Krüger series y = K.ys(y) * A0 # ξ x = K.xs(x) * A0 # η # convergence: Karney 2011 Eq 23, 24 p_ = K.ps(1) q_ = K.qs(0) c = degrees(atan(T_ / hypot1(T_) * tan(b)) + atan2(q_, p_)) # scale: Karney 2011 Eq 25 k = E.e2s(sin(a)) * T12 / H * (A0 / E.a * hypot(p_, q_)) t = z, lat, x, y, B, d, c, k, f return _toXtm8(Utm, t, name, latlon, EPS) def _toXtm8(Xtm, zlxyBdckf, name, latlon, eps): '''(INTERNAL) Helper for L{toEtm8} and L{toUtm8}. ''' z, lat, x, y, B, d, c, k, f = zlxyBdckf h = _hemi(lat) if f: x, y = _false2(x, y, h) if Xtm is None: # DEPRECATED r = UtmUps8Tuple(z, h, x, y, B, d, c, k) else: r = Xtm(z, h, x, y, band=B, datum=d, falsed=f, convergence=c, scale=k) if isinstance(latlon, _LLEB) and d is latlon.datum: r._latlon_to(latlon, eps, f) # XXX weakref(latlon)? latlon._convergence = c latlon._scale = k return _xnamed(r, name) 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) # **) MIT License # # Copyright (C) 2016-2020 -- 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. 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