# Coverage for pygeodesy/latlonBase.py : 94%

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1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 | # -*- coding: utf-8 -*- u'''(INTERNAL) Base class L{LatLonBase} for elliposiodal, spherical and N-vectorial C{LatLon}s. After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see U{https://www.Movable-Type.co.UK/scripts/latlong.html}, U{<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>} and U{https://www.Movable-Type.co.UK/scripts/latlong-vectors.html}. ''' from pygeodesy.basics import isstr, _xinstanceof from pygeodesy.dms import F_D, F_DMS, latDMS, lonDMS, parse3llh from pygeodesy.errors import _datum_datum, _incompatible, IntersectionError, \ _ValueError, _xError, _xkwds, _xkwds_not from pygeodesy.fmath import favg from pygeodesy.formy import antipode, compassAngle, cosineAndoyerLambert_, \ cosineForsytheAndoyerLambert_, cosineLaw, \ equirectangular, euclidean, flatLocal_, \ flatPolar, hartzell, haversine, isantipode, \ latlon2n_xyz, thomas_, vincentys from pygeodesy.interns import EPS, EPS0, EPS1, EPS4, NN, R_M, _COMMASPACE_, \ _concentric_, _height_, _intersection_, _m_, \ _no_, _overlap_, _point_, _0_0, _0_5, _1_0 from pygeodesy.iters import PointsIter, points2 from pygeodesy.lazily import _ALL_DOCS from pygeodesy.named import _NamedBase, notOverloaded from pygeodesy.namedTuples import Bounds2Tuple, LatLon2Tuple, PhiLam2Tuple, \ Trilaterate5Tuple, Vector3Tuple from pygeodesy.props import deprecated_method, Property, Property_RO, \ property_doc_, property_RO from pygeodesy.streprs import Fmt, hstr from pygeodesy.units import Distance_, Lat, Lon, Height, Radius, Radius_, Scalar_ from pygeodesy.utily import _unrollon, unrollPI from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, Circum3Tuple, \ circum4_, Circum4Tuple, _radii11ABC from pygeodesy.vector3d import nearestOn6, Vector3d from math import asin, cos, degrees, radians __all__ = () __version__ = '21.10.19' class LatLonBase(_NamedBase): '''(INTERNAL) Base class for C{LatLon} points on spherical or ellipsoidal earth models. ''' _datum = None # L{Datum}, to be overriden _height = 0 # height (C{meter}), default _lat = 0 # latitude (C{degrees}) _lon = 0 # longitude (C{degrees}) def __init__(self, lat, lon, height=0, name=NN): '''New C{LatLon}. @arg lat: Latitude (C{degrees} or DMS C{str} with N or S suffix). @arg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix). @kwarg height: Optional height (C{meter} above or below the earth surface). @kwarg name: Optional name (C{str}). @return: New instance (C{LatLon}). @raise RangeError: Value of B{C{lat}} or B{C{lon}} outside the valid range and C{rangerrors} set to C{True}. @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}. @example: >>> p = LatLon(50.06632, -5.71475) >>> q = LatLon('50°03′59″N', """005°42'53"W""") ''' if name: self.name = name self._lat = Lat(lat) # parseDMS2(lat, lon) self._lon = Lon(lon) # PYCHOK LatLon2Tuple if height: # elevation self._height = Height(height) def __eq__(self, other): return self.isequalTo(other) def __ne__(self, other): return not self.isequalTo(other) def __str__(self): return self.toStr(form=F_D, prec=6) def antipode(self, height=None): '''Return the antipode, the point diametrically opposite to this point. @kwarg height: Optional height of the antipode (C{meter}), this point's height otherwise. @return: The antipodal point (C{LatLon}). ''' a, b = antipode(self.lat, self.lon) # PYCHOK LatLon2Tuple h = self.height if height is None else Height(height) return self.classof(a, b, height=h) @deprecated_method def bounds(self, wide, tall, radius=R_M): # PYCHOK no cover '''DEPRECATED, use method C{boundsOf}.''' return self.boundsOf(wide, tall, radius=radius) def boundsOf(self, wide, tall, radius=R_M, height=None): '''Return the SW and NE lat-/longitude of a great circle bounding box centered at this location. @arg wide: Longitudinal box width (C{meter}, same units as B{C{radius}} or C{degrees} if B{C{radius}} is C{None}). @arg tall: Latitudinal box size (C{meter}, same units as B{C{radius}} or C{degrees} if B{C{radius}} is C{None}). @kwarg radius: Mean earth radius (C{meter}). @kwarg height: Height for C{latlonSW} and C{latlonNE} (C{meter}), overriding the point's height. @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)}, the lower-left and upper-right corner (C{LatLon}). @see: U{https://www.Movable-Type.co.UK/scripts/latlong-db.html} ''' x = Scalar_(wide=wide) * _0_5 y = Scalar_(tall=tall) * _0_5 if radius is not None: r = Radius_(radius) c = cos(self.phi) x = degrees(asin(x / r) / c) if abs(c) > EPS0 else _0_0 # XXX y = degrees(y / r) x, y = abs(x), abs(y) h = self.height if height is None else Height(height) sw = self.classof(self.lat - y, self.lon - x, height=h) ne = self.classof(self.lat + y, self.lon + x, height=h) return Bounds2Tuple(sw, ne, name=self.name) def chordTo(self, other, height=None): '''Compute the length of the chord through the earth between this and an other point. @arg other: The other point (C{LatLon}). @kwarg height: Overriding height for both points (C{meter}) or C{None} for each point's height. @return: The chord length (conventionally C{meter}). @raise TypeError: The B{C{other}} point is not C{LatLon}. ''' def _v3d(ll): t = ll.toEcef(height=height) # .toVector(Vector=Vector3d) return Vector3d(t.x, t.y, t.z) self.others(other) return _v3d(self).minus(_v3d(other)).length def circin6(self, point2, point3, eps=EPS4): '''Return the radius and center of the I{inscribed} aka I{In- circle} of the (planar) triangle formed by this and two other points. @arg point2: Second point (C{LatLon}). @arg point3: Third point (C{LatLon}). @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}. @return: L{Circin6Tuple}C{(radius, center, deltas, cA, cB, cC)}. The C{center} and contact points C{cA}, C{cB} and C{cC}, each an instance of this (sub-)class, are co-planar with this and the two given points. @raise ImportError: Package C{numpy} not found, not installed or older than version 1.10. @raise IntersectionError: Near-coincident or -colinear points or a trilateration or C{numpy} issue. @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. @note: The C{center} is trilaterated in cartesian (ECEF) space and converted back to geodetic lat-, longitude and height. The latter, conventionally in C{meter} indicates whether the C{center} is above, below or on the surface of the earth model. If C{deltas} is C{None}, the C{center} is I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon, height)} representing the difference between both results from L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof. @see: Function L{pygeodesy.circin6}, method L{circum3}, U{Incircle <https://MathWorld.Wolfram.com/Incircle.html>} and U{Contact Triangle <https://MathWorld.Wolfram.com/ContactTriangle.html>}. ''' try: cs = self._toCartesian3(point2, point3) r, c, d, cA, cB, cC = _circin6(*cs, eps=eps, useZ=True, dLL3=True, datum=self.datum) # PYCHOK unpack return Circin6Tuple(r, c.toLatLon(), d, cA.toLatLon(), cB.toLatLon(), cC.toLatLon()) except (AssertionError, TypeError, ValueError) as x: raise _xError(x, point=self, point2=point2, point3=point3) def circum3(self, point2, point3, circum=True, eps=EPS4): '''Return the radius and center of the smallest circle I{through} or I{containing} this and two other points. @arg point2: Second point (C{LatLon}). @arg point3: Third point (C{LatLon}). @kwarg circum: If C{True} return the C{circumradius} and C{circumcenter}, always, ignoring the I{Meeus}' Type I case (C{bool}). @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}. @return: A L{Circum3Tuple}C{(radius, center, deltas)}. The C{center}, an instance of this (sub-)class, is co-planar with this and the two given points. If C{deltas} is C{None}, the C{center} is I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon, height)} representing the difference between both results from L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof. @raise ImportError: Package C{numpy} not found, not installed or older than version 1.10. @raise IntersectionError: Near-concentric, -coincident or -colinear points, incompatible C{Ecef} classes or a trilateration or C{numpy} issue. @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. @note: The C{center} is trilaterated in cartesian (ECEF) space and converted back to geodetic lat-, longitude and height. The latter, conventionally in C{meter} indicates whether the C{center} is above, below or on the surface of the earth model. If C{deltas} is C{None}, the C{center} is I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon, height)} representing the difference between both results from L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof. @see: Function L{pygeodesy.circum3} and methods L{circin6} and L{circum4_}. ''' try: cs = self._toCartesian3(point2, point3) r, c, d = _circum3(*cs, circum=circum, eps=eps, useZ=True, dLL3=True, # XXX -3d2 clas=cs[0].classof, datum=self.datum) # PYCHOK unpack return Circum3Tuple(r, c.toLatLon(), d) except (AssertionError, TypeError, ValueError) as x: raise _xError(x, point=self, point2=point2, point3=point3, circum=circum) def circum4_(self, *points): '''Best-fit a sphere through this and two or more other points. @arg points: The other points (each a C{LatLon}). @return: L{Circum4Tuple}C{(radius, center, rank, residuals)} with C{center} an instance of this (sub-)class. @raise ImportError: Package C{numpy} not found, not installed or older than version 1.10. @raise NumPyError: Some C{numpy} issue. @raise TypeError: One of the B{C{points}} invalid. @raise ValueError: Too few B{C{points}}. @see: Function L{pygeodesy.circum4_} and L{circum3}. ''' C = self._toCartesianEcef c = C(point=self) t = circum4_(c, Vector=c.classof, *(C(i=i, points=p) for i, p in enumerate(points))) c = t.center.toLatLon(LatLon=self.classof, name=t.name) return Circum4Tuple(t.radius, c, t.rank, t.residuals, name=c.name) @deprecated_method def compassAngle(self, other, adjust=True, wrap=False): # PYCHOK no cover '''DEPRECATED, use method L{compassAngleTo}.''' return self.compassAngleTo(other, adjust=adjust, wrap=wrap) def compassAngleTo(self, other, adjust=True, wrap=False): '''Return the angle from North for the direction vector between this and an other point. Suitable only for short, non-near-polar vectors up to a few hundred Km or Miles. Use method C{initialBearingTo} for larger distances. @arg other: The other point (C{LatLon}). @kwarg adjust: Adjust the longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg wrap: Wrap and L{pygeodesy.unroll180} longitudes and longitudinal delta (C{bool}). @return: Compass angle from North (C{degrees360}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @note: Courtesy Martin Schultz. @see: U{Local, flat earth approximation <https://www.EdWilliams.org/avform.htm#flat>}. ''' self.others(other) return compassAngle(self.lat, self.lon, other.lat, other.lon, adjust=adjust, wrap=wrap) def cosineAndoyerLambertTo(self, other, wrap=False): '''Compute the distance between this and an other point using the U{Andoyer-Lambert correction<https://navlib.net/wp-content/uploads/ 2013/10/admiralty-manual-of-navigation-vol-1-1964-english501c.pdf>} of the U{Law of Cosines<https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>} formula. @arg other: The other point (C{LatLon}). @kwarg wrap: Wrap and L{pygeodesy.unroll180} longitudes (C{bool}). @return: Distance (C{meter}, same units as the axes of this point's datum ellipsoid). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{pygeodesy.cosineAndoyerLambert} and methods L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}. ''' return self._distanceTo_(cosineAndoyerLambert_, other, wrap=wrap) def cosineForsytheAndoyerLambertTo(self, other, wrap=False): '''Compute the distance between this and an other point using the U{Forsythe-Andoyer-Lambert correction <https://www2.UNB.CA/gge/Pubs/TR77.pdf>} of the U{Law of Cosines <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>} formula. @arg other: The other point (C{LatLon}). @kwarg wrap: Wrap and L{pygeodesy.unroll180} longitudes (C{bool}). @return: Distance (C{meter}, same units as the axes of this point's datum ellipsoid). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{pygeodesy.cosineForsytheAndoyerLambert} and methods L{cosineAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}. ''' return self._distanceTo_(cosineForsytheAndoyerLambert_, other, wrap=wrap) def cosineLawTo(self, other, radius=None, wrap=False): '''Compute the distance between this and an other point using the U{spherical Law of Cosines <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>} formula. @arg other: The other point (C{LatLon}). @kwarg radius: Mean earth radius (C{meter}) or C{None} for the mean radius of this point's datum ellipsoid. @kwarg wrap: Wrap and L{pygeodesy.unroll180} longitudes (C{bool}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{pygeodesy.cosineLaw} and methods L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}. ''' return self._distanceTo(cosineLaw, other, radius, wrap=wrap) @property_RO def datum(self): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. ''' notOverloaded(self) def destinationXyz(self, delta, LatLon=None, **LatLon_kwds): '''Calculate the destination using a I{local} delta from this point. @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu}, L{Ned} or L{Local9Tuple}). @kwarg LatLon: Optional (geodetic) class to return the destination or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None}. @return: Destination as a C{B{LatLon}(lat, lon, **B{LatLon_kwds})} instance or if C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon, height)} respectively L{LatLon4Tuple}C{(lat, lon, height, datum)} depending on whether a C{datum} keyword is un-/specified. @raise TypeError: Invalid B{C{delta}}, B{C{LatLon}} or B{C{LatLon_kwds}}. ''' t = self._ltp._local2ecef(delta, nine=True) return t.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, name=self.name)) def _distanceTo(self, func, other, radius, **options): '''(INTERNAL) Helper for methods C{<func>To}. ''' self.others(other) # up=2 if radius is None: radius = self._datum.ellipsoid.R1 if self._datum else R_M return func(self.lat, self.lon, other.lat, other.lon, radius=radius, **options) def _distanceTo_(self, func_, other, wrap=False): '''(INTERNAL) Helper for (ellipsoidal) methods C{<func>To}. ''' self.others(other) # up=2 r, _ = unrollPI(self.lam, other.lam, wrap=wrap) r = func_(other.phi, self.phi, r, datum=self.datum) return r * self.datum.ellipsoid.a @Property_RO def Ecef(self): '''Get the ECEF I{class} (L{EcefKarney}), I{lazily}. ''' from pygeodesy.ecef import EcefKarney return EcefKarney # default @Property_RO def _Ecef_forward(self): '''(INTERNAL) Helper for L{_ecef9} and L{toEcef} (C{callable}). ''' return self.Ecef(self.datum, name=self.name).forward @Property_RO def _ecef9(self): '''(INTERNAL) Helper for L{toCartesian}, L{toEcef} and L{toCartesian} (L{Ecef9Tuple}). ''' return self._Ecef_forward(self, M=True) @deprecated_method def equals(self, other, eps=None): # PYCHOK no cover '''DEPRECATED, use method L{isequalTo}.''' return self.isequalTo(other, eps=eps) @deprecated_method def equals3(self, other, eps=None): # PYCHOK no cover '''DEPRECATED, use method L{isequalTo3}.''' return self.isequalTo3(other, eps=eps) def equirectangularTo(self, other, radius=None, **options): '''Compute the distance between this and an other point using the U{Equirectangular Approximation / Projection <https://www.Movable-Type.co.UK/scripts/latlong.html#equirectangular>}. Suitable only for short, non-near-polar distances up to a few hundred Km or Miles. Use method L{haversineTo} or C{distanceTo*} for more accurate and/or larger distances. See function L{pygeodesy.equirectangular_} for more details, the available B{C{options}} and errors raised. @arg other: The other point (C{LatLon}). @kwarg radius: Mean earth radius (C{meter}) or C{None} for the mean radius of this point's datum ellipsoid. @kwarg options: Optional keyword arguments for function L{pygeodesy.equirectangular}. @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{pygeodesy.equirectangular} and methods L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, C{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}. ''' return self._distanceTo(equirectangular, other, radius, **options) def euclideanTo(self, other, radius=None, **options): '''Approximate the C{Euclidian} distance between this and an other point. See function L{pygeodesy.euclidean} for the available B{C{options}}. @arg other: The other point (C{LatLon}). @kwarg radius: Mean earth radius (C{meter}) or C{None} for the mean radius of this point's datum ellipsoid. @kwarg options: Optional keyword arguments for function L{pygeodesy.euclidean}. @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{pygeodesy.euclidean} and methods L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}. ''' return self._distanceTo(euclidean, other, radius, **options) def flatLocalTo(self, other, radius=None, wrap=False): '''Compute the distance between this and an other point using the U{ellipsoidal Earth to plane projection <https://WikiPedia.org/wiki/Geographical_distance#Ellipsoidal_Earth_projected_to_a_plane>} aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>} formula. @arg other: The other point (C{LatLon}). @kwarg radius: Mean earth radius (C{meter}) or C{None} for the major radius of this point's datum/ellipsoid. @kwarg wrap: Wrap and L{pygeodesy.unroll180} longitudes (C{bool}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @raise ValueError: Invalid B{C{radius}}. @see: Function L{pygeodesy.flatLocal}/L{pygeodesy.hubeny}, methods L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo} and U{local, flat Earth approximation<https://www.edwilliams.org/avform.htm#flat>}. ''' E = self.datum.ellipsoid r = self._distanceTo_(flatLocal_, other, wrap=wrap) * E.a2_ a = E.a if radius in (None, 1, _1_0) else Radius(radius) return r * a hubenyTo = flatLocalTo # for Karl Hubeny def flatPolarTo(self, other, radius=None, wrap=False): '''Compute the distance between this and an other point using the U{polar coordinate flat-Earth<https://WikiPedia.org/wiki/ Geographical_distance#Polar_coordinate_flat-Earth_formula>}formula. @arg other: The other point (C{LatLon}). @kwarg radius: Mean earth radius (C{meter}) or C{None} for the mean radius of this point's datum ellipsoid. @kwarg wrap: Wrap and L{pygeodesy.unroll180} longitudes (C{bool}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{pygeodesy.flatPolar} and methods L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}. ''' return self._distanceTo(flatPolar, other, radius, wrap=wrap) def hartzell(self, los=None): '''Compute the intersection of a Line-Of-Sight from this Point-Of-View (pov) with this C{datum}'s ellipsoid surface. @kwarg los: Line-Of-Sight, I{direction} to earth (L{Vector3d}) or C{None} to point to the ellipsoid's center. @return: The ellipsoid intersection (C{LatLon}) or this very instance if this C{pov's height} is C{0}. @raise IntersectionError: Null C{pov} or B{C{los}} vector, this C{pov's height} is negative or B{C{los}} points outside the ellipsoid or in an opposite direction. @raise TypeError: Invalid B{C{los}}. @see: Function C{hartzell} for further details. ''' h = self.height if not h: r = self elif h < 0: raise IntersectionError(pov=self, los=los, height=h, txt=_no_(_height_)) elif los is None: r = self.copy() r.rename(self.hartzell.__name__) r.height = 0 else: c = self.toCartesian() r = hartzell(c, los=los, earth=self.datum, LatLon=self.classof) return r def haversineTo(self, other, radius=None, wrap=False): '''Compute the distance between this and an other point using the U{Haversine<https://www.Movable-Type.co.UK/scripts/latlong.html>} formula. @arg other: The other point (C{LatLon}). @kwarg radius: Mean earth radius (C{meter}) or C{None} for the mean radius of this point's datum ellipsoid. @kwarg wrap: Wrap and L{pygeodesy.unroll180} longitudes (C{bool}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{pygeodesy.haversine} and methods L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{thomasTo} and L{vincentysTo}. ''' return self._distanceTo(haversine, other, radius, wrap=wrap) def _havg(self, other, f=_0_5): '''(INTERNAL) Weighted, average height. @arg other: An other point (C{LatLon}). @kwarg f: Optional fraction (C{float}). @return: Average, fractional height (C{float}). ''' return favg(self.height, other.height, f=f) @property_doc_(''' the height (C{meter}).''') def height(self): '''Get the height (C{meter}). ''' return self._height @height.setter # PYCHOK setter! def height(self, height): '''Set the height. @arg height: New height (C{meter}). @raise TypeError: Invalid B{C{height}} C{type}. @raise ValueError: Invalid B{C{height}}. ''' h = Height(height) self._update(h != self.height) self._height = h def height4(self, earth=None, normal=True, LatLon=None, **LatLon_kwds): '''Compute the height above or below and the projection on this datum's ellipsoid surface. @kwarg earth: A datum, ellipsoid or earth radius I{overriding} this datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally). @kwarg normal: If C{True} the projection is the nearest point on the ellipsoid's surface, otherwise the intersection of the radial line to the center and the ellipsoid's surface. @kwarg LatLon: Optional class to return the height and projection (C{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon} is None}. @note: Use keyword argument C{height=0} to override C{B{LatLon}.height} to {0} or any other C{scalar}, conventionally in C{meter}. @return: An instance of B{C{LatLon}} or if C{B{LatLon} is None}, a L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y} and C{z} coordinates and height C{h} in C{meter}, conventionally. @raise TypeError: Invalid B{C{earth}}. @see: L{Ellipsoid.height4} for more information. ''' if LatLon is None: r = self.toCartesian().height4(earth=earth, normal=normal) else: c = self.toCartesian() r = c.height4(earth=earth, normal=normal, Cartesian=c.classof, height=0) r = r.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, height=r.height)) return r def heightStr(self, prec=-2, m=_m_): '''Return this B{C{height}} as C{str}ing. @kwarg prec: Optional number of decimals, unstripped (C{int}). @kwarg m: Optional unit of the height (C{str}). @see: Function L{pygeodesy.hstr}. ''' return hstr(self.height, prec=prec, m=m) @deprecated_method def isantipode(self, other, eps=EPS): # PYCHOK no cover '''DEPRECATED, use method L{isantipodeTo}.''' return self.isantipodeTo(other, eps=eps) def isantipodeTo(self, other, eps=EPS): '''Check whether this and an other point are antipodal, on diametrically opposite sides of the earth. @arg other: The other point (C{LatLon}). @kwarg eps: Tolerance for near-equality (C{degrees}). @return: C{True} if points are antipodal within the given tolerance, C{False} otherwise. ''' return isantipode(self.lat, self.lon, other.lat, other.lon, eps=eps) @Property_RO def isEllipsoidal(self): '''Check whether this point is ellipsoidal (C{bool} or C{None} if unknown). ''' return self.datum.isEllipsoidal if self._datum else None def isequalTo(self, other, eps=None): '''Compare this point with an other point, I{ignoring} height. @arg other: The other point (C{LatLon}). @kwarg eps: Tolerance for equality (C{degrees}). @return: C{True} if both points are identical, I{ignoring} height, C{False} otherwise. @raise TypeError: The B{C{other}} point is not C{LatLon} or mismatch of the B{C{other}} and this C{class} or C{type}. @raise UnitError: Invalid B{C{eps}}. @see: Method L{isequalTo3}. ''' self.others(other) return _isequalTo(self, other, eps=Scalar_(eps=eps)) if eps else \ (self.lat == other.lat and self.lon == other.lon) def isequalTo3(self, other, eps=None): '''Compare this point with an other point, I{including} height. @arg other: The other point (C{LatLon}). @kwarg eps: Tolerance for equality (C{degrees}). @return: C{True} if both points are identical I{including} height, C{False} otherwise. @raise TypeError: The B{C{other}} point is not C{LatLon} or mismatch of the B{C{other}} and this C{class} or C{type}. @see: Method L{isequalTo}. ''' return self.height == other.height and self.isequalTo(other, eps=eps) @Property_RO def isSpherical(self): '''Check whether this point is spherical (C{bool} or C{None} if unknown). ''' return self.datum.isSpherical if self._datum else None @Property_RO def lam(self): '''Get the longitude (B{C{radians}}). ''' return self.philam.lam @property_doc_(''' the latitude (C{degrees90}).''') def lat(self): '''Get the latitude (C{degrees90}). ''' return self._lat @lat.setter # PYCHOK setter! def lat(self, lat): '''Set the latitude. @arg lat: New latitude (C{str[N|S]} or C{degrees}). @raise ValueError: Invalid B{C{lat}}. ''' lat = Lat(lat) # parseDMS(lat, suffix=_NS_, clip=90) self._update(lat != self._lat) self._lat = lat @Property def latlon(self): '''Get the lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}). ''' return LatLon2Tuple(self._lat, self._lon, name=self.name) @latlon.setter # PYCHOK setter! def latlon(self, latlonh): '''Set the lat- and longitude and optionally the height. @arg latlonh: New lat-, longitude and height (2- or 3-tuple or comma- or space-separated C{str} of C{degrees90}, C{degrees180} and C{meter}). @raise TypeError: Height of B{C{latlonh}} not C{scalar} or B{C{latlonh}} not C{list} or C{tuple}. @raise ValueError: Invalid B{C{latlonh}} or M{len(latlonh)}. @see: Function L{pygeodesy.parse3llh} to parse a B{C{latlonh}} string into a 3-tuple (lat, lon, h). ''' if isstr(latlonh): latlonh = parse3llh(latlonh, height=self.height) else: _xinstanceof(list, tuple, latlonh=latlonh) if len(latlonh) == 3: h = Height(latlonh[2], name=Fmt.SQUARE(latlonh=2)) elif len(latlonh) != 2: raise _ValueError(latlonh=latlonh) else: h = self.height lat = Lat(latlonh[0]) # parseDMS2(latlonh[0], latlonh[1]) lon = Lon(latlonh[1]) self._update(lat != self._lat or lon != self._lon or h != self.height) self._lat, self._lon, self._height = lat, lon, h def latlon2(self, ndigits=0): '''Return this point's lat- and longitude in C{degrees}, rounded. @kwarg ndigits: Number of decimal digits (C{int}). @return: A L{LatLon2Tuple}C{(lat, lon)}, both C{float} and rounded away from zero. @note: The C{round}ed values are always C{float}, also if B{C{ndigits}} is omitted. ''' return LatLon2Tuple(round(self.lat, ndigits), round(self.lon, ndigits), name=self.name) @deprecated_method def latlon_(self, ndigits=0): # PYCHOK no cover '''DEPRECATED, use method L{latlon2}.''' return self.latlon2(ndigits=ndigits) latlon2round = latlon_ # PYCHOK no cover @Property_RO def latlonheight(self): '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}). ''' return self.latlon.to3Tuple(self.height) @property_doc_(''' the longitude (C{degrees180}).''') def lon(self): '''Get the longitude (C{degrees180}). ''' return self._lon @lon.setter # PYCHOK setter! def lon(self, lon): '''Set the longitude. @arg lon: New longitude (C{str[E|W]} or C{degrees}). @raise ValueError: Invalid B{C{lon}}. ''' lon = Lon(lon) # parseDMS(lon, suffix=_EW_, clip=180) self._update(lon != self._lon) self._lon = lon @Property_RO def _ltp(self): '''(INTERNAL) Cache for L{toLtp}. ''' from pygeodesy.ltp import Ltp return Ltp(self, ecef=self.Ecef(self.datum), name=self.name) def nearestOn6(self, points, closed=False, height=None, wrap=False): '''Locate the point on a path or polygon closest to this point. Points are converted to and distances are computed in I{geocentric}, cartesian space. @arg points: The path or polygon points (C{LatLon}[]). @kwarg closed: Optionally, close the polygon (C{bool}). @kwarg height: Optional height, overriding the height of this and all other points (C{meter}). If C{None}, take the height of points into account for distances. @kwarg wrap: Wrap and L{pygeodesy.unroll180} longitudes (C{bool}). @return: A L{NearestOn6Tuple}C{(closest, distance, fi, j, start, end)} with the C{closest}, the C{start} and the C{end} point each an instance of this C{LatLon} and C{distance} in C{meter}, same units as the cartesian axes. @raise PointsError: Insufficient number of B{C{points}}. @raise TypeError: Some B{C{points}} or some B{C{points}}' C{Ecef} invalid. @raise ValueError: Some B{C{points}}' C{Ecef} is incompatible. @see: Function L{pygeodesy.nearestOn6}. ''' def _cs(Ps, h, w, C): p = None # not used for i, q in Ps.enumerate(): if w and i != 0: q = _unrollon(p, q) yield C(height=h, i=i, up=3, points=q) p = q C = self._toCartesianEcef # to verify datum and Ecef Ps = self.PointsIter(points) c = C(height=height, this=self) # this Cartesian t = nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed) c, s, e = t.closest, t.start, t.end kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon height=height) r = self.Ecef(self.datum).reverse p = r(c).toLatLon(**kwds) s = r(s).toLatLon(**kwds) if s is not c else p e = r(e).toLatLon(**kwds) if e is not c else p return t.dup(closest=p, start=s, end=e) @Property_RO def _N_vector(self): '''(INTERNAL) Get the (C{nvectorBase._N_vector_}) ''' from pygeodesy.nvectorBase import _N_vector_ return _N_vector_(*self.xyzh) @Property_RO def phi(self): '''Get the latitude (B{C{radians}}). ''' return self.philam.phi @Property_RO def philam(self): '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}). ''' return PhiLam2Tuple(radians(self.lat), radians(self.lon), name=self.name) def philam2(self, ndigits=0): '''Return this point's lat- and longitude in C{radians}, rounded. @kwarg ndigits: Number of decimal digits (C{int}). @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float} and rounded away from zero. @note: The C{round}ed values are always C{float}, also if B{C{ndigits}} is omitted. ''' return PhiLam2Tuple(round(self.phi, ndigits), round(self.lam, ndigits), name=self.name) @Property_RO def philamheight(self): '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). ''' return self.philam.to3Tuple(self.height) @deprecated_method def points(self, points, closed=True): # PYCHOK no cover '''DEPRECATED, use method L{points2}.''' return self.points2(points, closed=closed) def points2(self, points, closed=True): '''Check a path or polygon represented by points. @arg points: The path or polygon points (C{LatLon}[]) @kwarg closed: Optionally, consider the polygon closed, ignoring any duplicate or closing final B{C{points}} (C{bool}). @return: A L{Points2Tuple}C{(number, points)}, C{int} and C{list} or C{tuple}. @raise PointsError: Insufficient number of B{C{points}}. @raise TypeError: Some B{C{points}} are not C{LatLon}. ''' return points2(points, closed=closed, base=self) def PointsIter(self, points, loop=0, dedup=False): '''Return a C{PointsIter} iterator. @arg points: The path or polygon points (C{LatLon}[]) @kwarg loop: Number of loop-back points (non-negative C{int}). @kwarg dedup: Skip duplicate points (C{bool}). @return: A new C{PointsIter} iterator. @raise PointsError: Insufficient number of B{C{points}}. ''' return PointsIter(points, base=self, loop=loop, dedup=dedup) def radii11(self, point2, point3): '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent} circles of a (planar) triangle formed by this and two other points. @arg point2: Second point (C{LatLon}). @arg point3: Third point (C{LatLon}). @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}. @raise IntersectionError: Near-coincident or -colinear points. @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. @see: Function L{pygeodesy.radii11}, U{Incircle <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}. ''' try: cs = self._toCartesian3(point2, point3) return _radii11ABC(*cs, useZ=True)[0] except (TypeError, ValueError) as x: raise _xError(x, point=self, point2=point2, point3=point3) def thomasTo(self, other, wrap=False): '''Compute the distance between this and an other point using U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>} formula. @arg other: The other point (C{LatLon}). @kwarg wrap: Wrap and L{pygeodesy.unrollPI} longitudes (C{bool}). @return: Distance (C{meter}, same units as the axes of this point's datum ellipsoid). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo} and L{vincentysTo}. ''' return self._distanceTo_(thomas_, other, wrap=wrap) @deprecated_method def to2ab(self): # PYCHOK no cover '''DEPRECATED, use property L{philam}.''' return self.philam def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds): '''Convert this point to cartesian, I{geocentric} coordinates, also known as I{Earth-Centered, Earth-Fixed} (ECEF). @kwarg height: Optional height, overriding this point's height (C{meter}, conventionally). @kwarg Cartesian: Optional class to return the geocentric coordinates (C{Cartesian}) or C{None}. @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored if C{B{Cartesian} is None}. @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C=0} and C{M} if available. @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}. ''' r = self._ecef9 if height is None else self.toEcef(height=height) if Cartesian is not None: # class or .classof r = self._xnamed(Cartesian(r, **Cartesian_kwds)) _datum_datum(r.datum, self.datum) return r def _toCartesian3(self, point2, point3): '''(INTERNAL) Convert this and 2 other points. ''' return (self. toCartesian().copy(name=_point_), # copy to rename self._toCartesianEcef(up=3, point2=point2), self._toCartesianEcef(up=3, point3=point3)) def _toCartesianEcef(self, height=None, i=None, up=2, **name_point): '''(INTERNAL) Convert to cartesian and check Ecef's before and after. ''' p = self.others(up=up, **name_point) c = p.toCartesian(height=height) E = self.Ecef if E: for p in (p, c): e = getattr(p, LatLonBase.Ecef.name, None) if e not in (None, E): n, _ = name_point.popitem() if i is not None: Fmt.SQUARE(n, i) raise _ValueError(n, e, txt=_incompatible(E.__name__)) return c def toEcef(self, height=None, M=False): '''Convert this point to I{geocentric} coordinates, also known as I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}). @kwarg height: Optional height, overriding this point's height (C{meter}, conventionally). @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}). @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C=0} and C{M} if available. @raise EcefError: A C{.datum} or an ECEF issue. ''' return self._ecef9 if height in (None, self.height) else \ self._Ecef_forward(self.lat, self.lon, height=height, M=M) @deprecated_method def to3llh(self, height=None): # PYCHOK no cover '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.''' return self.latlonheight if height in (None, self.height) else \ self.latlon.to3Tuple(height) def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds): '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}. @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}. @kwarg ltp: The I{local tangent plane} (LTP) to use, overriding this point's LTP (L{Ltp}). @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword arguments, ignored if C{B{Xyz} is None}. @return: An B{C{Xyz}} instance or if C{B{Xyz} is None}, a L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)} with C{M=None}, always. @raise TypeError: Invalid B{C{ltp}}. ''' p = self._ltp if ltp is None else self._xLtp(ltp) return p._ecef2local(self._ecef9, Xyz, Xyz_kwds) def toLtp(self, Ecef=None): '''Return the I{local tangent plane} (LTP) for this point. @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ... L{EcefYou}), overriding this point's C{Ecef}. ''' if Ecef in (None, self.Ecef): r = self._ltp else: from pygeodesy.ltp import Ltp r = Ltp(self, ecef=Ecef(self.datum), name=self.name) return r def toNvector(self, h=None, Nvector=None, **Nvector_kwds): '''Convert this point to C{n-vector} (normal to the earth's surface) components, I{including height}. @kwarg h: Optional height, overriding this point's height (C{meter}). @kwarg Nvector: Optional class to return the C{n-vector} components (C{Nvector}) or C{None}. @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector} is None}. @return: A B{C{Nvector}} or an L{Vector4Tuple}C{(x, y, z, h)} if B{C{Nvector}} is C{None}. @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}. ''' return self.toVector(Vector=Nvector, h=self.height if h is None else h, ll=self, **Nvector_kwds) def toStr(self, form=F_DMS, prec=None, m=_m_, sep=_COMMASPACE_): # PYCHOK expected '''Convert this point to a "lat, lon [+/-height]" string, formatted in the given form. @kwarg form: Optional format, F_D, F_DM, F_DMS for deg°, deg°min′, deg°min′sec″ (C{str}). @kwarg prec: Optional number of decimal digits (0..8 or C{None}). @kwarg m: Optional unit of the height (C{str}), use C{None} to exclude height from the returned string. @kwarg sep: Optional separator to join (C{str}). @return: Point in the specified form (C{str}). @example: >>> LatLon(51.4778, -0.0016).toStr() # 51°28′40″N, 000°00′06″W >>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W >>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m ''' t = [latDMS(self.lat, form=form, prec=prec), lonDMS(self.lon, form=form, prec=prec)] if self.height and m is not None: t += [self.heightStr(m=m)] return sep.join(t) def toVector(self, Vector=None, **Vector_kwds): '''Convert this point to C{n-vector} (normal to the earth's surface) components, I{ignoring height}. @kwarg Vector: Optional class to return the C{n-vector} components (L{Vector3d}) or C{None}. @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments, ignored if C{B{Vector} is None}. @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} if B{C{Vector}} is C{None}. @raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}. @note: These are C{n-vector} x, y and z components, I{NOT} geocentric (ECEF) x, y and z coordinates! ''' r = self._vector3tuple if Vector is not None: r = self._xnamed(Vector(r.x, r.y, r.z, **Vector_kwds)) return r def toVector3d(self): '''Convert this point to C{n-vector} (normal to the earth's surface) components, I{ignoring height}. @return: Unit vector (L{Vector3d}). @note: These are C{n-vector} x, y and z components, I{NOT} geocentric (ECEF) x, y and z coordinates! ''' return self._vector3d # XXX .unit() @deprecated_method def to3xyz(self): # PYCHOK no cover '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector}, L{toVector3d} or perhaps (geocentric) L{toEcef}.''' return self.xyz # self.toVector() @Property_RO def _vector3d(self): '''(INTERNAL) Cache for L{toVector3d}. ''' return self.toVector(Vector=Vector3d) # XXX .unit() @Property_RO def _vector3tuple(self): '''(INTERNAL) Cache for L{toVector}. ''' return latlon2n_xyz(self.lat, self.lon, name=self.name) def vincentysTo(self, other, radius=None, wrap=False): '''Compute the distance between this and an other point using U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>} spherical formula. @arg other: The other point (C{LatLon}). @kwarg radius: Mean earth radius (C{meter}) or C{None} for the mean radius of this point's datum ellipsoid. @kwarg wrap: Wrap and L{pygeodesy.unroll180} longitudes (C{bool}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo} and L{thomasTo}. ''' return self._distanceTo(vincentys, other, radius, wrap=wrap) @Property_RO def _xLtp(self): '''(INTERNAL) Import and cache function C{ltp._xLtp}. ''' from pygeodesy.ltp import _xLtp return _xLtp @Property_RO def xyz(self): '''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}) @note: These are C{n-vector} x, y and z components, I{NOT} geocentric (ECEF) x, y and z coordinates! ''' return self.toVector(Vector=Vector3Tuple) @Property_RO def xyzh(self): '''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)}) @note: These are C{n-vector} x, y and z components, I{NOT} geocentric (ECEF) x, y and z coordinates! ''' return self.xyz.to4Tuple(self.height) def _isequalTo(point1, point2, eps=EPS): # in .ellipsoidalBaseDI._intersect3._on '''(INTERNAL) Compare point lat-/lon without type. ''' return max(abs(point1.lat - point2.lat), abs(point1.lon - point2.lon)) < eps def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, radius=R_M, wrap=False): '''(INTERNAL) Trilaterate three points by area overlap or by perimeter intersection of three circles. @note: The B{C{radius}} is only needed for both the n-vectorial and sphericalTrigonometry C{LatLon.distanceTo} methods and silently ignored by the C{ellipsoidalExact} C{-GeodSolve}, C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods. ''' r1 = Distance_(distance1=d1) r2 = Distance_(distance2=d2) r3 = Distance_(distance3=d3) m = 0 if area else (r1 + r2 + r3) pc = 0 t = [] for _ in range(3): try: # intersection of circle (p1, r1) and (p2, r2) c1, c2 = p1.intersections2(r1, p2, r2, wrap=wrap) if area: # check overlap if c1 is c2: # abutting c = c1 else: # nearest point on radical c = p3.nearestOn(c1, c2, within=True, wrap=wrap) d = r3 - p3.distanceTo(c, radius=radius, wrap=wrap) if d > eps: # sufficient overlap t.append((d, c)) m = max(m, d) else: # check intersection for c in ((c1,) if c1 is c2 else (c1, c2)): d = abs(r3 - p3.distanceTo(c, radius=radius, wrap=wrap)) if d < eps: # below margin t.append((d, c)) m = min(m, d) except IntersectionError as x: if _concentric_ in str(x): # XXX ConcentricError? pc += 1 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate if t: # get min, max, points and count ... t = tuple(sorted(t)) n = len(t), # as tuple # ... or for a single trilaterated result, # min *is* max, min- *is* maxPoint and n=1 return Trilaterate5Tuple(*(t[0] + t[-1] + n)) elif area and pc == 3: # all pairwise concentric ... r, p = min((r1, p1), (r2, p2), (r3, p3)) m = max(r1, r2, r3) # ... return "smallest" point twice, the smallest # and largest distance and n=0 for concentric return Trilaterate5Tuple(float(r), p, float(m), p, 0) n, f = (_overlap_, max) if area else (_intersection_, min) t = '%s (%s %.3f)' % (_no_(n), f.__name__, m) raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t) __all__ += _ALL_DOCS(LatLonBase) # **) 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.