# Coverage for pygeodesy/azimuthal.py : 99%

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Classes L{Equidistant}, L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney}, L{Gnomonic}, L{GnomonicExact}, L{GnomonicKarney}, L{LambertEqualArea}, L{Orthographic} and L{Stereographic}, classes L{AzimuthalError}, L{Azimuthal7Tuple} and functions L{equidistant} and L{gnomonic}. L{EquidistantExact} and L{GnomonicExact} are based on exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact}, Python versions of I{Charles Karney}'s C++ original U{GeodesicExact<https://GeographicLib.SourceForge.io/C++/doc/ classGeographicLib_1_1GeodesicExact.html>}, respectively U{GeodesicLineExact <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicLineExact.html>}. Using L{EquidistantGeodSolve} requires I{Karney}'s utility U{GeodSolve <https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} to be executable and set in env variable C{PYGEODESY_GEODSOLVE}, see module L{geodsolve} for more details. L{EquidistantKarney} and L{GnomonicKarney} require I{Karney}'s Python package U{geographiclib<https://PyPI.org/project/geographiclib>} to be installed. Other azimuthal classes implement only (***) U{Snyder's FORMULAS FOR THE SPHERE <https://Pubs.USGS.gov/pp/1395/report.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.USGS.gov/pp/1395/report.pdf>}. Page numbers in C{Snyder} references apply to U{John P. Snyder, "Map Projections -- A Working Manual", 1987<https://Pubs.USGS.gov/pp/1395/report.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>}. ''' # make sure int/int division yields float quotient, see .basics from __future__ import division as _; del _ # PYCHOK semicolon # from pygeodesy.basics import _xinstanceof # from .datums from pygeodesy.constants import EPS, EPS0, EPS1, NAN, isnon0, \ _EPStol, _umod_360, _0_0, _0_1, \ _0_5, _1_0, _N_1_0, _2_0 from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB, \ _spherical_datum, _WGS84, _xinstanceof # from pygeodesy.datums import _spherical_datum, _WGS84, _xinstanceof from pygeodesy.errors import _ValueError, _xdatum, _xkwds from pygeodesy.fmath import euclid, Fsum, hypot # from pygeodesy.fsums import Fsum # from .fmath # from pygeodesy.formy import antipode # from latlonBase from pygeodesy.interns import NN, _azimuth_, _datum_, _lat_, _lon_, \ _scale_, _SPACE_, _x_, _y_ from pygeodesy.karney import _norm180 from pygeodesy.latlonBase import antipode, LatLonBase as _LLB from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _FOR_DOCS from pygeodesy.named import _NamedBase, _NamedTuple, notOverloaded, _Pass from pygeodesy.namedTuples import LatLon2Tuple, LatLon4Tuple from pygeodesy.props import deprecated_Property_RO, Property_RO, \ property_doc_, _update_all from pygeodesy.streprs import Fmt, _fstrLL0, unstr from pygeodesy.units import Bearing, Easting, Lat_, Lon_, \ Northing, Scalar, Scalar_ from pygeodesy.utily import asin1, atan2b, atan2d, sincos2, \ sincos2d, sincos2d_ from math import acos, atan, atan2, degrees, fabs, sin, sqrt __all__ = _ALL_LAZY.azimuthal __version__ = '23.03.21' _EPS_K = _EPStol * _0_1 # Karney's eps_ or _EPSmin * _0_1? _over_horizon_ = 'over horizon' _TRIPS = 21 # numit, 4 sufficient def _enzh4(x, y, *h): '''(INTERNAL) Return 4-tuple (easting, northing, azimuth, hypot). ''' e = Easting( x=x) n = Northing(y=y) z = atan2b(e, n) # (x, y) for azimuth from true North return e, n, z, (h[0] if h else hypot(e, n)) 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>} and U{Gnomonic <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Gnomonic.html>} or the C{PyGeodesy} versions thereof L{EquidistantKarney} respectively L{GnomonicKarney}. ''' _datum = _WGS84 # L{Datum} _latlon0 = LatLon2Tuple(_0_0, _0_0) # lat0, lon0 (L{LatLon2Tuple}) _sc0 = _0_0, _1_0 # 2-Tuple C{sincos2d(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}} or B{C{lon0}} or (spherical) B{C{datum}}. @raise TypeError: Invalid B{C{datum}}. ''' if datum not in (None, self._datum): self._datum = _spherical_datum(datum, name=name) if name: self.name = name if lat0 or lon0: # often both 0 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 radius, semi-axis (C{meter}). ''' return self.datum.ellipsoid.a @Property_RO def flattening(self): '''Get the geodesic's flattening (C{float}). ''' return self.datum.ellipsoid.f def forward(self, lat, lon, name=NN): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. ''' notOverloaded(self, lat, lon, name=name) def _forward(self, lat, lon, name, _k_t_2): '''(INTERNAL) Azimuthal (spherical) forward C{lat, lon} to C{x, y}. ''' lat, lon = Lat_(lat), Lon_(lon) sa, ca, sb, cb = sincos2d_(lat, lon - self.lon0) s0, c0 = self._sc0 cb *= ca k, t = _k_t_2(s0 * sa + c0 * cb) if t: r = k * self.radius y = r * (c0 * sa - s0 * cb) e, n, z, _ = _enzh4(r * sb * ca, y, None) else: # 0 or 180 e = n = z = _0_0 t = Azimuthal7Tuple(e, n, lat, lon, z, k, self.datum, name=name or self.name) return t def _forwards(self, *lls): '''(INTERNAL) One or more C{.forward} calls, see .ellipsoidalBaseDI. ''' _fwd = self.forward for ll in lls: yield _fwd(ll.lat, ll.lon) @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_): _xdatum(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 @deprecated_Property_RO def majoradius(self): # PYCHOK no cover '''DEPRECATED, use property C{equatoradius}.''' return self.equatoradius @Property_RO def radius(self): '''Get this projection's mean radius of curvature (C{meter}). ''' return self.datum.ellipsoid.rocMean(self.lat0) 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}}. ''' _update_all(self) # zap caches self._reset(lat0, lon0) def _reset(self, lat0, lon0): '''(INTERNAL) Update the center point. ''' self._latlon0 = LatLon2Tuple(Lat_(lat0=lat0, Error=AzimuthalError), Lon_(lon0=lon0, Error=AzimuthalError)) self._sc0 = sincos2d(self.lat0) def reverse(self, x, y, name=NN, **LatLon_and_kwds): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. ''' notOverloaded(self, x, y, name=name, **LatLon_and_kwds) def _reverse(self, x, y, name, _c, lea, LatLon=None, **LatLon_kwds): '''(INTERNAL) Azimuthal (spherical) reverse C{x, y} to C{lat, lon}. ''' e, n, z, r = _enzh4(x, y) c = _c(r / self.radius) if c is None: lat, lon = self.latlon0 k, z = _1_0, _0_0 else: s0, c0 = self._sc0 sc, cc = sincos2(c) k = c / sc s = s0 * cc if r > EPS0: s += c0 * sc * (n / r) lat = degrees(asin1(s)) if lea or fabs(c0) > EPS: d = atan2d(e * sc, r * c0 * cc - n * s0 * sc) else: d = atan2d(e, (n if s0 < 0 else -n)) lon = _norm180(self.lon0 + d) if LatLon is None: t = Azimuthal7Tuple(e, n, lat, lon, z, k, self.datum, name=name or self.name) else: t = self._toLatLon(lat, lon, LatLon, LatLon_kwds, name) return t def _reverse2(self, x_t, *y): '''(INTERNAL) See iterating functions .ellipsoidalBaseDI._intersect3, .ellipsoidalBaseDI._intersects2 and .ellipsoidalBaseDI._nearestOne. ''' t = self.reverse(x_t, *y) if y else self.reverse(x_t.x, x_t.y) # LatLon=None d = euclid(t.lat - self.lat0, t.lon - self.lon0) # degrees return t, d def _toLatLon(self, lat, lon, LatLon, LatLon_kwds, name): '''(INTERNAL) Check B{C{LatLon}} and return an instance. ''' kwds = _xkwds(LatLon_kwds, datum=self.datum) r = self._xnamed(LatLon(lat, lon, **kwds), name=name) # 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: Number of (decimal) digits, unstripped (C{int}). @return: This projection as C{"<classname>(lat0, lon0, ...)"} (C{str}). ''' return _fstrLL0(self, prec, True) def toStr(self, prec=6, sep=_SPACE_, **unused): # PYCHOK expected '''Return a string representation of this projection. @kwarg prec: Number of (decimal) digits, unstripped (C{int}). @kwarg sep: Separator to join (C{str}). @return: This projection as C{"lat0 lon0"} (C{str}). ''' t = _fstrLL0(self, prec, False) return t if sep is None else sep.join(t) class AzimuthalError(_ValueError): '''An azimuthal L{Equidistant}, L{EquidistantKarney}, L{Gnomonic}, L{LambertEqualArea}, L{Orthographic}, L{Stereographic} or L{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}, compass C{degrees}, C{scalar} and C{Datum} where C{(x, y)} is the easting and northing of a projected point, C{(lat, lon)} the geodetic location, C{azimuth} the azimuth, 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_ = ( Easting, Northing, Lat_, Lon_, Bearing, Scalar, _Pass) def antipodal(self, azimuth=None): '''Return this tuple with the antipodal C{lat} and C{lon}. @kwarg azimuth: Optional azimuth, overriding the current azimuth (C{compass degrees360}). ''' a = antipode(self.lat, self.lon) # PYCHOK named z = self.azimuth if azimuth is None else Bearing(azimuth=azimuth) # PYCHOK named return _NamedTuple.dup(self, lat=a.lat, lon=a.lon, azimuth=z) class Equidistant(_AzimuthalBase): '''Azimuthal equidistant projection for the sphere***, see U{Snyder, pp 195-197 <https://Pubs.USGS.gov/pp/1395/report.pdf>} and U{MathWorld-Wolfram <https://MathWorld.Wolfram.com/AzimuthalEquidistantProjection.html>}. @note: Results from this L{Equidistant} and an L{EquidistantExact}, L{EquidistantGeodSolve} or L{EquidistantKarney} projection C{may differ} by 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 easting C{x} and northing C{y} of point 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}}. @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): k = _N_1_0 if c < 0 else _1_0 t = fabs(c) < EPS1 if t: a = acos(c) s = sin(a) if s: k = a / s return k, t return self._forward(lat, lon, name, _k_t) def reverse(self, x, y, name=NN, **LatLon_and_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_and_kwds: Optional, C{B{LatLon}=None} class to use and additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None} or not given. @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(c): return c if c > EPS else None return self._reverse(x, y, name, _c, False, **LatLon_and_kwds) def equidistant(lat0, lon0, datum=_WGS84, exact=False, geodsolve=False, name=NN): '''Return an L{EquidistantExact}, L{EquidistantGeodSolve} or (if I{Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>} package is installed) 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 exact: Return an L{EquidistantExact} instance. @kwarg geodsolve: Return an L{EquidistantGeodSolve} instance. @kwarg name: Optional name for the projection (C{str}). @return: An L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney} or L{Equidistant} instance. @raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}} or (spherical) B{C{datum}}. @raise GeodesicError: Issue with L{GeodesicExact}, L{GeodesicSolve} or I{Karney}'s wrapped C{Geodesic}. @raise TypeError: Invalid B{C{datum}}. ''' E = EquidistantExact if exact else (EquidistantGeodSolve if geodsolve else Equidistant) if E is Equidistant: try: return EquidistantKarney(lat0, lon0, datum=datum, name=name) # PYCHOK types except ImportError: pass return E(lat0, lon0, datum=datum, name=name) # PYCHOK types class _AzimuthalGeodesic(_AzimuthalBase): '''(INTERNAL) Base class for azimuthal projections using U{Karney Geodesic <https://GeographicLib.SourceForge.io/C++/doc/python/code.html>} or exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact}. ''' _mask = 0 @Property_RO def geodesic(self): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. ''' notOverloaded(self) def _7Tuple(self, e, n, r, M=None, name=NN): '''(INTERNAL) Return an C{Azimuthal7Tuple}. ''' s = M if M is not None else ( # reciprocal, azimuthal scale (r.m12 / r.s12) if r.a12 > _EPS_K else _1_0) z = _umod_360(r.azi2) # -180 <= r.azi2 < 180 ... 0 <= z < 360 return Azimuthal7Tuple(e, n, r.lat2, r.lon2, z, s, self.datum, name=name or self.name) class _EquidistantBase(_AzimuthalGeodesic): '''(INTERNAL) Base for classes L{EquidistantExact}, L{EquidistantGeodSolve} and L{EquidistantKarney}. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{EquidistantExact}, L{EquidistantGeodSolve} or L{EquidistantKarney} projection. ''' _AzimuthalGeodesic.__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 easting C{x} and northing C{y} of point 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}}. @note: A call to C{.forward} followed by a call to C{.reverse} will return the original C{lat, lon} to within roundoff. ''' r = self.geodesic.Inverse(self.lat0, self.lon0, Lat_(lat), Lon_(lon), self._mask) x, y = sincos2d(r.azi1) return self._7Tuple(x * r.s12, y * r.s12, r, name=name) def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): # PYCHOK signature '''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 C{B{LatLon} is 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. ''' e, n, z, s = _enzh4(x, y) r = self.geodesic.Direct(self.lat0, self.lon0, z, s, self._mask) return self._7Tuple(e, n, r, name=name) if LatLon is None else \ self._toLatLon(r.lat2, r.lon2, LatLon, LatLon_kwds, name) class EquidistantExact(_EquidistantBase): '''Azimuthal equidistant projection, a Python version of I{Karney}'s C++ class U{AzimuthalEquidistant <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>}, based on exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact}. 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=_WGS84, name=NN): '''New azimuthal L{EquidistantExact} 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 AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}} or B{C{datum}}. ''' _EquidistantBase.__init__(self, lat0, lon0, datum=datum, name=name) if _FOR_DOCS: forward = _EquidistantBase.forward reverse = _EquidistantBase.reverse @Property_RO def geodesic(self): '''Get this projection's exact geodesic (L{GeodesicExact}). ''' return self.datum.ellipsoid.geodesicx class EquidistantGeodSolve(_EquidistantBase): '''Azimuthal equidistant projection, a Python version of I{Karney}'s C++ class U{AzimuthalEquidistant <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>}, based on (exact) geodesic I{wrappers} L{GeodesicSolve} and L{GeodesicLineSolve} and intended I{for testing purposes only}. @see: L{EquidistantExact} and module L{geodsolve}. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{EquidistantGeodSolve} 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 AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}} or B{C{datum}}. ''' _EquidistantBase.__init__(self, lat0, lon0, datum=datum, name=name) if _FOR_DOCS: forward = _EquidistantBase.forward reverse = _EquidistantBase.reverse @Property_RO def geodesic(self): '''Get this projection's (exact) geodesic (L{GeodesicSolve}). ''' return self.datum.ellipsoid.geodsolve class EquidistantKarney(_EquidistantBase): '''Azimuthal equidistant projection, a Python version of I{Karney}'s C++ class U{AzimuthalEquidistant <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>}, requiring package U{geographiclib<https://PyPI.org/project/geographiclib>} to be installed. @see: L{EquidistantExact}. ''' def __init__(self, lat0, lon0, datum=_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>} not installed or not found. @raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}} or B{C{datum}}. ''' _EquidistantBase.__init__(self, lat0, lon0, datum=datum, name=name) if _FOR_DOCS: forward = _EquidistantBase.forward reverse = _EquidistantBase.reverse @Property_RO def geodesic(self): '''Get this projection's I{wrapped} U{Karney Geodesic <https://GeographicLib.SourceForge.io/C++/doc/python/code.html>}, provided package U{geographiclib <https://PyPI.org/project/geographiclib>} is installed. ''' return self.datum.ellipsoid.geodesic _Equidistants = (Equidistant, EquidistantExact, EquidistantGeodSolve, EquidistantKarney) # PYCHOK in .ellipsoidalBaseDI class Gnomonic(_AzimuthalBase): '''Azimuthal gnomonic projection for the sphere***, see U{Snyder, pp 164-168 <https://Pubs.USGS.gov/pp/1395/report.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 easting C{x} and northing C{y} of point 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 k = (_1_0 / c) if t else _1_0 return k, t return self._forward(lat, lon, name, _k_t) def reverse(self, x, y, name=NN, **LatLon_and_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_and_kwds: Optional, C{B{LatLon}=None} class to use and additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None} or not given. @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(c): return atan(c) if c > EPS else None return self._reverse(x, y, name, _c, False, **LatLon_and_kwds) def gnomonic(lat0, lon0, datum=_WGS84, exact=False, geodsolve=False, name=NN): '''Return a L{GnomonicExact} or (if I{Karney}'s U{geographiclib <https://PyPI.org/project/geographiclib>} package is installed) a L{GnomonicKarney}, otherwise a 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 exact: Return a L{GnomonicExact} instance. @kwarg geodsolve: Return a L{GnomonicGeodSolve} instance. @kwarg name: Optional name for the projection (C{str}). @return: A L{GnomonicExact}, L{GnomonicGeodSolve}, L{GnomonicKarney} or L{Gnomonic} instance. @raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}} or (spherical) B{C{datum}}. @raise GeodesicError: Issue with L{GeodesicExact}, L{GeodesicSolve} or I{Karney}'s wrapped C{Geodesic}. @raise TypeError: Invalid B{C{datum}}. ''' G = GnomonicExact if exact else (GnomonicGeodSolve if geodsolve else Gnomonic) if G is Gnomonic: try: return GnomonicKarney(lat0, lon0, datum=datum, name=name) # PYCHOK types except ImportError: pass return G(lat0, lon0, datum=datum, name=name) # PYCHOK types class _GnomonicBase(_AzimuthalGeodesic): '''(INTERNAL) Base for classes L{GnomonicExact}, L{GnomonicGeodSolve} and L{GnomonicKarney}. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{GnomonicExact} or L{GnomonicKarney} projection. ''' _AzimuthalGeodesic.__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): # PYCHOK signature '''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 don't throw an error (C{bool}) if the location lies over the horizon. @return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} with easting C{x} and northing 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 C{B{raiser}=False}. @raise AzimuthalError: Invalid B{C{lat}}, B{C{lon}} or the location lies over the horizon and C{B{raiser}=True}. ''' self._iteration = 0 r = self.geodesic.Inverse(self.lat0, self.lon0, Lat_(lat), Lon_(lon), self._mask) M = r.M21 if M > EPS0: q = r.m12 / M # .M12 e, n = sincos2d(r.azi1) e *= q n *= q elif raiser: # PYCHOK no cover raise AzimuthalError(lat=lat, lon=lon, txt=_over_horizon_) else: # PYCHOK no cover e = n = NAN t = self._7Tuple(e, n, r, M=M, name=name) t._iteraton = 0 return t def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): # PYCHOK signature '''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 C{B{LatLon} is 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. ''' e, n, z, q = _enzh4(x, y) d = a = self.equatoradius s = a * atan(q / a) if q > a: # PYCHOK no cover def _d(r, q): return (r.M12 - q * r.m12) * r.m12 # negated q = _1_0 / q else: # little == True def _d(r, q): # PYCHOK _d return (q * r.M12 - r.m12) * r.M12 # negated a *= _EPS_K m = self._mask g = self.geodesic P = g.Line(self.lat0, self.lon0, z, m | g.LINE_OFF).Position _S2 = Fsum(s).fsum2_ for i in range(1, _TRIPS): r = P(s, m) if fabs(d) < a: break s, d = _S2(_d(r, q)) else: # PYCHOK no cover self._iteration = _TRIPS raise AzimuthalError(Fmt.no_convergence(d, a), txt=unstr(self.reverse, x, y)) t = self._7Tuple(e, n, r, M=r.M12, name=name) if LatLon is None else \ self._toLatLon(r.lat2, r.lon2, LatLon, LatLon_kwds, name) t._iteration = self._iteration = i return t class GnomonicExact(_GnomonicBase): '''Azimuthal gnomonic projection, a Python version of I{Karney}'s C++ class U{Gnomonic <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Gnomonic.html>}, based on exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact}. @see: I{Karney}'s U{Detailed Description<https://GeographicLib.SourceForge.io/C++/doc/ classGeographicLib_1_1Gnomonic.html>}, especially the B{Warning}. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{GnomonicExact} 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 AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}}. ''' _GnomonicBase.__init__(self, lat0, lon0, datum=datum, name=name) if _FOR_DOCS: forward = _GnomonicBase.forward reverse = _GnomonicBase.reverse @Property_RO def geodesic(self): '''Get this projection's exact geodesic (L{GeodesicExact}). ''' return self.datum.ellipsoid.geodesicx class GnomonicGeodSolve(_GnomonicBase): '''Azimuthal gnomonic projection, a Python version of I{Karney}'s C++ class U{Gnomonic <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Gnomonic.html>}, based on (exact) geodesic I{wrappers} L{GeodesicSolve} and L{GeodesicLineSolve} and intended I{for testing purposes only}. @see: L{GnomonicExact} and module L{geodsolve}. ''' def __init__(self, lat0, lon0, datum=_WGS84, name=NN): '''New azimuthal L{GnomonicGeodSolve} 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 AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}}. ''' _GnomonicBase.__init__(self, lat0, lon0, datum=datum, name=name) if _FOR_DOCS: forward = _GnomonicBase.forward reverse = _GnomonicBase.reverse @Property_RO def geodesic(self): '''Get this projection's (exact) geodesic (L{GeodesicSolve}). ''' return self.datum.ellipsoid.geodsolve class GnomonicKarney(_GnomonicBase): '''Azimuthal gnomonic projection, a Python version of I{Karney}'s C++ class U{Gnomonic <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Gnomonic.html>}, requiring package U{geographiclib<https://PyPI.org/project/geographiclib>} to be installed. @see: L{GnomonicExact}. ''' def __init__(self, lat0, lon0, datum=_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>} not installed or not found. @raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}}. ''' _GnomonicBase.__init__(self, lat0, lon0, datum=datum, name=name) if _FOR_DOCS: forward = _GnomonicBase.forward reverse = _GnomonicBase.reverse @Property_RO def geodesic(self): '''Get this projection's I{wrapped} U{Karney Geodesic <https://GeographicLib.SourceForge.io/C++/doc/python/code.html>}, provided package U{geographiclib<https://PyPI.org/project/geographiclib>} is installed. ''' return self.datum.ellipsoid.geodesic class LambertEqualArea(_AzimuthalBase): '''Lambert-equal-area projection for the sphere*** (aka U{Lambert zenithal equal-area projection<https://WikiPedia.org/wiki/Lambert_azimuthal_equal-area_projection>}, see U{Snyder, pp 185-187<https://Pubs.USGS.gov/pp/1395/report.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 easting C{x} and northing C{y} of point 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): c += _1_0 t = c > EPS0 k = sqrt(_2_0 / c) if t else _1_0 return k, t return self._forward(lat, lon, name, _k_t) def reverse(self, x, y, name=NN, **LatLon_and_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_and_kwds: Optional, C{B{LatLon}=None} class to use and additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None} or not given. @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(c): c *= _0_5 return (asin1(c) * _2_0) if c > EPS else None return self._reverse(x, y, name, _c, True, **LatLon_and_kwds) class Orthographic(_AzimuthalBase): '''Orthographic projection for the sphere***, see U{Snyder, pp 148-153 <https://Pubs.USGS.gov/pp/1395/report.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 easting C{x} and northing C{y} of point 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): return _1_0, (c >= 0) return self._forward(lat, lon, name, _k_t) def reverse(self, x, y, name=NN, **LatLon_and_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_and_kwds: Optional, C{B{LatLon}=None} class to use and additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None} or not given. @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(c): return asin1(c) if c > EPS else None return self._reverse(x, y, name, _c, False, **LatLon_and_kwds) class Stereographic(_AzimuthalBase): '''Stereographic projection for the sphere***, see U{Snyder, pp 157-160 <https://Pubs.USGS.gov/pp/1395/report.pdf>} and U{MathWorld-Wolfram <https://MathWorld.Wolfram.com/StereographicProjection.html>}. ''' _k0 = _1_0 # central scale factor (C{scalar}) _k02 = _2_0 # double ._k0 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 easting C{x} and northing C{y} of point 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): c += _1_0 t = isnon0(c) k = (self._k02 / c) if t else _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? self._k02 = self._k0 * _2_0 def reverse(self, x, y, name=NN, **LatLon_and_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_and_kwds: Optional, C{B{LatLon}=None} class to use and additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None} or not given. @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(c): return (_2_0 * atan2(c, self._k02)) if c > EPS else None return self._reverse(x, y, name, _c, False, **LatLon_and_kwds) __all__ += _ALL_DOCS(_AzimuthalBase, _AzimuthalGeodesic, _EquidistantBase, _GnomonicBase) # **) MIT License # # Copyright (C) 2016-2023 -- 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.