# Coverage for pygeodesy/ellipsoidalBase.py : 95%

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Pure Python implementation of geodesy tools for ellipsoidal earth models, transcribed in part from JavaScript originals by I{(C) Chris Veness 2005-2016} and published under the same MIT Licence**, see for example U{latlon-ellipsoidal <https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}. @newfield example: Example, Examples ''' from pygeodesy.basics import issubclassof, property_doc_, property_RO, \ _xinstanceof from pygeodesy.cartesianBase import CartesianBase from pygeodesy.datums import Datum, Datums, _ellipsoidal_datum from pygeodesy.errors import _AssertionError, _incompatible, IntersectionError, \ _IsnotError, TRFError, _ValueError, _xellipsoidal from pygeodesy.fmath import euclid, favg, fmean_, fsum_ from pygeodesy.formy import _radical2 from pygeodesy.interns import _ellipsoidal_ # PYCHOK used! from pygeodesy.interns import EPS, EPS1, MISSING, NN, PI, _COMMA_, \ _conversion_, _datum_, _DOT_, _exceed_PI_radians_, \ _N_, _no_, _near_concentric_, _SPACE_, _too_ from pygeodesy.latlonBase import LatLonBase, _trilaterate5 from pygeodesy.lazily import _ALL_DOCS from pygeodesy.named import _xnamed from pygeodesy.namedTuples import _LatLon4Tuple, Vector3Tuple from pygeodesy.streprs import Fmt from pygeodesy.units import Epoch, Height, Radius_, Scalar from pygeodesy.utily import m2degrees, unroll180 __all__ = () __version__ = '20.12.19' _TOL_M = 1e-3 # 1 millimeter, in .ellipsoidKarney, -Vincenty _TRIPS = 17 # _intersects2, _nearestOn interations, 6 is sufficient class CartesianEllipsoidalBase(CartesianBase): '''(INTERNAL) Base class for ellipsoidal C{Cartesian}s. ''' _datum = Datums.WGS84 # L{Datum} def convertRefFrame(self, reframe2, reframe, epoch=None): '''Convert this cartesian point from one to an other reference frame. @arg reframe2: Reference frame to convert I{to} (L{RefFrame}). @arg reframe: Reference frame to convert I{from} (L{RefFrame}). @kwarg epoch: Optional epoch to observe for B{C{reframe}}, a fractional calendar year (C{scalar}). @return: The converted point (C{Cartesian}) or this point if conversion is C{nil}. @raise TRFError: No conversion available from B{C{reframe}} to B{C{reframe2}}. @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a L{RefFrame} or B{C{epoch}} not C{scalar}. ''' from pygeodesy.trf import RefFrame, _reframeTransforms _xinstanceof(RefFrame, reframe2=reframe2, reframe=reframe) c, d = self, self.datum for t in _reframeTransforms(reframe2, reframe, reframe.epoch if epoch is None else Epoch(epoch)): c = c._applyHelmert(t, False, datum=d) return c class LatLonEllipsoidalBase(LatLonBase): '''(INTERNAL) Base class for ellipsoidal C{LatLon}s. ''' _convergence = None # UTM/UPS meridian convergence (C{degrees}) _datum = Datums.WGS84 # L{Datum} _elevation2 = () # cached C{elevation2} result _epoch = None # overriding .reframe.epoch (C{float}) _etm = None # cached toEtm (L{Etm}) _geoidHeight2 = () # cached C{geoidHeight2} result _iteration = None # iteration number (C{int} or C{None}) _lcc = None # cached toLcc (C{Lcc}) _osgr = None # cached toOsgr (C{Osgr}) _reframe = None # reference frame (L{RefFrame}) _scale = None # UTM/UPS scale factor (C{float}) _ups = None # cached toUps (L{Ups}) _utm = None # cached toUtm (L{Utm}) _wm = None # cached toWm (webmercator.Wm instance) def __init__(self, lat, lon, height=0, datum=None, reframe=None, epoch=None, name=NN): '''Create an ellipsoidal C{LatLon} point frome the given lat-, longitude and height on the given datum and with the given reference frame and epoch. @arg lat: Latitude (C{degrees} or DMS C{[N|S]}). @arg lon: Longitude (C{degrees} or DMS C{str[E|W]}). @kwarg height: Optional elevation (C{meter}, the same units as the datum's half-axes). @kwarg datum: Optional, ellipsoidal datum to use (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg reframe: Optional reference frame (L{RefFrame}). @kwarg epoch: Optional epoch to observe for B{C{reframe}} (C{scalar}), a non-zero, fractional calendar year. @kwarg name: Optional name (string). @raise RangeError: Value of B{C{lat}} or B{C{lon}} outside the valid range and C{rangerrors} set to C{True}. @raise TypeError: B{C{datum}} is not a L{datum}, B{C{reframe}} is not a L{RefFrame} or B{C{epoch}} is not C{scalar} non-zero. @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}. @example: >>> p = LatLon(51.4778, -0.0016) # height=0, datum=Datums.WGS84 ''' LatLonBase.__init__(self, lat, lon, height=height, name=name) if datum not in (None, self._datum): self.datum = _ellipsoidal_datum(datum, name=name) if reframe: self.reframe = reframe self.epoch = epoch def _Radjust2(self, adjust, datum, meter_text2): '''(INTERNAL) Adjust elevation or geoidHeight with difference in Gaussian radii of curvature of given datum and NAD83. @note: This is an arbitrary, possibly incorrect adjustment. ''' if adjust: # Elevation2Tuple or GeoidHeight2Tuple m, t = meter_text2 if isinstance(m, float): n = Datums.NAD83.ellipsoid.rocGauss(self.lat) if min(abs(m), n) > EPS: # use ratio, datum and NAD83 units may differ e = self.ellipsoid(datum).rocGauss(self.lat) if min(abs(e - n), e) > EPS: m *= e / n meter_text2 = meter_text2.classof(m, t) return self._xnamed(meter_text2) def _update(self, updated, *attrs): '''(INTERNAL) Zap cached attributes if updated. ''' if updated: LatLonBase._update(self, updated, '_etm', '_lcc', '_osgr', '_ups', '_utm', '_wm', *attrs) if self._elevation2: self._elevation2 = () if self._geoidHeight2: self._geoidHeight2 = () def antipode(self, height=None): '''Return the antipode, the point diametrically opposite to this point. @kwarg height: Optional height of the antipode, height of this point otherwise (C{meter}). @return: The antipodal point (C{LatLon}). ''' lla = LatLonBase.antipode(self, height=height) if lla.datum != self.datum: lla.datum = self.datum return lla @property_RO def convergence(self): '''Get this point's UTM or UPS meridian convergence (C{degrees}) or C{None} if not converted from L{Utm} or L{Ups}. ''' return self._convergence def convertDatum(self, datum2): '''Convert this point to an other datum. @arg datum2: Datum to convert I{to} (L{Datum}). @return: The converted point (ellipsoidal C{LatLon}). @raise TypeError: The B{C{datum2}} invalid. @example: >>> p = LatLon(51.4778, -0.0016) # default Datums.WGS84 >>> p.convertDatum(Datums.OSGB36) # 51.477284°N, 000.00002°E ''' d2 = _ellipsoidal_datum(datum2, name=self.name) if self.datum == d2: return self.copy() c = self.toCartesian().convertDatum(d2) return c.toLatLon(datum=d2, LatLon=self.classof) def convertRefFrame(self, reframe2): '''Convert this point to an other reference frame. @arg reframe2: Reference frame to convert I{to} (L{RefFrame}). @return: The converted point (ellipsoidal C{LatLon}) or this point if conversion is C{nil}. @raise TRFError: No B{C{.reframe}} or no conversion available from B{C{.reframe}} to B{C{reframe2}}. @raise TypeError: The B{C{reframe2}} is not a L{RefFrame}. @example: >>> p = LatLon(51.4778, -0.0016, reframe=RefFrames.ETRF2000) # default Datums.WGS84 >>> p.convertRefFrame(RefFrames.ITRF2014) # 51.477803°N, 000.001597°W, +0.01m ''' from pygeodesy.trf import RefFrame, _reframeTransforms _xinstanceof(RefFrame, reframe2=reframe2) if not self.reframe: t = _SPACE_(_DOT_(repr(self), 'reframe'), MISSING) raise TRFError(_no_(_conversion_), txt=t) ts = _reframeTransforms(reframe2, self.reframe, self.epoch) if ts: c = self.toCartesian() for t in ts: c = c._applyHelmert(t, False) ll = c.toLatLon(datum=self.datum, LatLon=self.classof, epoch=self.epoch, reframe=reframe2) # ll.reframe, ll.epoch = reframe2, self.epoch else: ll = self return ll @property_doc_(''' this points's datum (L{Datum}).''') def datum(self): '''Get this point's datum (L{Datum}). ''' return self._datum @datum.setter # PYCHOK setter! def datum(self, datum): '''Set this point's datum I{without conversion}. @arg datum: New datum (L{Datum}). @raise TypeError: The B{C{datum}} is not a L{Datum} or not ellipsoidal. ''' _xinstanceof(Datum, datum=datum) if not datum.isEllipsoidal: raise _IsnotError(_ellipsoidal_, datum=datum) self._update(datum != self._datum) self._datum = datum def distanceTo2(self, other): '''I{Approximate} the distance and (initial) bearing between this and an other (ellipsoidal) point based on the radii of curvature. I{Suitable only for short distances up to a few hundred Km or Miles and only between points not near-polar}. @arg other: The other point (C{LatLon}). @return: An L{Distance2Tuple}C{(distance, initial)}. @raise TypeError: The B{C{other}} point is not C{LatLon}. @raise ValueError: Incompatible datum ellipsoids. @see: Method L{Ellipsoid.distance2} and U{Local, flat earth approximation<https://www.EdWilliams.org/avform.htm#flat>} aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>} formula. ''' return self.ellipsoids(other).distance2(self.lat, self.lon, other.lat, other.lon) def elevation2(self, adjust=True, datum=Datums.WGS84, timeout=2): '''Return elevation of this point for its or the given datum. @kwarg adjust: Adjust the elevation for a B{C{datum}} other than C{NAD83} (C{bool}). @kwarg datum: Optional datum (L{Datum}). @kwarg timeout: Optional query timeout (C{seconds}). @return: An L{Elevation2Tuple}C{(elevation, data_source)} or C{(None, error)} in case of errors. @note: The adjustment applied is the difference in geocentric earth radius between the B{C{datum}} and C{NAV83} upon which the L{elevations.elevation2} is based. @note: NED elevation is only available for locations within the U{Conterminous US (CONUS) <https://WikiPedia.org/wiki/Contiguous_United_States>}. @see: Function L{elevations.elevation2} and method L{Ellipsoid.Rgeocentric} for further details and possible C{error}s. ''' if not self._elevation2: # get elevation and data source from pygeodesy.elevations import elevation2 self._elevation2 = elevation2(self.lat, self.lon, timeout=timeout) return self._Radjust2(adjust, datum, self._elevation2) def ellipsoid(self, datum=Datums.WGS84): '''Return the ellipsoid of this point's datum or the given datum. @kwarg datum: Default datum (L{Datum}). @return: The ellipsoid (L{Ellipsoid} or L{Ellipsoid2}). ''' return getattr(self, _datum_, datum).ellipsoid def ellipsoids(self, other): '''Check the type and ellipsoid of this and an other point's datum. @arg other: The other point (C{LatLon}). @return: This point's datum ellipsoid (L{Ellipsoid} or L{Ellipsoid2}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @raise ValueError: Incompatible datum ellipsoids. ''' self.others(other, up=2) # ellipsoids' caller E = self.ellipsoid() try: # other may be Sphere, etc. e = other.ellipsoid() except AttributeError: # PYCHOK no cover try: # no ellipsoid method, try datum e = other.datum.ellipsoid except AttributeError: e = E # no datum, XXX assume equivalent? if e != E: raise _ValueError(e.named2, txt=_incompatible(E.named2)) return E @property_doc_(''' this point's observed or C{reframe} epoch (C{float}).''') def epoch(self): '''Get this point's observed or C{reframe} epoch (C{float}) or C{None}. ''' return self._epoch or (self.reframe.epoch if self.reframe else None) @epoch.setter # PYCHOK setter! def epoch(self, epoch): '''Set or clear this point's observed epoch. @arg epoch: Observed epoch, a fractional calendar year (L{Epoch}, C{scalar}) or C{None}. @raise TRFError: Invalid B{C{epoch}}. ''' self._epoch = None if epoch is None else Epoch(epoch) def geoidHeight2(self, adjust=False, datum=Datums.WGS84, timeout=2): '''Return geoid height of this point for its or the given datum. @kwarg adjust: Adjust the geoid height for a B{C{datum}} other than C{NAD83/NADV88} (C{bool}). @kwarg datum: Optional datum (L{Datum}). @kwarg timeout: Optional query timeout (C{seconds}). @return: An L{GeoidHeight2Tuple}C{(height, model_name)} or C{(None, error)} in case of errors. @note: The adjustment applied is the difference in geocentric earth radius between the B{C{datum}} and C{NAV83/NADV88} upon which the L{elevations.geoidHeight2} is based. @note: The geoid height is only available for locations within the U{Conterminous US (CONUS) <https://WikiPedia.org/wiki/Contiguous_United_States>}. @see: Function L{elevations.geoidHeight2} and method L{Ellipsoid.Rgeocentric} for further details and possible C{error}s. ''' if not self._geoidHeight2: # get elevation and data source from pygeodesy.elevations import geoidHeight2 self._geoidHeight2 = geoidHeight2(self.lat, self.lon, model=0, timeout=timeout) return self._Radjust2(adjust, datum, self._geoidHeight2) def intersections2(self, radius1, other, radius2, height=None, wrap=True, equidistant=None, tol=_TOL_M): '''Compute the intersection points of two circles each defined by a center point and a radius. @arg radius1: Radius of the this circle (C{meter}, conventionally). @arg other: Center of the other circle (C{LatLon}). @arg radius2: Radius of the other circle (C{meter}, same units as B{C{radius1}}). @kwarg height: Optional height for the intersection points, overriding the "radical height" at the "radical line" between both centers (C{meter}) or C{None}. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg equidistant: An azimuthal equidistant projection class (L{Equidistant} or L{EquidistantKarney}), function L{equidistant} will be invoked if left unspecified. @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}} and B{C{radius2}}). @return: 2-Tuple of the intersection points, each a C{LatLon} instance. For abutting circles, both intersection points are the same instance. @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting circles or no convergence for B{C{tol}}. @raise TypeError: Invalid B{C{other}} or B{C{equidistant}}. @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}. @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ calculating-intersection-of-two-circles>}, U{Karney's paper <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{I{14. MARITIME BOUNDARIES}}, U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>} intersections. ''' self.others(other) return _intersects2(self, radius1, other, radius2, height=height, wrap=wrap, equidistant=equidistant, tol=tol, LatLon=self.classof, datum=self.datum) def nearestOn(self, point1, point2, within=True, height=None, wrap=True, equidistant=None, tol=_TOL_M): '''Locate the closest point between two other points. @arg point1: Start point (C{LatLon}). @arg point2: End point (C{LatLon}). @kwarg within: If C{True} return the closest point I{between} B{C{point1}} and B{C{point2}}, otherwise the closest point elsewhere on the arc (C{bool}). @kwarg height: Optional height for the closest point (C{meter}) or C{None} to interpolate the height. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg equidistant: An azimuthal equidistant projection class (L{Equidistant} or L{EquidistantKarney}), function L{equidistant} will be invoked if left unspecified. @kwarg tol: Convergence tolerance (C{meter}). @return: Closest point (C{LatLon}). @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @raise TypeError: Invalid B{C{point1}}, B{C{point2}} or B{C{equidistant}}. ''' p1 = self.others(point1=point1) p2 = self.others(point2=point2) return _nearestOn(self, p1, p2, within=within, height=height, wrap=wrap, equidistant=equidistant, tol=tol, LatLon=self.classof, datum=self.datum) @property_RO def iteration(self): '''Get the iteration number (C{int} or C{None} if not available/applicable) of the most recent C{intersections2} or C{nearestOn} invokation. ''' return self._iteration def parse(self, strllh, height=0, datum=None, sep=_COMMA_, name=NN): '''Parse a string representing a similar, ellipsoidal C{LatLon} point, consisting of C{"lat, lon[, height]"}. @arg strllh: Lat, lon and optional height (C{str}), see function L{parse3llh}. @kwarg height: Optional, default height (C{meter} or C{None}). @kwarg datum: Optional datum (L{Datum}), overriding this datum I{without conversion}. @kwarg sep: Optional separator (C{str}). @kwarg name: Optional instance name (C{str}), overriding this name. @return: The similar point (ellipsoidal C{LatLon}). @raise ParseError: Invalid B{C{strllh}}. ''' from pygeodesy.dms import parse3llh a, b, h = parse3llh(strllh, height=height, sep=sep) r = self.classof(a, b, height=h, datum=self.datum) if datum not in (None, self.datum): r.datum = datum return _xnamed(r, name or self.name, force=True) @property_doc_(''' this point's reference frame (L{RefFrame}).''') def reframe(self): '''Get this point's reference frame (L{RefFrame}) or C{None}. ''' return self._reframe @reframe.setter # PYCHOK setter! def reframe(self, reframe): '''Set or clear this point's reference frame. @arg reframe: Reference frame (L{RefFrame}) or C{None}. @raise TypeError: The B{C{reframe}} is not a L{RefFrame}. ''' if reframe is not None: from pygeodesy.trf import RefFrame _xinstanceof(RefFrame, reframe=reframe) self._reframe = reframe elif self.reframe is not None: self._reframe = None @property_RO def scale(self): '''Get this point's UTM grid or UPS point scale factor (C{float}) or C{None} if not converted from L{Utm} or L{Ups}. ''' return self._scale def to3xyz(self): # PYCHOK no cover '''DEPRECATED, use method C{toEcef}. @return: A L{Vector3Tuple}C{(x, y, z)}. @note: Overloads C{LatLonBase.to3xyz} ''' r = self.toEcef() return self._xnamed(Vector3Tuple(r.x, r.y, r.z)) def toEtm(self): '''Convert this C{LatLon} point to an ETM coordinate. @return: The ETM coordinate (L{Etm}). @see: Function L{toEtm8}. ''' if self._etm is None: from pygeodesy.etm import toEtm8, Etm # PYCHOK recursive import self._etm = toEtm8(self, datum=self.datum, Etm=Etm) return self._etm def toLcc(self): '''Convert this C{LatLon} point to a Lambert location. @see: Function L{toLcc} in module L{lcc}. @return: The Lambert location (L{Lcc}). ''' if self._lcc is None: from pygeodesy.lcc import Lcc, toLcc # PYCHOK recursive import self._lcc = toLcc(self, height=self.height, Lcc=Lcc, name=self.name) return self._lcc def toOsgr(self): '''Convert this C{LatLon} point to an OSGR coordinate. @see: Function L{toOsgr} in module L{osgr}. @return: The OSGR coordinate (L{Osgr}). ''' if self._osgr is None: from pygeodesy.osgr import Osgr, toOsgr # PYCHOK recursive import self._osgr = toOsgr(self, datum=self.datum, Osgr=Osgr, name=self.name) return self._osgr def toUps(self, pole=_N_, falsed=True): '''Convert this C{LatLon} point to a UPS coordinate. @kwarg pole: Optional top/center of (stereographic) projection (C{str}, 'N[orth]' or 'S[outh]'). @kwarg falsed: False easting and northing (C{bool}). @return: The UPS coordinate (L{Ups}). @see: Function L{toUps8}. ''' if self._ups is None: from pygeodesy.ups import toUps8, Ups # PYCHOK recursive import self._ups = toUps8(self, datum=self.datum, Ups=Ups, pole=pole, falsed=falsed) return self._ups def toUtm(self): '''Convert this C{LatLon} point to a UTM coordinate. @return: The UTM coordinate (L{Utm}). @see: Function L{toUtm8}. ''' if self._utm is None: from pygeodesy.utm import toUtm8, Utm # PYCHOK recursive import self._utm = toUtm8(self, datum=self.datum, Utm=Utm) return self._utm def toUtmUps(self, pole=NN): '''Convert this C{LatLon} point to a UTM or UPS coordinate. @kwarg pole: Optional top/center of UPS (stereographic) projection (C{str}, 'N[orth]' or 'S[outh]'). @return: The UTM or UPS coordinate (L{Utm} or L{Ups}). @raise TypeError: Result in L{Utm} or L{Ups}. @see: Function L{toUtmUps}. ''' if self._utm: u = self._utm elif self._ups and (self._ups.pole == pole or not pole): u = self._ups else: from pygeodesy.utmups import toUtmUps8, Utm, Ups # PYCHOK recursive import u = toUtmUps8(self, datum=self.datum, Utm=Utm, Ups=Ups, pole=pole) if isinstance(u, Utm): self._utm = u elif isinstance(u, Ups): self._ups = u else: _xinstanceof(Utm, Ups, toUtmUps8=u) return u def toWm(self): '''Convert this C{LatLon} point to a WM coordinate. @see: Function L{toWm} in module L{webmercator}. @return: The WM coordinate (L{Wm}). ''' if self._wm is None: from pygeodesy.webmercator import toWm # PYCHOK recursive import self._wm = toWm(self) return self._wm def trilaterate5(self, distance1, point2, distance2, point3, distance3, area=True, eps=EPS1, wrap=False): '''Trilaterate three points by area overlap or perimeter intersection of three intersecting circles. @arg distance1: Distance to this point (C{meter}), same units as B{C{eps}}). @arg point2: Second center point (C{LatLon}). @arg distance2: Distance to point2 (C{meter}, same units as B{C{eps}}). @arg point3: Third center point (C{LatLon}). @arg distance3: Distance to point3 (C{meter}, same units as B{C{eps}}). @kwarg area: If C{True} compute the area overlap, otherwise the perimeter intersection of the circles (C{bool}). @kwarg eps: The required I{minimal overlap} for C{B{area}=True} or the I{intersection margin} for C{B{area}=False} (C{meter}, conventionally). @kwarg wrap: Wrap/unroll angular distances (C{bool}). @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} with C{min} and C{max} in C{meter}, same units as B{C{eps}}, the corresponding trilaterated points C{minPoint} and C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number of trilatered points found for the given B{C{eps}}. If only a single trilaterated point is found, C{min I{is} max}, C{minPoint I{is} maxPoint} and C{n = 1}. For C{B{area}=True}, C{min} and C{max} are the smallest respectively largest I{radial} overlap found. For C{B{area}=False}, C{min} and C{max} represent the nearest respectively farthest intersection margin. If C{B{area}=True} and all 3 circles are concentric, C{n=0} and C{minPoint} and C{maxPoint} are the B{C{point#}} with the smallest B{C{distance#}} C{min} respectively C{max} the largest B{C{distance#}}. @raise IntersectionError: Trilateration failed for the given B{C{eps}}, insufficient overlap for C{B{area}=True} or no intersection or all (near-)concentric for C{B{area}=False}. @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. @raise ValueError: Some B{C{points}} coincide or invalid B{C{distance1}}, B{C{distance2}} or B{C{distance3}}. @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2} and C{LatLon.nearestOn}. Install Karney's Python package U{geographiclib<https://PyPI.org/project/geographiclib>} to obtain the most accurate results for both C{ellipsoidalVincenty.LatLon} and C{ellipsoidalKarney.LatLon} points. ''' return _trilaterate5(self, distance1, self.others(point2=point2), distance2, self.others(point3=point3), distance3, area=area, eps=eps, wrap=wrap) def _Equidistant2(equidistant, datum): # (INTERNAL) Get an C{Equidistant} or C{EquidistantKarney} instance import pygeodesy.azimuthal as _az if equidistant is None or not callable(equidistant): equidistant = _az.equidistant elif not (issubclassof(equidistant, _az.Equidistant) or issubclassof(equidistant, _az.EquidistantKarney)): raise _IsnotError(_az.Equidistant.__name__, _az.EquidistantKarney.__name__, equidistant=equidistant) return equidistant(0, 0, datum) def _intermediateTo(p1, p2, fraction, height, wrap): # (INTERNAL) Helper for C{ellipsoidalKarney.LatLon.intermediateTo} # and C{ellipsoidalVincenty.LatLon.intermediateTo}. t = p1.distanceTo3(p2, wrap=wrap) f = Scalar(fraction=fraction) h = p1._havg(p2, f=f) if height is None else Height(height) return p1.destination(t.distance * f, t.initial, height=h) def _intersections2(center1, radius1, center2, radius2, height=None, wrap=True, equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): # (INTERNAL) Iteratively compute the intersection points of two circles # each defined by an (ellipsoidal) center point and a radius, imported # by .ellipsoidalKarney and -Vincenty c1 = _xellipsoidal(center1=center1) c2 = c1.others(center2=center2) r1 = Radius_(radius1=radius1) r2 = Radius_(radius2=radius2) try: return _intersects2(c1, r1, c2, r2, height=height, wrap=wrap, equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds) except (TypeError, ValueError) as x: raise IntersectionError(center1=center1, radius1=radius1, center2=center2, radius2=radius2, txt=str(x)) def _intersects2(c1, r1, c2, r2, height=None, wrap=True, # MCCABE 17 equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): # (INTERNAL) Intersect two spherical circles, see L{_intersections2} # above, separated to allow callers to embellish any exceptions from pygeodesy.sphericalTrigonometry import _intersects2 as _si2, LatLon as _LLS from pygeodesy.vector3d import _intersects2 as _vi2 def _latlon4(t, h, n): r = _LatLon4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds) r._iteration = t.iteration # ._iteration for tests return _xnamed(r, n) if r1 < r2: c1, c2 = c2, c1 r1, r2 = r2, r1 E = c1.ellipsoids(c2) if r1 > (min(E.b, E.a) * PI): raise ValueError(_exceed_PI_radians_) if wrap: # unroll180 == .karney._unroll2 c2 = _unrollon(c1, c2) # distance between centers and radii are # measured along the ellipsoid's surface m = c1.distanceTo(c2, wrap=False) # meter if m < max(r1 - r2, EPS): raise ValueError(_near_concentric_) if fsum_(r1, r2, -m) < 0: raise ValueError(_too_(Fmt.distant(m))) f = _radical2(m, r1, r2).ratio # "radical fraction" r = E.rocMean(favg(c1.lat, c2.lat, f=f)) e = max(m2degrees(tol, radius=r), EPS) # get the azimuthal equidistant projection A = _Equidistant2(equidistant, c1.datum) # gu-/estimate initial intersections, spherically ... t1, t2 = _si2(_LLS(c1.lat, c1.lon, height=c1.height), r1, _LLS(c2.lat, c2.lon, height=c2.height), r2, radius=r, height=height, wrap=False, too_d=m) h, n = t1.height, t1.name # ... and then iterate like Karney suggests to find # tri-points of median lines, @see: references under # method LatLonEllipsoidalBase.intersections2 above ts, ta = [], None for t in ((t1,) if t1 is t2 else (t1, t2)): p = None # force first d == p to False for i in range(1, _TRIPS): A.reset(t.lat, t.lon) # gu-/estimate as origin # convert centers to projection space t1 = A.forward(c1.lat, c1.lon) t2 = A.forward(c2.lat, c2.lon) # compute intersections in projection space v1, v2 = _vi2(t1, r1, # XXX * t1.scale?, t2, r2, # XXX * t2.scale?, sphere=False, too_d=m) # convert intersections back to geodetic t1 = A.reverse(v1.x, v1.y) d1 = euclid(t1.lat - t.lat, t1.lon - t.lon) if v1 is v2: # abutting t, d = t1, d1 else: t2 = A.reverse(v2.x, v2.y) d2 = euclid(t2.lat - t.lat, t2.lon - t.lon) # consider only the closer intersection t, d = (t1, d1) if d1 < d2 else (t2, d2) # break if below tolerance or if unchanged if d < e or d == p: t._iteration = i # _NamedTuple._iteration ts.append(t) if v1 is v2: # abutting ta = t break p = d else: raise ValueError(_no_(Fmt.convergence(tol))) if ta: # abutting circles pass elif len(ts) == 2: return (_latlon4(ts[0], h, n), _latlon4(ts[1], h, n)) elif len(ts) == 1: ta = ts[0] # assume abutting else: raise _AssertionError(ts=ts) r = _latlon4(ta, h, n) return r, r def _unrollon(p1, p2): # unroll180 == .karney._unroll2 # wrap, unroll and replace longitude if different _, lon = unroll180(p1.lon, p2.lon, wrap=True) if abs(lon - p2.lon) > EPS: p2 = p2.classof(p2.lat, lon, p2.height, datum=p2.datum) return p2 def _nearestOn(p, p1, p2, within=True, height=None, wrap=True, equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): # (INTERNAL) Get closet point, like L{_intersects2} above, # separated to allow callers to embellish any exceptions from pygeodesy.sphericalNvector import LatLon as _LLS from pygeodesy.vector3d import _nearestOn as _vnOn, Vector3d def _v(t, h): return Vector3d(t.x, t.y, h) _ = p.ellipsoids(p1) E = p.ellipsoids(p2) if wrap: p1 = _unrollon(p, p1) p2 = _unrollon(p, p2) p2 = _unrollon(p1, p2) r = E.rocMean(fmean_(p.lat, p1.lat, p2.lat)) e = max(m2degrees(tol, radius=r), EPS) # get the azimuthal equidistant projection A = _Equidistant2(equidistant, p.datum) # gu-/estimate initial nearestOn, spherically ... wrap=False t = _LLS(p.lat, p.lon, height=p.height).nearestOn( _LLS(p1.lat, p1.lon, height=p1.height), _LLS(p2.lat, p2.lon, height=p2.height), within=within, height=height) n = t.name h = h1 = h2 = 0 if height is False: # use height as Z component h = t.height h1 = p1.height h2 = p2.height # ... and then iterate like Karney suggests to find # tri-points of median lines, @see: references under # method LatLonEllipsoidalBase.intersections2 above c = None # force first d == c to False # closest to origin, .z to interpolate height p = Vector3d(0, 0, h) for i in range(1, _TRIPS): A.reset(t.lat, t.lon) # gu-/estimate as origin # convert points to projection space t1 = A.forward(p1.lat, p1.lon) t2 = A.forward(p2.lat, p2.lon) # compute nearestOn in projection space v = _vnOn(p, _v(t1, h1), _v(t2, h2), within=within) # convert nearestOn back to geodetic r = A.reverse(v.x, v.y) d = euclid(r.lat - t.lat, r.lon - t.lon) # break if below tolerance or if unchanged t = r if d < e or d == c: t._iteration = i # _NamedTuple._iteration if height is False: h = v.z # nearest interpolated break c = d else: raise ValueError(_no_(Fmt.convergence(tol))) r = _LatLon4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds) r._iteration = t.iteration # ._iteration for tests return _xnamed(r, n) __all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase) # **) MIT License # # Copyright (C) 2016-2021 -- 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.