# Coverage for pygeodesy/azimuthal.py : 96%

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L{EquidistantKarney} and L{GnomonicKarney} require I{Charles Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib/>} package to be installed. Other azimuthal classes implement only (**) U{Snyder's FORMULAS FOR THE SPHERE <https://pubs.er.USGS.gov/djvu/PP/PP_1395.pdf>} and use those for any datum, spherical and ellipsoidal. The radius used for the latter is the ellipsoid's I{mean radius of curvature} at the latitude of the projection center point. For further justification, see the first paragraph under U{Snyder's FORMULAS FOR THE ELLIPSOID, page 197<https://pubs.er.USGS.gov/djvu/PP/PP_1395.pdf>}. Page numbers in C{Snyder} references apply to U{John P. Snyder, "Map Projections -- A Working Manual", 1987<https://pubs.er.USGS.gov/djvu/PP/PP_1395.pdf>}. See also U{here<https://WikiPedia.org/wiki/Azimuthal_equidistant_projection>}, especially the U{Comparison of the Azimuthal equidistant projection and some azimuthal projections centred on 90° N at the same scale, ordered by projection altitude in Earth radii<https://WikiPedia.org/wiki/Azimuthal_equidistant_projection #/media/File:Comparison_azimuthal_projections.svg>}. @newfield example: Example, Examples ''' from pygeodesy.basics import property_doc_, property_RO, \ _xinstanceof, _xkwds from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB from pygeodesy.datums import Datums, _spherical_datum from pygeodesy.errors import _datum_datum, _ValueError from pygeodesy.fmath import Fsum from pygeodesy.interns import EPS, EPS1, NAN, PI, PI_2, _azimuth_, \ _COMMA_SPACE_, _datum_, _lat_, _lat0_, \ _lon_, _lon0_, _name_, NN, \ _no_convergence_fmt_, _scale_, _SPACE_, \ _x_, _y_, _0_0, _0_5, _1_0, _2_0, _360_0 from pygeodesy.karney import _norm180 from pygeodesy.latlonBase import LatLonBase as _LLB from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _FOR_DOCS from pygeodesy.named import _NamedBase, _NamedTuple, _Pass from pygeodesy.namedTuples import LatLon2Tuple, LatLon4Tuple from pygeodesy.streprs import strs from pygeodesy.units import Bearing, Lat_, Lon_, Meter, Scalar, Scalar_ from pygeodesy.utily import asin1, atan2b, atan2d, sincos2, sincos2d from math import acos, asin, atan, atan2, degrees, hypot, sin, sqrt __all__ = _ALL_LAZY.azimuthal __version__ = '20.09.12' _EPS_Karney = sqrt(EPS) * 0.01 # Karney's eps_ _over_horizon_ = 'over horizon' _TRIPS = 21 # numit, 4 sufficient class _AzimuthalBase(_NamedBase): '''(INTERNAL) Base class for azimuthal projections. @see: I{Karney}'s C++ class U{AzimuthalEquidistant<https://GeographicLib.SourceForge.io/ html/classGeographicLib_1_1AzimuthalEquidistant.html>} or L{EquidistantKarney} or U{Gnomonic<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Gnomonic.html>} or L{GnomonicKarney}. ''' _datum = Datums.WGS84 # L{Datum} _iteration = None # iteration number for L{GnomonicKarney} _latlon0 = () # lat0, lon0 (L{LatLon2Tuple}) _radius = None # geodentric radius (L{Radius}) _sc0 = () # 2-Tuple C{sincos2(lat0)} def __init__(self, lat0, lon0, datum=None, name=NN): '''New azimuthal projection. @arg lat0: Latitude of the center point (C{degrees90}). @arg lon0: Longitude of the center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg name: Optional name for the projection (C{str}). @raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or spherical B{C{datum}}. @raise TypeError: Invalid B{C{datum}}. ''' if name: self.name = name if datum not in (None, self._datum): self._datum = _spherical_datum(datum, name=name) self.reset(lat0, lon0) @property_RO def datum(self): '''Get the datum (L{Datum}). ''' return self._datum @property_RO def equatoradius(self): '''Get the geodesic's equatorial (major) radius, semi-axis (C{meter}). ''' return self.datum.ellipsoid.a majoradius = equatoradius # for compatibility @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, name, _k_t): '''(INTERNAL) Azimuthal (spherical) forward C{lat, lon} to C{x, y}. ''' sa, ca, sb, cb = sincos2d(Lat_(lat), Lon_(lon) - self.lon0) s0, c0 = self._sc0 k, t = _k_t(s0 * sa + c0 * ca * cb) if t: r = k * self.radius x = r * ca * sb y = r * (c0 * sa - s0 * ca * cb) z = atan2b(x, y) # (x, y) for azimuth from true North else: # 0 or 180 x = y = z = 0 t = Azimuthal7Tuple(x, y, lat, lon, z, k, self.datum) return self._xnamed(t, name=name) @property_RO def lat0(self): '''Get the center latitude (C{degrees90}). ''' return self._latlon0.lat @property def latlon0(self): '''Get the center lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}) in (C{degrees90}, C{degrees180}). ''' return self._latlon0 @latlon0.setter # PYCHOK setter! def latlon0(self, latlon0): '''Set the center lat- and longitude (C{LatLon}, L{LatLon2Tuple} or L{LatLon4Tuple}). @raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}} or ellipsoidal mismatch of B{C{latlon0}} and this projection. ''' B = _LLEB if self.datum.isEllipsoidal else _LLB _xinstanceof(B, LatLon2Tuple, LatLon4Tuple, latlon0=latlon0) if hasattr(latlon0, _datum_): _datum_datum(self.datum, latlon0.datum, Error=AzimuthalError) self.reset(latlon0.lat, latlon0.lon) @property_RO def lon0(self): '''Get the center longitude (C{degrees180}). ''' return self._latlon0.lon @property_RO def radius(self): '''Get this projection's mean radius of curvature (C{meter}). ''' if self._radius is None: self._radius = self.datum.ellipsoid.rocMean(self.lat0) return self._radius def reset(self, lat0, lon0): '''Set or reset the center point of this azimuthal projection. @arg lat0: Center point latitude (C{degrees90}). @arg lon0: Center point longitude (C{degrees180}). @raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}}. ''' self._latlon0 = LatLon2Tuple(Lat_(lat0, name=_lat0_, Error=AzimuthalError), Lon_(lon0, name=_lon0_, Error=AzimuthalError)) self._sc0 = tuple(sincos2d(self.lat0)) self._radius = None def _reverse(self, x, y, name, LatLon, LatLon_kwds, _c_t, lea): '''(INTERNAL) Azimuthal (spherical) reverse C{x, y} to C{lat, lon}. ''' x = Scalar(x, name=_x_) y = Scalar(y, name=_y_) r = hypot(x, y) c, t = _c_t(r / self.radius) if t: s0, c0 = self._sc0 sc, cc = sincos2(c) k = c / sc z = atan2b(x, y) # (x, y) for azimuth from true North lat = degrees(asin1(s0 * cc + c0 * sc * (y / r))) if lea or abs(c0) > EPS: lon = atan2(x * sc, c0 * cc * r - s0 * sc * y) else: lon = atan2(x, (y if s0 < 0 else -y)) lon = _norm180(self.lon0 + degrees(lon)) else: k, z = _1_0, _0_0 lat, lon = self.latlon0 t = self._toLatLon(lat, lon, LatLon, LatLon_kwds) if LatLon else \ Azimuthal7Tuple(x, y, lat, lon, z, k, self.datum) return self._xnamed(t, name=name) def _toLatLon(self, lat, lon, LatLon, LatLon_kwds): '''(INTERNAL) Check B{C{LatLon}} and return an instance. ''' kwds = _xkwds(LatLon_kwds, datum=self.datum) r = LatLon(lat, lon, **kwds) # handle .classof B = _LLEB if self.datum.isEllipsoidal else _LLB _xinstanceof(B, LatLon=r) return r def toRepr(self, prec=6, **unused): # PYCHOK expected '''Return a string representation of this projection. @kwarg prec: Optional number of decimals, unstripped (C{int}). @return: This projection as C{"<classname>(lat0, lon0, ...)"} (C{str}). ''' t = self.toStr(prec=prec, sep=_COMMA_SPACE_) n = self.name or NN if n: n = ', %s=%r' % (_name_, n) return '%s(%s%s)' % (self.classname, t, n) def toStr(self, prec=6, sep=_SPACE_, **unused): # PYCHOK expected '''Return a string representation of this projection. @kwarg prec: Optional number of decimal, unstripped (C{int}). @kwarg sep: Optional separator to join (C{str}). @return: This projection as C{"lat0 lon0"} (C{str}). ''' return sep.join(strs(self.latlon0, prec=prec)) class AzimuthalError(_ValueError): '''An azimuthal L{Equidistant}, L{EquidistantKarney}, L{Gnomonic}, L{LambertEqualArea}, L{Orthographic}, L{Stereographic} or {Azimuthal7Tuple} issue. ''' pass class Azimuthal7Tuple(_NamedTuple): '''7-Tuple C{(x, y, lat, lon, azimuth, scale, datum)}, in C{meter}, C{meter}, C{degrees90}, C{degrees180}, C{degrees360}, C{float} and C{Datum} where C{(x, y)} is the projected, C{(lat, lon)} the geodetic location, C{azimuth} the azimuth direction clockwise from true North and C{scale} is the projection scale, either (C{1 / reciprocal} or C{1} or C{-1} in the L{Equidistant} case). ''' _Names_ = (_x_, _y_, _lat_, _lon_, _azimuth_, _scale_, _datum_) _Units_ = ( Meter, Meter, Lat_, Lon_, Bearing, Scalar, _Pass) class Equidistant(_AzimuthalBase): '''Azimuthal equidistant projection for the sphere**, see U{Snyder, pp 195-197 <https://pubs.er.USGS.gov/djvu/PP/PP_1395.pdf>} and U{MathWorld-Wolfram <https://MathWorld.Wolfram.com/AzimuthalEquidistantProjection.html>}. @note: Results from this L{Equidistant} and the L{EquidistantKarney} projection C{may differ} up to 10% or more. For an example, see method C{testDiscrepancies} in module C{testAzimuthal.py}. ''' if _FOR_DOCS: __init__ = _AzimuthalBase.__init__ def forward(self, lat, lon, name=NN): '''Convert a geodetic location to azimuthal equidistant east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with C{x} and C{y} in C{meter} and C{lat} and C{lon} in C{degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. @raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. @note: The C{scale} will be C{-1} if B{C{(lat, lon)}} is antipodal to the projection center C{(lat0, lon0)}. ''' def _k_t(c): t = abs(c) < EPS1 if t: c = acos(c) # XXX .utily.acos1 k = c / sin(c) else: k = -_1_0 if c < 0 else _1_0 # copysign(1, c) return k, t return self._forward(lat, lon, name, _k_t) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal equidistant location to geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @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 B{C{LatLon=None}}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. ''' def _c_t(c): return c, (c > EPS) return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, False) def equidistant(lat0, lon0, datum=Datums.WGS84, name=NN): '''If I{Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>} package is installed, return an L{EquidistantKarney} otherwise an L{Equidistant} instance. @arg lat0: Latitude of center point (C{degrees90}). @arg lon0: Longitude of center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg name: Optional name for the projection (C{str}). @return: An L{EquidistantKarney} or L{Equidistant} instance. @raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or sperical B{C{datum}}. @raise TypeError: Invalid B{C{datum}}. ''' try: return EquidistantKarney(lat0, lon0, datum=datum, name=name) except ImportError: return Equidistant(lat0, lon0, datum=datum, name=name) # PYCHOK expected class _AzimuthalBaseKarney(_AzimuthalBase): '''(INTERNAL) Base class for azimuthal projections using U{Karney Geodesic <https://GeographicLib.SourceForge.io/html/python/code.html>}. ''' _mask = 0 @property_RO def geodesic(self): '''Get this projection's I{wrapped} U{Karney Geodesic <https://GeographicLib.SourceForge.io/html/python/code.html>}, provided package U{geographiclib <https://PyPI.org/project/geographiclib>} is installed. ''' return self.datum.ellipsoid.geodesic def _7Tuple(self, x, y, r, s): '''(INTERNAL) Return an C{Azimuthal7Tuple}. ''' return Azimuthal7Tuple(x, y, r.lat2, r.lon2, r.azi2 % _360_0, s, self.datum) class EquidistantKarney(_AzimuthalBaseKarney): '''Azimuthal equidistant projection, a Python version of I{Karney}'s C++ class U{AzimuthalEquidistant <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1AzimuthalEquidistant.html>}, requiring package U{geographiclib<https://PyPI.org/project/geographiclib>} to be installed. An azimuthal equidistant projection is centered at an arbitrary position on the ellipsoid. For a point in projected space C{(x, y)}, the geodesic distance from the center position is C{hypot(x, y)} and the C{azimuth} of the geodesic from the center point is C{atan2(x, y)}, clockwise from true North. The C{.forward} and C{.reverse} methods also return the C{azimuth} of the geodesic at C{(x, y)} and the C{scale} in the azimuthal direction which, together with the basic properties of the projection, serve to specify completely the local affine transformation between geographic and projected coordinates. ''' def __init__(self, lat0, lon0, datum=Datums.WGS84, name=NN): '''New azimuthal L{EquidistantKarney} projection. @arg lat0: Latitude of center point (C{degrees90}). @arg lon0: Longitude of center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg name: Optional name for the projection (C{str}). @raise ImportError: Package U{geographiclib<https://PyPI.org/ project/geographiclib>} missing. @raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or B{C{datum}}. ''' _AzimuthalBaseKarney.__init__(self, lat0, lon0, datum=datum, name=name) g = self.geodesic # g.STANDARD = g.AZIMUTH | g.DISTANCE | g.LATITUDE | g.LONGITUDE self._mask = g.REDUCEDLENGTH | g.STANDARD # | g.LONG_UNROLL def forward(self, lat, lon, name=NN): '''Convert an (ellipsoidal) geodetic location to azimuthal equidistant east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with C{x} and C{y} in C{meter} and C{lat} and C{lon} in C{degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. @see: Method L{EquidistantKarney.reverse}. A call to C{.forward} followed by a call to C{.reverse} will return the original C{lat, lon} to within roundoff. @raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. ''' r = self.geodesic.Inverse(self.lat0, self.lon0, Lat_(lat), Lon_(lon), self._mask) x, y = sincos2d(r.azi1) t = self._7Tuple(x * r.s12, y * r.s12, r, self._1_rk(r)) return self._xnamed(t, name=name) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal equidistant location to (ellipsoidal) geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @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 B{C{LatLon=None}}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The scale of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. ''' x = Meter(x, name=_x_) y = Meter(y, name=_y_) z = atan2d(x, y) # (x, y) for azimuth from true North s = hypot( x, y) r = self.geodesic.Direct(self.lat0, self.lon0, z, s, self._mask) t = self._toLatLon(r.lat2, r.lon2, LatLon, LatLon_kwds) if LatLon else \ self._7Tuple(x, y, r, self._1_rk(r)) return self._xnamed(t, name=name) def _1_rk(self, r): '''(INTERNAL) Compute the reciprocal, azimuthal scale. ''' return (r.m12 / r.s12) if r.a12 > _EPS_Karney else _1_0 class Gnomonic(_AzimuthalBase): '''Azimuthal gnomonic projection for the sphere**, see U{Snyder, pp 164-168 <https://pubs.er.USGS.gov/djvu/PP/PP_1395.pdf>} and U{MathWorld-Wolfram <https://MathWorld.Wolfram.com/GnomonicProjection.html>}. ''' if _FOR_DOCS: __init__ = _AzimuthalBase.__init__ def forward(self, lat, lon, name=NN): '''Convert a geodetic location to azimuthal equidistant east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with C{x} and C{y} in C{meter} and C{lat} and C{lon} in C{degrees} and C{azimuth} clockwise from true North. The C{scale} of the projection is C{1} in I{radial} direction and is C{1 / reciprocal} in the direction perpendicular to this. @raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. ''' def _k_t(c): t = c > EPS if t: k = _1_0 / c else: k = _1_0 return k, t return self._forward(lat, lon, name, _k_t) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal equidistant location to geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @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 B{C{LatLon=None}}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and C{1 / reciprocal} in the direction perpendicular to this. ''' def _c_t(c): return atan(c), (c > EPS) return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, False) def gnomonic(lat0, lon0, datum=Datums.WGS84, name=NN): '''If I{Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>} package is installed, return an L{GnomonicKarney} otherwise an L{Gnomonic} instance. @arg lat0: Latitude of center point (C{degrees90}). @arg lon0: Longitude of center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg name: Optional name for the projection (C{str}). @return: An L{GnomonicKarney} or L{Gnomonic} instance. @raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or sperical B{C{datum}}. @raise TypeError: Invalid B{C{datum}}. ''' try: return GnomonicKarney(lat0, lon0, datum=datum, name=name) except ImportError: return Gnomonic(lat0, lon0, datum=datum, name=name) # PYCHOK expected class GnomonicKarney(_AzimuthalBaseKarney): '''Azimuthal gnomonic projection, a Python version of I{Karney}'s C++ class U{Gnomonic <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Gnomonic.html>}, requiring package U{geographiclib<https://PyPI.org/project/geographiclib>} to be installed. @see: I{Karney}'s U{Detailed Description<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1Gnomonic.html>}, especially the B{Warning}. ''' def __init__(self, lat0, lon0, datum=Datums.WGS84, name=NN): '''New azimuthal L{GnomonicKarney} projection. @arg lat0: Latitude of center point (C{degrees90}). @arg lon0: Longitude of center point (C{degrees180}). @kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth radius (C{meter}). @kwarg name: Optional name for the projection (C{str}). @raise ImportError: Package U{geographiclib<https://PyPI.org/ project/geographiclib>} missing. @raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}}. ''' _AzimuthalBaseKarney.__init__(self, lat0, lon0, datum=datum, name=name) g = self.geodesic self._mask = g.ALL # | g.LONG_UNROLL def forward(self, lat, lon, name=NN, raiser=True): '''Convert an (ellipsoidal) geodetic location to azimuthal gnomonic east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @kwarg raiser: Do or do not throw an error (C{bool}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with C{x} and C{y} in C{meter} and C{lat} and C{lon} in C{degrees} and C{azimuth} clockwise from true North. The C{scale} of the projection is C{1 / reciprocal**2} in I{radial} direction and C{1 / reciprocal} in the direction perpendicular to this. Both C{x} and C{y} will be C{NAN} if the geodetic location lies over the horizon and B{C{raiser}} is C{False}. @raise AzimuthalError: Invalid B{C{lat}}, B{C{lon}} or the geodetic location lies over the horizon and B{C{raiser}} is C{True}. ''' self._iteration = 0 r = self.geodesic.Inverse(self.lat0, self.lon0, Lat_(lat), Lon_(lon), self._mask) if r.M21 < EPS: if raiser: raise AzimuthalError(lat=lat, lon=lon, txt=_over_horizon_) x = y = NAN else: q = r.m12 / r.M21 # .M12 x, y = sincos2d(r.azi1) x *= q y *= q t = self._7Tuple(x, y, r, r.M21) t._iteraton = self._iteration # = 0 return self._xnamed(t, name=name) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal gnomonic location to (ellipsoidal) geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @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 B{C{LatLon=None}}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @raise AzimuthalError: No convergence. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The C{azimuth} is clockwise from true North. The scale is C{1 / reciprocal**2} in C{radial} direction and C{1 / reciprocal} in the direction perpendicular to this. ''' x = Scalar(x, name=_x_) y = Scalar(y, name=_y_) z = atan2d(x, y) # (x, y) for azimuth from true North q = hypot( x, y) d = e = self.equatoradius s = e * atan(q / e) if q > e: def _d(r, q): return (r.M12 - q * r.m12) * r.m12 # negated q = 1 / q else: # little == True def _d(r, q): # PYCHOK _d return (q * r.M12 - r.m12) * r.M12 # negated e *= _EPS_Karney S = Fsum(s) g = self.geodesic.Line(self.lat0, self.lon0, z, self._mask) for self._iteration in range(1, _TRIPS): r = g.Position(s, self._mask) if abs(d) < e: break s, d = S.fsum2_(_d(r, q)) else: raise AzimuthalError(x=x, y=y, txt=_no_convergence_fmt_ % (e,)) t = self._toLatLon(r.lat2, r.lon2, LatLon, LatLon_kwds) if LatLon else \ self._7Tuple(x, y, r, r.M12) t._iteration = self._iteration return self._xnamed(t, name=name) class LambertEqualArea(_AzimuthalBase): '''Lambert-equal-area projection for the sphere**, see U{Snyder, pp 185-187 <https://pubs.er.USGS.gov/djvu/PP/PP_1395.pdf>} and U{MathWorld-Wolfram <https://MathWorld.Wolfram.com/LambertAzimuthalEqual-AreaProjection.html>}. ''' if _FOR_DOCS: __init__ = _AzimuthalBase.__init__ def forward(self, lat, lon, name=NN): '''Convert a geodetic location to azimuthal Lambert-equal-area east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with C{x} and C{y} in C{meter} and C{lat} and C{lon} in C{degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. @raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. ''' def _k_t(c): c = c + _1_0 t = c > EPS if t: k = sqrt(_2_0 / c) else: k = _1_0 return k, t return self._forward(lat, lon, name, _k_t) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal Lambert-equal-area location to geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @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 B{C{LatLon=None}}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. ''' def _c_t(c): c = c * _0_5 t = c > EPS if t: c = PI if c > EPS1 else (2 * asin(c)) # utily.asin1 return c, t return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, True) class Orthographic(_AzimuthalBase): '''Orthographic projection for the sphere**, see U{Snyder, pp 148-153 <https://pubs.er.USGS.gov/djvu/PP/PP_1395.pdf>} and U{MathWorld-Wolfram <https://MathWorld.Wolfram.com/OrthographicProjection.html>}. ''' if _FOR_DOCS: __init__ = _AzimuthalBase.__init__ def forward(self, lat, lon, name=NN): '''Convert a geodetic location to azimuthal orthographic east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with C{x} and C{y} in C{meter} and C{lat} and C{lon} in C{degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. @raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. ''' def _k_t(c): return _1_0, (c >= 0) return self._forward(lat, lon, name, _k_t) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal orthographic location to geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @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 B{C{LatLon=None}}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. ''' def _c_t(c): t = c > EPS if t: c = PI_2 if c > EPS1 else asin(c) # utily.asin1 return c, t return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, False) class Stereographic(_AzimuthalBase): '''Stereographic projection for the sphere**, see U{Snyder, pp 157-160 <https://pubs.er.USGS.gov/djvu/PP/PP_1395.pdf>} and U{MathWorld-Wolfram <https://MathWorld.Wolfram.com/StereographicProjection.html>}. ''' _k0 = _1_0 # central scale factor (C{scalar}) if _FOR_DOCS: __init__ = _AzimuthalBase.__init__ def forward(self, lat, lon, name=NN): '''Convert a geodetic location to azimuthal stereographic east- and northing. @arg lat: Latitude of the location (C{degrees90}). @arg lon: Longitude of the location (C{degrees180}). @kwarg name: Optional name for the location (C{str}). @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with C{x} and C{y} in C{meter} and C{lat} and C{lon} in C{degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. @raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. ''' def _k_t(c): c = c + _1_0 t = abs(c) > EPS if t: k = 2 * self._k0 / c else: k = _1_0 return k, t return self._forward(lat, lon, name, _k_t) @property_doc_('''optional, central scale factor (C{scalar}).''') def k0(self): '''Get the central scale factor (C{scalar}). ''' return self._k0 @k0.setter # PYCHOK setter! def k0(self, factor): '''Set the central scale factor (C{scalar}). ''' n = Stereographic.k0.fget.__name__ self._k0 = Scalar_(factor, name=n, low=EPS, high=2) # XXX high=1, 2, other? def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): '''Convert an azimuthal stereographic location to geodetic lat- and longitude. @arg x: Easting of the location (C{meter}). @arg y: Northing of the location (C{meter}). @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 B{C{LatLon=None}}. @return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. @note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} in the range C{[-180..180] degrees}. The C{scale} of the projection is C{1} in I{radial} direction, C{azimuth} clockwise from true North and is C{1 / reciprocal} in the direction perpendicular to this. ''' def _c_t(c): t = c > EPS if t: c = 2 * atan2(c, 2 * self._k0) return c, t return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, False) __all__ += _ALL_DOCS(Azimuthal7Tuple, _AzimuthalBase) # **) 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. 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.