Coverage for pygeodesy/latlonBase.py: 93%
475 statements
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2# -*- coding: utf-8 -*-
4u'''(INTERNAL) Base class L{LatLonBase} for all elliposiodal, spherical and N-vectorial C{LatLon} classes.
6@see: I{(C) Chris Veness 2005-2024}' U{latlong<https://www.Movable-Type.co.UK/scripts/latlong.html>},
7 U{-ellipsoidal<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>} and
8 U{-vectors<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>} and I{Charles Karney}'s
9 U{Rhumb<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>} and
10 U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>} classes.
11'''
13from pygeodesy.basics import _isin, isstr, map1, _xinstanceof
14from pygeodesy.constants import EPS, EPS0, EPS1, EPS4, INT0, R_M, \
15 _EPSqrt as _TOL, _0_0, _0_5, _1_0, \
16 _360_0, _umod_360
17from pygeodesy.datums import _spherical_datum
18from pygeodesy.dms import F_D, F_DMS, latDMS, lonDMS, parse3llh
19# from pygeodesy.ecef import EcefKarney # _MODS
20from pygeodesy.ecefLocals import _EcefLocal
21from pygeodesy.errors import _AttributeError, IntersectionError, \
22 _incompatible, _IsnotError, _TypeError, \
23 _ValueError, _xattr, _xdatum, _xError, \
24 _xkwds, _xkwds_get, _xkwds_item2, _xkwds_not
25# from pygeodesy.fmath import favg # _MODS
26# from pygeodesy import formy as _formy # _MODS.into
27from pygeodesy.internals import _passarg, typename
28from pygeodesy.interns import NN, _COMMASPACE_, _concentric_, _height_, \
29 _intersection_, _LatLon_, _m_, _negative_, \
30 _no_, _overlap_, _too_, _point_ # PYCHOK used!
31# from pygeodesy.iters import PointsIter, points2 # _MODS
32# from pygeodesy.karney import Caps # _MODS
33from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
34from pygeodesy.named import _name2__, _NamedBase, Fmt
35from pygeodesy.namedTuples import Bounds2Tuple, LatLon2Tuple, PhiLam2Tuple, \
36 Trilaterate5Tuple, Vector3Tuple
37# from pygeodesy.nvectorBase import _N_vector_ # _MODS
38from pygeodesy.props import deprecated_method, Property, Property_RO, \
39 property_RO, _update_all
40# from pygeodesy.streprs import Fmt, hstr # from .named, _MODS
41from pygeodesy.units import _isDegrees, _isRadius, Distance_, Lat, Lon, \
42 Height, Radius, Radius_, Scalar, Scalar_
43from pygeodesy.utily import sincos2d_, _unrollon, _unrollon3, _Wrap
44# from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, circum4_, \
45# Circum3Tuple, _radii11ABC4 # _MODS
46# from pygeodesy.vector3d import nearestOn6, Vector3d # _MODS
48from contextlib import contextmanager
49from math import asin, cos, degrees, fabs, radians
51__all__ = _ALL_LAZY.latlonBase
52__version__ = '25.04.28'
54_formy = _MODS.into(formy=__name__)
57class LatLonBase(_NamedBase, _EcefLocal):
58 '''(INTERNAL) Base class for ellipsoidal and spherical C{satLon}s.
59 '''
60 _clipid = INT0 # polygonal clip, see .booleans
61 _datum = None # L{Datum}, to be overriden
62 _height = INT0 # height (C{meter}), default
63 _lat = 0 # latitude (C{degrees})
64 _lon = 0 # longitude (C{degrees})
66 def __init__(self, lat_llh, lon=None, height=0, datum=None, **wrap_name):
67 '''New C{LatLon}.
69 @arg lat_llh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or
70 a previous C{LatLon} instance provided C{B{lon}=None}.
71 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix),
72 required if B{C{lat_llh}} is C{degrees} or C{str}.
73 @kwarg height: Optional height above (or below) the earth surface
74 (C{meter}, conventionally).
75 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},
76 L{a_f2Tuple} or I{scalar} radius) or C{None}.
77 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword
78 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}
79 B{C{lat}} and B{C{lon}} (C{bool}).
81 @return: New instance (C{LatLon}).
83 @raise RangeError: A B{C{lon}} or C{lat} value outside the valid
84 range and L{rangerrors} set to C{True}.
86 @raise TypeError: If B{C{lat_llh}} is not a C{LatLon}.
88 @raise UnitError: Invalid C{lat}, B{C{lon}} or B{C{height}}.
89 '''
90 w, n = self._wrap_name2(**wrap_name)
91 if n:
92 self.name = n
94 if lon is None:
95 lat, lon, height = _latlonheight3(lat_llh, height, w)
96 elif w:
97 lat, lon = _Wrap.latlonDMS2(lat_llh, lon)
98 else:
99 lat = lat_llh
101 self._lat = Lat(lat) # parseDMS2(lat, lon)
102 self._lon = Lon(lon) # PYCHOK LatLon2Tuple
103 if height: # elevation
104 self._height = Height(height)
105 if datum is not None:
106 self._datum = _spherical_datum(datum, name=self.name)
108 def __eq__(self, other):
109 return self.isequalTo(other)
111 def __ne__(self, other):
112 return not self.isequalTo(other)
114 def __str__(self):
115 return self.toStr(form=F_D, prec=6)
117 def antipode(self, height=None):
118 '''Return the antipode, the point diametrically opposite to
119 this point.
121 @kwarg height: Optional height of the antipode (C{meter}),
122 this point's height otherwise.
124 @return: The antipodal point (C{LatLon}).
125 '''
126 a = _formy.antipode(*self.latlon)
127 h = self._heigHt(height)
128 return self.classof(*a, height=h)
130 @deprecated_method
131 def bounds(self, wide, tall, radius=R_M): # PYCHOK no cover
132 '''DEPRECATED, use method C{boundsOf}.'''
133 return self.boundsOf(wide, tall, radius=radius)
135 def boundsOf(self, wide, tall, radius=R_M, height=None, **name):
136 '''Return the SW and NE lat-/longitude of a great circle
137 bounding box centered at this location.
139 @arg wide: Longitudinal box width (C{meter}, same units as
140 B{C{radius}} or C{degrees} if C{B{radius} is None}).
141 @arg tall: Latitudinal box size (C{meter}, same units as
142 B{C{radius}} or C{degrees} if C{B{radius} is None}).
143 @kwarg radius: Mean earth radius (C{meter}) or C{None} if I{both}
144 B{C{wide}} and B{C{tall}} are in C{degrees}.
145 @kwarg height: Height for C{latlonSW} and C{latlonNE} (C{meter}),
146 overriding the point's height.
147 @kwarg name: Optional C{B{name}=NN} (C{str}).
149 @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)}, the lower-left
150 and upper-right corner (C{LatLon}).
152 @see: U{https://www.Movable-Type.co.UK/scripts/latlong-db.html}
153 '''
154 w = Scalar_(wide=wide) * _0_5
155 t = Scalar_(tall=tall) * _0_5
156 if radius is not None:
157 r = Radius_(radius)
158 c = cos(self.phi)
159 w = degrees(asin(w / r) / c) if fabs(c) > EPS0 else _0_0 # XXX
160 t = degrees(t / r)
161 y, t = self.lat, fabs(t)
162 x, w = self.lon, fabs(w)
164 h = self._heigHt(height)
165 sw = self.classof(y - t, x - w, height=h)
166 ne = self.classof(y + t, x + w, height=h)
167 return Bounds2Tuple(sw, ne, name=self._name__(name))
169 def chordTo(self, other, height=None, wrap=False):
170 '''Compute the length of the chord through the earth between
171 this and an other point.
173 @arg other: The other point (C{LatLon}).
174 @kwarg height: Overriding height for both points (C{meter}),
175 or if C{None}, use each point's height.
176 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{other}}
177 point (C{bool}).
179 @return: The chord length (conventionally C{meter}).
181 @raise TypeError: The B{C{other}} point is not C{LatLon}.
182 '''
183 def _v3d(ll, V3d=_MODS.vector3d.Vector3d):
184 t = ll.toEcef(height=height) # .toVector(Vector=V3d)
185 return V3d(t.x, t.y, t.z)
187 p = self.others(other)
188 if wrap:
189 p = _Wrap.point(p)
190 return _v3d(self).minus(_v3d(p)).length
192 def circin6(self, point2, point3, eps=EPS4, **wrap_name):
193 '''Return the radius and center of the I{inscribed} aka I{In-}circle
194 of the (planar) triangle formed by this and two other points.
196 @arg point2: Second point (C{LatLon}).
197 @arg point3: Third point (C{LatLon}).
198 @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}.
199 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword
200 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}
201 the B{C{points}} (C{bool}).
203 @return: A L{Circin6Tuple}C{(radius, center, deltas, cA, cB, cC)}. The
204 C{center} and contact points C{cA}, C{cB} and C{cC}, each an
205 instance of this (sub-)class, are co-planar with this and the
206 two given points, see the B{Note} below.
208 @raise ImportError: Package C{numpy} not found, not installed or older
209 than version 1.10.
211 @raise IntersectionError: Near-coincident or -colinear points or
212 a trilateration or C{numpy} issue.
214 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
216 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted
217 back to geodetic lat-, longitude and height. The latter, conventionally
218 in C{meter} indicates whether the C{center} is above, below or on the
219 surface of the earth model. If C{deltas} is C{None}, the C{center} is
220 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon,
221 height)} representing the differences between both results from
222 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
224 @see: Function L{pygeodesy.circin6}, method L{circum3}, U{Incircle
225 <https://MathWorld.Wolfram.com/Incircle.html>} and U{Contact Triangle
226 <https://MathWorld.Wolfram.com/ContactTriangle.html>}.
227 '''
228 w, n = self._wrap_name2(**wrap_name)
230 with _toCartesian3(self, point2, point3, w) as cs:
231 m = _MODS.vector2d
232 r, c, d, A, B, C = m._circin6(*cs, eps=eps, useZ=True, dLL3=True,
233 datum=self.datum) # PYCHOK unpack
234 return m.Circin6Tuple(r, c.toLatLon(), d, A.toLatLon(),
235 B.toLatLon(),
236 C.toLatLon(), name=n)
238 def circum3(self, point2, point3, circum=True, eps=EPS4, **wrap_name):
239 '''Return the radius and center of the smallest circle I{through} or I{containing}
240 this and two other points.
242 @arg point2: Second point (C{LatLon}).
243 @arg point3: Third point (C{LatLon}).
244 @kwarg circum: If C{True}, return the C{circumradius} and C{circumcenter},
245 always, ignoring the I{Meeus}' Type I case (C{bool}).
246 @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}.
247 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword
248 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}
249 the B{C{points}} (C{bool}).
251 @return: A L{Circum3Tuple}C{(radius, center, deltas)}. The C{center}, an
252 instance of this (sub-)class, is co-planar with this and the two
253 given points. If C{deltas} is C{None}, the C{center} is
254 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat,
255 lon, height)} representing the difference between both results
256 from L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
258 @raise ImportError: Package C{numpy} not found, not installed or older than
259 version 1.10.
261 @raise IntersectionError: Near-concentric, -coincident or -colinear points,
262 incompatible C{Ecef} classes or a trilateration
263 or C{numpy} issue.
265 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
267 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted
268 back to geodetic lat-, longitude and height. The latter, conventionally
269 in C{meter} indicates whether the C{center} is above, below or on the
270 surface of the earth model. If C{deltas} is C{None}, the C{center} is
271 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon,
272 height)} representing the difference between both results from
273 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
275 @see: Function L{pygeodesy.circum3} and methods L{circin6} and L{circum4_}.
276 '''
277 w, n = self._wrap_name2(**wrap_name)
279 with _toCartesian3(self, point2, point3, w, circum=circum) as cs:
280 m = _MODS.vector2d
281 r, c, d = m._circum3(*cs, circum=circum, eps=eps, useZ=True, dLL3=True, # XXX -3d2
282 clas=cs[0].classof, datum=self.datum) # PYCHOK unpack
283 return m.Circum3Tuple(r, c.toLatLon(), d, name=n)
285 def circum4_(self, *points, **wrap_name):
286 '''Best-fit a sphere through this and two or more other points.
288 @arg points: The other points (each a C{LatLon}).
289 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument
290 C{B{wrap}=False}, if C{True}, wrap or I{normalize} the B{C{points}}
291 (C{bool}).
293 @return: A L{Circum4Tuple}C{(radius, center, rank, residuals)} with C{center} an
294 instance of this (sub-)class.
296 @raise ImportError: Package C{numpy} not found, not installed or older than
297 version 1.10.
299 @raise NumPyError: Some C{numpy} issue.
301 @raise TypeError: One of the B{C{points}} invalid.
303 @raise ValueError: Too few B{C{points}}.
305 @see: Function L{pygeodesy.circum4_} and L{circum3}.
306 '''
307 w, n = self._wrap_name2(**wrap_name)
309 def _cs(ps, C, w):
310 _wp = _Wrap.point if w else _passarg
311 for i, p in enumerate(ps):
312 yield C(i=i, points=_wp(p))
314 C = self._toCartesianEcef
315 c = C(point=self)
316 t = _MODS.vector2d.circum4_(c, Vector=c.classof, *_cs(points, C, w))
317 c = t.center.toLatLon(LatLon=self.classof)
318 return t.dup(center=c, name=n)
320 @property
321 def clipid(self):
322 '''Get the (polygonal) clip (C{int}).
323 '''
324 return self._clipid
326 @clipid.setter # PYCHOK setter!
327 def clipid(self, clipid):
328 '''Get the (polygonal) clip (C{int}).
329 '''
330 self._clipid = int(clipid)
332 @deprecated_method
333 def compassAngle(self, other, **adjust_wrap): # PYCHOK no cover
334 '''DEPRECATED, use method L{compassAngleTo}.'''
335 return self.compassAngleTo(other, **adjust_wrap)
337 def compassAngleTo(self, other, **adjust_wrap):
338 '''Return the angle from North for the direction vector between
339 this and an other point.
341 Suitable only for short, non-near-polar vectors up to a few
342 hundred Km or Miles. Use method C{initialBearingTo} for
343 larger distances.
345 @arg other: The other point (C{LatLon}).
346 @kwarg adjust_wrap: Optional keyword arguments for function
347 L{pygeodesy.compassAngle}.
349 @return: Compass angle from North (C{degrees360}).
351 @raise TypeError: The B{C{other}} point is not C{LatLon}.
353 @note: Courtesy of Martin Schultz.
355 @see: U{Local, flat earth approximation
356 <https://www.EdWilliams.org/avform.htm#flat>}.
357 '''
358 p = self.others(other)
359 return _formy.compassAngle(self.lat, self.lon, p.lat, p.lon, **adjust_wrap)
361 @deprecated_method
362 def cosineAndoyerLambertTo(self, other, **wrap):
363 '''DEPRECATED on 2024.12.31, use method L{cosineLawTo} with C{B{corr}=1}.'''
364 return self.cosineLawTo(other, corr=1, **wrap)
366 @deprecated_method
367 def cosineForsytheAndoyerLambertTo(self, other, **wrap):
368 '''DEPRECATED on 2024.12.31, use method L{cosineLawTo} with C{B{corr}=2}.'''
369 return self.cosineLawTo(other, corr=2, **wrap)
371 def cosineLawTo(self, other, **radius__corr_wrap):
372 '''Compute the distance between this and an other point using the U{Law of
373 Cosines<https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>}
374 formula, optionally corrected.
376 @arg other: The other point (C{LatLon}).
377 @kwarg radius__corr_wrap: Optional earth C{B{radius}=None} (C{meter}),
378 overriding the equatorial or mean radius of this point's
379 datum's ellipsoid and keyword arguments for function
380 L{pygeodesy.cosineLaw}.
382 @return: Distance (C{meter}, same units as B{C{radius}}).
384 @raise TypeError: The B{C{other}} point is not C{LatLon}.
386 @see: Function L{pygeodesy.cosineLaw} and methods C{distanceTo*},
387 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo} /
388 L{hubenyTo}, L{flatPolarTo}, L{haversineTo}, L{thomasTo} and
389 L{vincentysTo}.
390 '''
391 c = _xkwds_get(radius__corr_wrap, corr=0)
392 return self._distanceTo_(_formy.cosineLaw_, other, **radius__corr_wrap) if c else \
393 self._distanceTo( _formy.cosineLaw, other, **radius__corr_wrap)
395 @property_RO
396 def datum(self): # PYCHOK no cover
397 '''I{Must be overloaded}.'''
398 self._notOverloaded()
400 def destinationXyz(self, delta, LatLon=None, **LatLon_kwds):
401 '''Calculate the destination using a I{local} delta from this point.
403 @arg delta: Local delta to the destination (L{XyzLocal}, L{Aer}, L{Enu}, L{Ned}
404 or L{Local9Tuple}).
405 @kwarg LatLon: Optional (geodetic) class to return the destination or C{None}.
406 @kwarg LatLon_kwds: Optionally, additional B{C{LatLon}} keyword arguments,
407 ignored if C{B{LatLon} is None}.
409 @return: An B{C{LatLon}} instance or if C{B{LatLon} is None}, a
410 L{LatLon4Tuple}C{(lat, lon, height, datum)} or L{LatLon3Tuple}C{(lat,
411 lon, height)} if a C{datum} keyword is specified or not.
413 @raise TypeError: Invalid B{C{delta}}, B{C{LatLon}} or B{C{LatLon_kwds}} item.
414 '''
415 t = self._ltp._local2ecef(delta, nine=True) # _EcefLocal._ltp
416 return t.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, name=self.name))
418 def _distanceTo(self, func, other, radius=None, **kwds):
419 '''(INTERNAL) Helper for distance methods C{<func>To}.
420 '''
421 p = self.others(other, up=2)
422 R = radius or (self._datum.ellipsoid.R1 if self._datum else R_M)
423 return func(self.lat, self.lon, p.lat, p.lon, radius=R, **kwds)
425 def _distanceTo_(self, func_, other, wrap=False, radius=None, **kwds):
426 '''(INTERNAL) Helper for (ellipsoidal) distance methods C{<func>To}.
427 '''
428 p = self.others(other, up=2)
429 D = self.datum or _spherical_datum(radius or R_M, func_)
430 lam21, phi2, _ = _Wrap.philam3(self.lam, p.phi, p.lam, wrap)
431 r = func_(phi2, self.phi, lam21, datum=D, **kwds)
432 return r * (radius or D.ellipsoid.a)
434 @Property_RO
435 def _Ecef_forward(self):
436 '''(INTERNAL) Helper for L{_ecef9} and L{toEcef} (C{callable}).
437 '''
438 return self.Ecef(self.datum, name=self.name).forward
440 @Property_RO
441 def _ecef9(self):
442 '''(INTERNAL) Helper for L{toCartesian}, L{toEcef} and L{toCartesian} (L{Ecef9Tuple}).
443 '''
444 return self._Ecef_forward(self, M=True)
446 @property_RO
447 def ellipsoidalLatLon(self):
448 '''Get the C{LatLon type} iff ellipsoidal, overloaded in L{LatLonEllipsoidalBase}.
449 '''
450 return False
452 @deprecated_method
453 def equals(self, other, eps=None): # PYCHOK no cover
454 '''DEPRECATED, use method L{isequalTo}.'''
455 return self.isequalTo(other, eps=eps)
457 @deprecated_method
458 def equals3(self, other, eps=None): # PYCHOK no cover
459 '''DEPRECATED, use method L{isequalTo3}.'''
460 return self.isequalTo3(other, eps=eps)
462 def equirectangularTo(self, other, **radius_adjust_limit_wrap):
463 '''Compute the distance between this and an other point
464 using the U{Equirectangular Approximation / Projection
465 <https://www.Movable-Type.co.UK/scripts/latlong.html#equirectangular>}.
467 Suitable only for short, non-near-polar distances up to a
468 few hundred Km or Miles. Use method L{haversineTo} or
469 C{distanceTo*} for more accurate and/or larger distances.
471 @arg other: The other point (C{LatLon}).
472 @kwarg radius_adjust_limit_wrap: Optional keyword arguments
473 for function L{pygeodesy.equirectangular},
474 overriding the default mean C{radius} of this
475 point's datum ellipsoid.
477 @return: Distance (C{meter}, same units as B{C{radius}}).
479 @raise TypeError: The B{C{other}} point is not C{LatLon}.
481 @see: Function L{pygeodesy.equirectangular} and methods L{cosineLawTo},
482 C{distanceTo*}, C{euclideanTo}, L{flatLocalTo} / L{hubenyTo},
483 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}.
484 '''
485 return self._distanceTo(_formy.equirectangular, other, **radius_adjust_limit_wrap)
487 def euclideanTo(self, other, **radius_adjust_wrap):
488 '''Approximate the C{Euclidian} distance between this and
489 an other point.
491 See function L{pygeodesy.euclidean} for the available B{C{options}}.
493 @arg other: The other point (C{LatLon}).
494 @kwarg radius_adjust_wrap: Optional keyword arguments for function
495 L{pygeodesy.euclidean}, overriding the default mean
496 C{radius} of this point's datum ellipsoid.
498 @return: Distance (C{meter}, same units as B{C{radius}}).
500 @raise TypeError: The B{C{other}} point is not C{LatLon}.
502 @see: Function L{pygeodesy.euclidean} and methods L{cosineLawTo}, C{distanceTo*},
503 L{equirectangularTo}, L{flatLocalTo} / L{hubenyTo}, L{flatPolarTo},
504 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
505 '''
506 return self._distanceTo(_formy.euclidean, other, **radius_adjust_wrap)
508 def flatLocalTo(self, other, radius=None, **wrap):
509 '''Compute the distance between this and an other point using the
510 U{ellipsoidal Earth to plane projection
511 <https://WikiPedia.org/wiki/Geographical_distance#Ellipsoidal_Earth_projected_to_a_plane>}
512 aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>} formula.
514 @arg other: The other point (C{LatLon}).
515 @kwarg radius: Mean earth radius (C{meter}) or C{None} for the I{equatorial
516 radius} of this point's datum ellipsoid.
517 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap
518 or I{normalize} and unroll the B{C{other}} point (C{bool}).
520 @return: Distance (C{meter}, same units as B{C{radius}}).
522 @raise TypeError: The B{C{other}} point is not C{LatLon}.
524 @raise ValueError: Invalid B{C{radius}}.
526 @see: Function L{pygeodesy.flatLocal}/L{pygeodesy.hubeny}, methods L{cosineLawTo},
527 C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, L{flatPolarTo},
528 L{haversineTo}, L{thomasTo} and L{vincentysTo} and U{local, flat Earth
529 approximation<https://www.edwilliams.org/avform.htm#flat>}.
530 '''
531 r = radius if _isin(radius, None, R_M, _1_0, 1) else Radius(radius)
532 return self._distanceTo_(_formy.flatLocal_, other, radius=r, **wrap) # PYCHOK kwargs
534 hubenyTo = flatLocalTo # for Karl Hubeny
536 def flatPolarTo(self, other, **radius_wrap):
537 '''Compute the distance between this and an other point using
538 the U{polar coordinate flat-Earth<https://WikiPedia.org/wiki/
539 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula.
541 @arg other: The other point (C{LatLon}).
542 @kwarg radius_wrap: Optional C{B{radius}=R_M} and C{B{wrap}=False} for
543 function L{pygeodesy.flatPolar}, overriding the default
544 C{mean radius} of this point's datum ellipsoid.
546 @return: Distance (C{meter}, same units as B{C{radius}}).
548 @raise TypeError: The B{C{other}} point is not C{LatLon}.
550 @see: Function L{pygeodesy.flatPolar} and methods L{cosineLawTo}, C{distanceTo*},
551 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo} / L{hubenyTo},
552 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
553 '''
554 return self._distanceTo(_formy.flatPolar, other, **radius_wrap)
556 def hartzell(self, los=False, earth=None):
557 '''Compute the intersection of a Line-Of-Sight from this (geodetic) Point-Of-View
558 (pov) with this point's ellipsoid surface.
560 @kwarg los: Line-Of-Sight, I{direction} to the ellipsoid (L{Los}, L{Vector3d}),
561 C{True} for the I{normal, plumb} onto the surface or I{False} or
562 C{None} to point to the center of the ellipsoid.
563 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple}
564 or C{scalar} radius in C{meter}), overriding this point's C{datum}
565 ellipsoid.
567 @return: The intersection (C{LatLon}) with attribute C{.height} set to the distance
568 to this C{pov}.
570 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov} is inside
571 the ellipsoid or B{C{los}} points outside or away from
572 the ellipsoid.
574 @raise TypeError: Invalid B{C{los}} or invalid or undefined B{C{earth}} or C{datum}.
576 @see: Function L{hartzell<pygeodesy.formy.hartzell>} for further details.
577 '''
578 return _formy._hartzell(self, los, earth, LatLon=self.classof)
580 def haversineTo(self, other, **radius_wrap):
581 '''Compute the distance between this and an other point using the U{Haversine
582 <https://www.Movable-Type.co.UK/scripts/latlong.html>} formula.
584 @arg other: The other point (C{LatLon}).
585 @kwarg radius_wrap: Optional C{B{radius}=R_M} and C{B{wrap}=False} for function
586 L{pygeodesy.haversine}, overriding the default C{mean radius} of
587 this point's datum ellipsoid.
589 @return: Distance (C{meter}, same units as B{C{radius}}).
591 @raise TypeError: The B{C{other}} point is not C{LatLon}.
593 @see: Function L{pygeodesy.haversine} and methods L{cosineLawTo}, C{distanceTo*},
594 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo} / L{hubenyTo}, \
595 L{flatPolarTo}, L{thomasTo} and L{vincentysTo}.
596 '''
597 return self._distanceTo(_formy.haversine, other, **radius_wrap)
599 def _havg(self, other, f=_0_5, h=None):
600 '''(INTERNAL) Weighted, average height.
602 @arg other: An other point (C{LatLon}).
603 @kwarg f: Optional fraction (C{float}).
604 @kwarg h: Overriding height (C{meter}).
606 @return: Average, fractional height (C{float}) or the
607 overriding height B{C{h}} (C{Height}).
608 '''
609 return Height(h) if h is not None else \
610 _MODS.fmath.favg(self.height, other.height, f=f)
612 @Property
613 def height(self):
614 '''Get the height (C{meter}).
615 '''
616 return self._height
618 @height.setter # PYCHOK setter!
619 def height(self, height):
620 '''Set the height (C{meter}).
622 @raise TypeError: Invalid B{C{height}} C{type}.
624 @raise ValueError: Invalid B{C{height}}.
625 '''
626 h = Height(height)
627 if self._height != h:
628 _update_all(self)
629 self._height = h
631 def _heigHt(self, height):
632 '''(INTERNAL) Overriding this C{height}.
633 '''
634 return self.height if height is None else Height(height)
636 def height4(self, earth=None, normal=True, LatLon=None, **LatLon_kwds):
637 '''Compute the projection of this point on and the height above or below
638 this datum's ellipsoid surface.
640 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
641 I{overriding} this datum (L{Datum}, L{Ellipsoid},
642 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
643 L{JacobiConformal} or C{meter}, conventionally).
644 @kwarg normal: If C{True}, the projection is the normal to this ellipsoid's
645 surface, otherwise the intersection of the I{radial} line to
646 this ellipsoid's center (C{bool}).
647 @kwarg LatLon: Optional class to return the projection, height and datum
648 (C{LatLon}) or C{None}.
649 @kwarg LatLon_kwds: Optionally, additional B{C{LatLon}} keyword arguments,
650 ignored if C{B{LatLon} is None}.
652 @note: Use keyword argument C{height=0} to override C{B{LatLon}.height}
653 to {0} or any other C{scalar}, conventionally in C{meter}.
655 @return: A B{C{LatLon}} instance or if C{B{LatLon} is None}, a L{Vector4Tuple}C{(x,
656 y, z, h)} with the I{projection} C{x}, C{y} and C{z} coordinates and
657 height C{h} in C{meter}, conventionally.
659 @raise TriaxialError: No convergence in triaxial root finding.
661 @raise TypeError: Invalid B{C{LatLon}}, B{C{LatLon_kwds}} item, B{C{earth}}
662 or triaxial B{C{earth}} couldn't be converted to biaxial
663 B{C{LatLon}} datum.
665 @see: Methods L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
666 '''
667 c = self.toCartesian()
668 if LatLon is None:
669 r = c.height4(earth=earth, normal=normal)
670 else:
671 c = c.height4(earth=earth, normal=normal, Cartesian=c.classof, height=0)
672 r = c.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, datum=c.datum, height=c.height))
673 if r.datum != c.datum:
674 raise _TypeError(earth=earth, datum=r.datum)
675 return r
677 def heightStr(self, prec=-2, m=_m_):
678 '''Return this point's B{C{height}} as C{str}ing.
680 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
681 @kwarg m: Optional unit of the height (C{str}).
683 @see: Function L{pygeodesy.hstr}.
684 '''
685 return _MODS.streprs.hstr(self.height, prec=prec, m=m)
687 def intersecant2(self, *args, **kwds): # PYCHOK no cover
688 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
689 self._notImplemented(*args, **kwds)
691 def _intersecend2(self, p, q, wrap, height, g_or_r, P, Q, unused): # in .LatLonEllipsoidalBaseDI.intersecant2
692 '''(INTERNAL) Interpolate 2 heights along a geodesic or rhumb
693 line and return the 2 intersecant points accordingly.
694 '''
695 if height is None:
696 hp = hq = _xattr(p, height=INT0)
697 h = _xattr(q, height=hp) # if isLatLon(q) else hp
698 if h != hp:
699 s = g_or_r._Inverse(p, q, wrap).s12
700 if s: # fmath.fidw?
701 s = (h - hp) / s # slope
702 hq += s * Q.s12
703 hp += s * P.s12
704 else:
705 hp = hq = _MODS.fmath.favg(hp, h)
706 else:
707 hp = hq = Height(height)
709# n = self.name or typename(unused)
710 p = q = self.classof(P.lat2, P.lon2, datum=g_or_r.datum, height=hp) # name=n
711 p._iteration = P.iteration
712 if P is not Q:
713 q = self.classof(Q.lat2, Q.lon2, datum=g_or_r.datum, height=hq) # name=n
714 q._iteration = Q.iteration
715 return p, q
717 @deprecated_method
718 def isantipode(self, other, eps=EPS): # PYCHOK no cover
719 '''DEPRECATED, use method L{isantipodeTo}.'''
720 return self.isantipodeTo(other, eps=eps)
722 def isantipodeTo(self, other, eps=EPS):
723 '''Check whether this and an other point are antipodal, on diametrically
724 opposite sides of the earth.
726 @arg other: The other point (C{LatLon}).
727 @kwarg eps: Tolerance for near-equality (C{degrees}).
729 @return: C{True} if points are antipodal within the given tolerance,
730 C{False} otherwise.
731 '''
732 p = self.others(other)
733 return _formy.isantipode(*(self.latlon + p.latlon), eps=eps)
735 @Property_RO
736 def isEllipsoidal(self):
737 '''Check whether this point is ellipsoidal (C{bool} or C{None} if unknown).
738 '''
739 return _xattr(self.datum, isEllipsoidal=None)
741 def isequalTo(self, other, eps=None):
742 '''Compare this point with an other point, I{ignoring} height.
744 @arg other: The other point (C{LatLon}).
745 @kwarg eps: Tolerance for equality (C{degrees}).
747 @return: C{True} if both points are identical, I{ignoring} height,
748 C{False} otherwise.
750 @raise TypeError: The B{C{other}} point is not C{LatLon} or mismatch
751 of the B{C{other}} and this C{class} or C{type}.
753 @raise UnitError: Invalid B{C{eps}}.
755 @see: Method L{isequalTo3}.
756 '''
757 return _formy._isequalTo(self, self.others(other), eps=eps)
759 def isequalTo3(self, other, eps=None):
760 '''Compare this point with an other point, I{including} height.
762 @arg other: The other point (C{LatLon}).
763 @kwarg eps: Tolerance for equality (C{degrees}).
765 @return: C{True} if both points are identical I{including} height,
766 C{False} otherwise.
768 @raise TypeError: The B{C{other}} point is not C{LatLon} or mismatch
769 of the B{C{other}} and this C{class} or C{type}.
771 @see: Method L{isequalTo}.
772 '''
773 return self.height == self.others(other).height and \
774 _formy._isequalTo(self, other, eps=eps)
776 @Property_RO
777 def isnormal(self):
778 '''Return C{True} if this point is normal (C{bool}),
779 meaning C{abs(lat) <= 90} and C{abs(lon) <= 180}.
781 @see: Methods L{normal}, L{toNormal} and functions L{isnormal
782 <pygeodesy.isnormal>} and L{normal<pygeodesy.normal>}.
783 '''
784 return _formy.isnormal(self.lat, self.lon, eps=0)
786 @Property_RO
787 def isSpherical(self):
788 '''Check whether this point is spherical (C{bool} or C{None} if unknown).
789 '''
790 return _xattr(self.datum, isSpherical=None)
792 @Property_RO
793 def lam(self):
794 '''Get the longitude (B{C{radians}}).
795 '''
796 return radians(self.lon)
798 @Property
799 def lat(self):
800 '''Get the latitude (C{degrees90}).
801 '''
802 return self._lat
804 @lat.setter # PYCHOK setter!
805 def lat(self, lat):
806 '''Set the latitude (C{str[N|S]} or C{degrees}).
808 @raise ValueError: Invalid B{C{lat}}.
809 '''
810 lat = Lat(lat) # parseDMS(lat, suffix=_NS_, clip=90)
811 if self._lat != lat:
812 _update_all(self)
813 self._lat = lat
815 @Property
816 def latlon(self):
817 '''Get the lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).
818 '''
819 return LatLon2Tuple(self._lat, self._lon, name=self.name)
821 @latlon.setter # PYCHOK setter!
822 def latlon(self, latlonh):
823 '''Set the lat- and longitude and optionally the height (2- or 3-tuple
824 or comma- or space-separated C{str} of C{degrees90}, C{degrees180}
825 and C{meter}).
827 @raise TypeError: Height of B{C{latlonh}} not C{scalar} or B{C{latlonh}}
828 not C{list} or C{tuple}.
830 @raise ValueError: Invalid B{C{latlonh}} or M{len(latlonh)}.
832 @see: Function L{pygeodesy.parse3llh} to parse a B{C{latlonh}} string
833 into a 3-tuple C{(lat, lon, h)}.
834 '''
835 if isstr(latlonh):
836 latlonh = parse3llh(latlonh, height=self.height)
837 else:
838 _xinstanceof(list, tuple, latlonh=latlonh)
839 if len(latlonh) == 3:
840 h = Height(latlonh[2], name=Fmt.SQUARE(latlonh=2))
841 elif len(latlonh) != 2:
842 raise _ValueError(latlonh=latlonh)
843 else:
844 h = self.height
846 llh = Lat(latlonh[0]), Lon(latlonh[1]), h # parseDMS2(latlonh[0], latlonh[1])
847 if (self._lat, self._lon, self._height) != llh:
848 _update_all(self)
849 self._lat, self._lon, self._height = llh
851 def latlon2(self, ndigits=0):
852 '''Return this point's lat- and longitude in C{degrees}, rounded.
854 @kwarg ndigits: Number of (decimal) digits (C{int}).
856 @return: A L{LatLon2Tuple}C{(lat, lon)}, both C{float} and rounded
857 away from zero.
859 @note: The C{round}ed values are always C{float}, also if B{C{ndigits}}
860 is omitted.
861 '''
862 return LatLon2Tuple(round(self.lat, ndigits),
863 round(self.lon, ndigits), name=self.name)
865 @deprecated_method
866 def latlon_(self, ndigits=0): # PYCHOK no cover
867 '''DEPRECATED, use method L{latlon2}.'''
868 return self.latlon2(ndigits=ndigits)
870 latlon2round = latlon_ # PYCHOK no cover
872 @Property
873 def latlonheight(self):
874 '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).
875 '''
876 return self.latlon.to3Tuple(self.height)
878 @latlonheight.setter # PYCHOK setter!
879 def latlonheight(self, latlonh):
880 '''Set the lat- and longitude and optionally the height
881 (2- or 3-tuple or comma- or space-separated C{str} of
882 C{degrees90}, C{degrees180} and C{meter}).
884 @see: Property L{latlon} for more details.
885 '''
886 self.latlon = latlonh
888 @Property
889 def lon(self):
890 '''Get the longitude (C{degrees180}).
891 '''
892 return self._lon
894 @lon.setter # PYCHOK setter!
895 def lon(self, lon):
896 '''Set the longitude (C{str[E|W]} or C{degrees}).
898 @raise ValueError: Invalid B{C{lon}}.
899 '''
900 lon = Lon(lon) # parseDMS(lon, suffix=_EW_, clip=180)
901 if self._lon != lon:
902 _update_all(self)
903 self._lon = lon
905# _ltp = _EcefLocal._ltp(self)
907 def nearestOn6(self, points, closed=False, height=None, wrap=False):
908 '''Locate the point on a path or polygon closest to this point.
910 Points are converted to and distances are computed in I{geocentric},
911 cartesian space.
913 @arg points: The path or polygon points (C{LatLon}[]).
914 @kwarg closed: Optionally, close the polygon (C{bool}).
915 @kwarg height: Optional height, overriding the height of this and all
916 other points (C{meter}). If C{None}, take the height
917 of points into account for distances.
918 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{points}}
919 (C{bool}).
921 @return: A L{NearestOn6Tuple}C{(closest, distance, fi, j, start, end)}
922 with the C{closest}, the C{start} and the C{end} point each an
923 instance of this C{LatLon} and C{distance} in C{meter}, same
924 units as the cartesian axes.
926 @raise PointsError: Insufficient number of B{C{points}}.
928 @raise TypeError: Some B{C{points}} or some B{C{points}}' C{Ecef} invalid.
930 @raise ValueError: Some B{C{points}}' C{Ecef} is incompatible.
932 @see: Function L{nearestOn6<pygeodesy.nearestOn6>}.
933 '''
934 def _cs(Ps, h, w, C):
935 p = None # not used
936 for i, q in Ps.enumerate():
937 if w and i:
938 q = _unrollon(p, q)
939 yield C(height=h, i=i, up=3, points=q)
940 p = q
942 C = self._toCartesianEcef # to verify datum and Ecef
943 Ps = self.PointsIter(points, wrap=wrap)
945 c = C(height=height, this=self) # this Cartesian
946 t = _MODS.vector3d.nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed)
947 c, s, e = t.closest, t.start, t.end
949 kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon
950 height=height)
951 _r = self.Ecef(self.datum).reverse
952 p = _r(c).toLatLon(**kwds)
953 s = _r(s).toLatLon(**kwds) if s is not c else p
954 e = _r(e).toLatLon(**kwds) if e is not c else p
955 return t.dup(closest=p, start=s, end=e)
957 def nearestTo(self, *args, **kwds): # PYCHOK no cover
958 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
959 self._notImplemented(*args, **kwds)
961 def normal(self):
962 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and C{abs(lon) <= 180}.
964 @return: C{True} if this point was I{normal}, C{False} if it wasn't (but is now).
966 @see: Property L{isnormal} and method L{toNormal}.
967 '''
968 n = self.isnormal
969 if not n:
970 self.latlon = _formy.normal(*self.latlon)
971 return n
973 @property_RO
974 def _N_vector(self):
975 '''(INTERNAL) Get the C{Nvector} (C{nvectorBase._N_vector_})
976 '''
977 _N = _MODS.nvectorBase._N_vector_
978 return _N(*self._n_xyz3, h=self.height, name=self.name)
980 @Property_RO
981 def _n_xyz3(self):
982 '''(INTERNAL) Get the n-vector components as L{Vector3Tuple}.
983 '''
984 return philam2n_xyz(self.phi, self.lam, name=self.name)
986 @Property_RO
987 def phi(self):
988 '''Get the latitude (B{C{radians}}).
989 '''
990 return radians(self.lat)
992 @Property_RO
993 def philam(self):
994 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).
995 '''
996 return PhiLam2Tuple(self.phi, self.lam, name=self.name)
998 def philam2(self, ndigits=0):
999 '''Return this point's lat- and longitude in C{radians}, rounded.
1001 @kwarg ndigits: Number of (decimal) digits (C{int}).
1003 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float} and rounded
1004 away from zero.
1006 @note: The C{round}ed values are C{float}, always.
1007 '''
1008 return PhiLam2Tuple(round(self.phi, ndigits),
1009 round(self.lam, ndigits), name=self.name)
1011 @Property_RO
1012 def philamheight(self):
1013 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
1014 '''
1015 return self.philam.to3Tuple(self.height)
1017 @deprecated_method
1018 def points(self, points, **closed): # PYCHOK no cover
1019 '''DEPRECATED, use method L{points2}.'''
1020 return self.points2(points, **closed)
1022 def points2(self, points, closed=True):
1023 '''Check a path or polygon represented by points.
1025 @arg points: The path or polygon points (C{LatLon}[])
1026 @kwarg closed: Optionally, consider the polygon closed, ignoring any
1027 duplicate or closing final B{C{points}} (C{bool}).
1029 @return: A L{Points2Tuple}C{(number, points)}, an C{int} and a C{list}
1030 or C{tuple}.
1032 @raise PointsError: Insufficient number of B{C{points}}.
1034 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1035 '''
1036 return _MODS.iters.points2(points, closed=closed, base=self)
1038 def PointsIter(self, points, loop=0, dedup=False, wrap=False):
1039 '''Return a C{PointsIter} iterator.
1041 @arg points: The path or polygon points (C{LatLon}[])
1042 @kwarg loop: Number of loop-back points (non-negative C{int}).
1043 @kwarg dedup: If C{True}, skip duplicate points (C{bool}).
1044 @kwarg wrap: If C{True}, wrap or I{normalize} the enum-/iterated
1045 B{C{points}} (C{bool}).
1047 @return: A new C{PointsIter} iterator.
1049 @raise PointsError: Insufficient number of B{C{points}}.
1050 '''
1051 return _MODS.iters.PointsIter(points, base=self, loop=loop,
1052 dedup=dedup, wrap=wrap)
1054 def radii11(self, point2, point3, wrap=False):
1055 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent}
1056 circles of a (planar) triangle formed by this and two other points.
1058 @arg point2: Second point (C{LatLon}).
1059 @arg point3: Third point (C{LatLon}).
1060 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and
1061 B{C{point3}} (C{bool}).
1063 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.
1065 @raise IntersectionError: Near-coincident or -colinear points.
1067 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
1069 @see: Function L{pygeodesy.radii11}, U{Incircle
1070 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles
1071 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent
1072 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}.
1073 '''
1074 with _toCartesian3(self, point2, point3, wrap) as cs:
1075 return _MODS.vector2d._radii11ABC4(*cs, useZ=True)[0]
1077 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3
1078 '''(INTERNAL) Get the C{rhumb} for this point's datum or for
1079 the B{C{radius}}' earth model iff non-C{None}.
1080 '''
1081 try:
1082 d = self._rhumb3dict
1083 t = d[(exact, radius)]
1084 except KeyError:
1085 D = self.datum if radius is None else \
1086 _spherical_datum(radius) # ellipsoidal OK
1087 try:
1088 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical
1089 except AttributeError as x:
1090 raise _AttributeError(datum=D, radius=radius, cause=x)
1091 t = r, D, _MODS.karney.Caps
1092 if len(d) > 2:
1093 d.clear() # d[:] = {}
1094 d[(exact, radius)] = t # cache 3-tuple
1095 return t
1097 @Property_RO
1098 def _rhumb3dict(self): # in ._update
1099 return {} # 3-item cache
1101 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False, b360=False):
1102 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between this and
1103 an other (ellipsoidal) point.
1105 @arg other: The other point (C{LatLon}).
1106 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method
1107 L{Ellipsoid.rhumb_}.
1108 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid},
1109 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's datum.
1110 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} point (C{bool}).
1111 @kwarg b360: If C{True}, return the azimuth as bearing in compass degrees (C{bool}).
1113 @return: Rhumb azimuth (C{degrees180} or compass C{degrees360}).
1115 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}} is invalid.
1116 '''
1117 r, _, Cs = self._rhumb3(exact, radius)
1118 z = r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12
1119 return _umod_360(z + _360_0) if b360 else z
1121 def rhumbDestination(self, distance, azimuth, radius=None, height=None, exact=False, **name):
1122 '''Return the destination point having travelled the given distance from this point along
1123 a rhumb line (loxodrome) of the given azimuth.
1125 @arg distance: Distance travelled (C{meter}, same units as this point's datum (ellipsoid)
1126 axes or B{C{radius}}, may be negative.
1127 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}).
1128 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid},
1129 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's datum.
1130 @kwarg height: Optional height, overriding the default height (C{meter}).
1131 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method L{Ellipsoid.rhumb_}.
1132 @kwarg name: Optional C{B{name}=NN} (C{str}).
1134 @return: The destination point (ellipsoidal C{LatLon}).
1136 @raise TypeError: Invalid B{C{radius}}.
1138 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}} or B{C{height}}.
1139 '''
1140 r, D, _ = self._rhumb3(exact, radius)
1141 d = r._Direct(self, azimuth, distance)
1142 h = self._heigHt(height)
1143 return self.classof(d.lat2, d.lon2, datum=D, height=h, **name)
1145 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False):
1146 '''Return the distance from this to an other point along a rhumb line (loxodrome).
1148 @arg other: The other point (C{LatLon}).
1149 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method L{Ellipsoid.rhumb_}.
1150 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid},
1151 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's datum.
1152 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} point (C{bool}).
1154 @return: Distance (C{meter}, the same units as this point's datum (ellipsoid) axes or B{C{radius}}.
1156 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}} is invalid.
1158 @raise ValueError: Invalid B{C{radius}}.
1159 '''
1160 r, _, Cs = self._rhumb3(exact, radius)
1161 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12
1163 def rhumbIntersecant2(self, circle, point, other, height=None,
1164 **exact_radius_wrap_eps_tol):
1165 '''Compute the intersections of a circle and a rhumb line given as two points or as a
1166 point and azimuth.
1168 @arg circle: Radius of the circle centered at this location (C{meter}), or a point
1169 on the circle (same C{LatLon} class).
1170 @arg point: The start point of the rhumb line (same C{LatLon} class).
1171 @arg other: An other point I{on} (same C{LatLon} class) or the azimuth I{of} (compass
1172 C{degrees}) the rhumb line.
1173 @kwarg height: Optional height for the intersection points (C{meter}, conventionally)
1174 or C{None} for interpolated heights.
1175 @kwarg exact_radius_wrap_eps_tol: Optional keyword arguments, see methods L{rhumbLine}
1176 and L{RhumbLineAux.Intersecant2} or L{RhumbLine.Intersecant2}.
1178 @return: 2-Tuple of the intersection points (representing a chord), each an instance of
1179 this class. Both points are the same instance if the rhumb line is tangent to
1180 the circle.
1182 @raise IntersectionError: The circle and rhumb line do not intersect.
1184 @raise TypeError: Invalid B{C{point}}, B{C{circle}} or B{C{other}}.
1186 @raise ValueError: Invalid B{C{circle}}, B{C{other}}, B{C{height}} or B{C{exact_radius_wrap}}.
1188 @see: Methods L{RhumbLineAux.Intersecant2} and L{RhumbLine.Intersecant2}.
1189 '''
1190 def _kwds3(eps=EPS, tol=_TOL, wrap=False, **kwds):
1191 return kwds, wrap, dict(eps=eps, tol=tol)
1193 exact_radius, w, eps_tol = _kwds3(**exact_radius_wrap_eps_tol)
1195 p = _unrollon(self, self.others(point=point), wrap=w)
1196 try:
1197 r = Radius_(circle=circle) if _isRadius(circle) else \
1198 self.rhumbDistanceTo(self.others(circle=circle), wrap=w, **exact_radius)
1199 rl = p.rhumbLine(other, wrap=w, **exact_radius)
1200 P, Q = rl.Intersecant2(self.lat, self.lon, r, **eps_tol)
1202 return self._intersecend2(p, other, w, height, rl.rhumb, P, Q,
1203 self.rhumbIntersecant2)
1204 except (TypeError, ValueError) as x:
1205 raise _xError(x, center=self, circle=circle, point=point, other=other,
1206 **exact_radius_wrap_eps_tol)
1208 def rhumbLine(self, other, exact=False, radius=None, wrap=False, **name_caps):
1209 '''Get a rhumb line through this point at a given azimuth or through this and an other point.
1211 @arg other: The azimuth I{of} (compass C{degrees}) or an other point I{on} (same
1212 C{LatLon} class) the rhumb line.
1213 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method L{Ellipsoid.rhumb_}.
1214 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid},
1215 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's C{datum}.
1216 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}} point (C{bool}).
1217 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see L{RhumbLine} or L{RhumbLineAux} C{B{caps}}.
1219 @return: A C{RhumbLine} instance (C{RhumbLine} or C{RhumbLineAux}).
1221 @raise TypeError: Invalid B{C{radius}} or B{C{other}} not C{scalar} nor same C{LatLon} class.
1223 @see: Modules L{rhumb.aux_} and L{rhumb.ekx}.
1224 '''
1225 r, _, Cs = self._rhumb3(exact, radius)
1226 kwds = _xkwds(name_caps, name=self.name, caps=Cs.LINE_OFF)
1227 rl = r._DirectLine( self, other, **kwds) if _isDegrees(other) else \
1228 r._InverseLine(self, self.others(other), wrap, **kwds)
1229 return rl
1231 def rhumbMidpointTo(self, other, exact=False, radius=None, height=None, fraction=_0_5, **wrap_name):
1232 '''Return the (loxodromic) midpoint on the rhumb line between this and an other point.
1234 @arg other: The other point (same C{LatLon} class).
1235 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see method L{Ellipsoid.rhumb_}.
1236 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum}, L{Ellipsoid},
1237 L{Ellipsoid2} or L{a_f2Tuple}), overriding this point's datum.
1238 @kwarg height: Optional height, overriding the mean height (C{meter}).
1239 @kwarg fraction: Midpoint location from this point (C{scalar}), 0 for this, 1 for the B{C{other}},
1240 0.5 for halfway between this and the B{C{other}} point, may be negative or
1241 greater than 1.
1242 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and C{B{wrap}=False}, if C{True}, wrap or
1243 I{normalize} and unroll the B{C{other}} point (C{bool}).
1245 @return: The midpoint at the given B{C{fraction}} along the rhumb line (same C{LatLon} class).
1247 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}} is invalid.
1249 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}.
1250 '''
1251 w, n = self._wrap_name2(**wrap_name)
1252 r, D, _ = self._rhumb3(exact, radius)
1253 f = Scalar(fraction=fraction)
1254 d = r._Inverse(self, self.others(other), w) # C.AZIMUTH_DISTANCE
1255 d = r._Direct( self, d.azi12, d.s12 * f)
1256 h = self._havg(other, f=f, h=height)
1257 return self.classof(d.lat2, d.lon2, datum=D, height=h, name=n)
1259 @property_RO
1260 def sphericalLatLon(self):
1261 '''Get the C{LatLon type} iff spherical, overloaded in L{LatLonSphericalBase}.
1262 '''
1263 return False
1265 def thomasTo(self, other, **wrap):
1266 '''Compute the distance between this and an other point using U{Thomas'
1267 <https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>} formula.
1269 @arg other: The other point (C{LatLon}).
1270 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap
1271 or I{normalize} and unroll the B{C{other}} point (C{bool}).
1273 @return: Distance (C{meter}, same units as the axes of this point's datum ellipsoid).
1275 @raise TypeError: The B{C{other}} point is not C{LatLon}.
1277 @see: Function L{pygeodesy.thomas} and methods L{cosineLawTo}, C{distanceTo*},
1278 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo} / L{hubenyTo},
1279 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}.
1280 '''
1281 return self._distanceTo_(_formy.thomas_, other, **wrap)
1283 @deprecated_method
1284 def to2ab(self): # PYCHOK no cover
1285 '''DEPRECATED, use property L{philam}.'''
1286 return self.philam
1288 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds):
1289 '''Convert this point to cartesian, I{geocentric} coordinates, also known as
1290 I{Earth-Centered, Earth-Fixed} (ECEF).
1292 @kwarg height: Optional height, overriding this point's height (C{meter},
1293 conventionally).
1294 @kwarg Cartesian: Optional class to return the geocentric coordinates
1295 (C{Cartesian}) or C{None}.
1296 @kwarg Cartesian_kwds: Optionally, additional B{C{Cartesian}} keyword
1297 arguments, ignored if C{B{Cartesian} is None}.
1299 @return: A B{C{Cartesian}} instance or if B{C{Cartesian} is None}, an
1300 L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
1301 C{C=0} and C{M} if available.
1303 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}} item.
1305 @see: Methods C{toNvector}, C{toVector} and C{toVector3d}.
1306 '''
1307 r = self._ecef9 if height is None else self.toEcef(height=height)
1308 if Cartesian is not None: # class or .classof
1309 r = Cartesian(r, **self._name1__(Cartesian_kwds))
1310 _xdatum(r.datum, self.datum)
1311 return r
1313 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point):
1314 '''(INTERNAL) Convert to cartesian and check Ecef's before and after.
1315 '''
1316 p = self.others(up=up, **name_point)
1317 c = p.toCartesian(height=height)
1318 E = self.Ecef
1319 if E:
1320 for p in (p, c):
1321 e = _xattr(p, Ecef=None)
1322 if not _isin(e, None, E): # PYCHOK no cover
1323 n, _ = _xkwds_item2(name_point)
1324 n = Fmt.INDEX(n, i)
1325 t = _incompatible(typename(E))
1326 raise _ValueError(n, e, txt=t) # txt__
1327 return c
1329 def toDatum(self, datum2, height=None, **name):
1330 '''I{Must be overloaded}.'''
1331 self._notOverloaded(datum2, height=height, **name)
1333 def toEcef(self, height=None, M=False):
1334 '''Convert this point to I{geocentric} coordinates, also known as
1335 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).
1337 @kwarg height: Optional height, overriding this point's height (C{meter},
1338 conventionally).
1339 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}).
1341 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
1342 C{C=0} and C{M} if available.
1344 @raise EcefError: A C{.datum} or an ECEF issue.
1345 '''
1346 return self._ecef9 if _isin(height, None, self.height) else \
1347 self._Ecef_forward(self.lat, self.lon, height=height, M=M)
1349 @deprecated_method
1350 def to3llh(self, height=None): # PYCHOK no cover
1351 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.'''
1352 return self.latlonheight if _isin(height, None, self.height) else \
1353 self.latlon.to3Tuple(height)
1355 def toNormal(self, deep=False, **name):
1356 '''Get this point I{normalized} to C{abs(lat) <= 90} and C{abs(lon) <= 180}.
1358 @kwarg deep: If C{True}, make a deep, otherwise a shallow copy (C{bool}).
1359 @kwarg name: Optional C{B{name}=NN} (C{str}).
1361 @return: A copy of this point, I{normalized} (C{LatLon}), optionally renamed.
1363 @see: Property L{isnormal}, method L{normal} and function L{pygeodesy.normal}.
1364 '''
1365 ll = self.copy(deep=deep)
1366 _ = ll.normal()
1367 if name:
1368 ll.rename(name)
1369 return ll
1371 def toNvector(self, h=None, Nvector=None, **name_Nvector_kwds):
1372 '''Convert this point to C{n-vector} (normal to the earth's surface) components,
1373 I{including height}.
1375 @kwarg h: Optional height, overriding this point's height (C{meter}).
1376 @kwarg Nvector: Optional class to return the C{n-vector} components (C{Nvector})
1377 or C{None}.
1378 @kwarg name_Nvector_kwds: Optional C{B{name}=NN} (C{str}) and optionally,
1379 additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector}
1380 is None}.
1382 @return: An B{C{Nvector}} instance or a L{Vector4Tuple}C{(x, y, z, h)} if
1383 C{B{Nvector} is None}.
1385 @raise TypeError: Invalid B{C{h}}, B{C{Nvector}} or B{C{name_Nvector_kwds}}.
1387 @see: Methods C{toCartesian}, C{toVector} and C{toVector3d}.
1388 '''
1389 h = self._heigHt(h)
1390 if Nvector is None:
1391 r = self._n_xyz3.to4Tuple(h)
1392 n, _ = _name2__(name_Nvector_kwds, _or_nameof=self)
1393 if n:
1394 r.rename(n)
1395 else:
1396 x, y, z = self._n_xyz3
1397 r = Nvector(x, y, z, h=h, ll=self, **self._name1__(name_Nvector_kwds))
1398 return r
1400 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected
1401 '''Convert this point to a "lat, lon[, +/-height]" string, formatted in the
1402 given C{B{form}at}.
1404 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see functions
1405 L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.
1406 @kwarg joined: Separator to join the lat-, longitude and height strings (C{str}
1407 or C{None} or C{NN} for non-joined).
1408 @kwarg m: Optional unit of the height (C{str}), use C{None} to exclude height
1409 from the returned string.
1410 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator}, B{C{s_D}},
1411 B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword arguments, see function
1412 L{pygeodesy.toDMS} for details.
1414 @return: This point in the specified C{B{form}at}, etc. (C{str} or a 2- or 3-tuple
1415 C{(lat_str, lon_str[, height_str])} if B{C{joined}} is C{NN} or C{None}).
1417 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more details about
1418 keyword arguments C{B{form}at}, C{B{prec}ision}, C{B{sep}arator}, B{C{s_D}},
1419 B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.
1420 '''
1421 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),
1422 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))
1423 if self.height and m is not None:
1424 t += (self.heightStr(m=m),)
1425 return joined.join(t) if joined else t
1427 def toVector(self, Vector=None, **Vector_kwds):
1428 '''Convert this point to a C{Vector} with the I{geocentric} C{(x, y, z)} (ECEF)
1429 coordinates, I{ignoring height}.
1431 @kwarg Vector: Optional class to return the I{geocentric} components (L{Vector3d})
1432 or C{None}.
1433 @kwarg Vector_kwds: Optionally, additional B{C{Vector}} keyword arguments,
1434 ignored if C{B{Vector} is None}.
1436 @return: A B{C{Vector}} instance or a L{Vector3Tuple}C{(x, y, z)} if C{B{Vector}
1437 is None}.
1439 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}.
1441 @see: Methods C{toCartesian}, C{toNvector} and C{toVector3d}.
1442 '''
1443 return self._ecef9.toVector(Vector=Vector, **self._name1__(Vector_kwds))
1445 def toVector3d(self, norm=True, **Vector3d_kwds):
1446 '''Convert this point to a L{Vector3d} with the I{geocentric} C{(x, y, z)}
1447 (ECEF) coordinates, I{ignoring height}.
1449 @kwarg norm: If C{False}, don't normalize the coordinates (C{bool}).
1450 @kwarg Vector3d_kwds: Optional L{Vector3d} keyword arguments.
1452 @return: Named, unit vector or vector (L{Vector3d}).
1454 @raise TypeError: Invalid B{C{Vector3d_kwds}}.
1456 @see: Methods C{toCartesian}, C{toNvector} and C{toVector}.
1457 '''
1458 r = self.toVector(Vector=_MODS.vector3d.Vector3d, **Vector3d_kwds)
1459 if norm:
1460 r = r.unit(ll=self)
1461 return r
1463 def toWm(self, **toWm_kwds):
1464 '''Convert this point to a WM coordinate.
1466 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments.
1468 @return: The WM coordinate (L{Wm}).
1470 @see: Function L{pygeodesy.toWm}.
1471 '''
1472 return _MODS.webmercator.toWm(self, **self._name1__(toWm_kwds))
1474 @deprecated_method
1475 def to3xyz(self): # PYCHOK no cover
1476 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector},
1477 L{toVector3d} or perhaps (geocentric) L{toEcef}.'''
1478 return self.xyz # self.toVector()
1480# def _update(self, updated, *attrs, **setters):
1481# '''(INTERNAL) See C{_NamedBase._update}.
1482# '''
1483# if updated:
1484# self._rhumb3dict.clear()
1485# return _NamedBase._update(self, updated, *attrs, **setters)
1487 def vincentysTo(self, other, **radius_wrap):
1488 '''Compute the distance between this and an other point using U{Vincenty's
1489 <https://WikiPedia.org/wiki/Great-circle_distance>} spherical formula.
1491 @arg other: The other point (C{LatLon}).
1492 @kwarg radius_wrap: Optional C{B{radius}=R_M} and C{B{wrap}=False} for
1493 function L{pygeodesy.vincentys}, overriding the default
1494 C{mean radius} of this point's datum ellipsoid.
1496 @return: Distance (C{meter}, same units as B{C{radius}}).
1498 @raise TypeError: The B{C{other}} point is not C{LatLon}.
1500 @see: Function L{pygeodesy.vincentys} and methods L{cosineLawTo}, C{distanceTo*},
1501 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo} / L{hubenyTo},
1502 L{flatPolarTo}, L{haversineTo} and L{thomasTo}.
1503 '''
1504 return self._distanceTo(_formy.vincentys, other, **_xkwds(radius_wrap, radius=None))
1506 def _wrap_name2(self, wrap=False, **name):
1507 '''(INTERNAL) Return the C{wrap} and C{name} value.
1508 '''
1509 return wrap, (self._name__(name) if name else NN)
1511 @property_RO
1512 def xyz(self):
1513 '''Get the I{geocentric} C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)})
1514 '''
1515 return self._ecef9.xyz
1517 @property_RO
1518 def xyz3(self):
1519 '''Get the I{geocentric} C{(x, y, z)} coordinates as C{3-tuple}.
1520 '''
1521 return tuple(self.xyz)
1523 @Property_RO
1524 def xyzh(self):
1525 '''Get the I{geocentric} C{(x, y, z)} coordinates and height (L{Vector4Tuple}C{(x, y, z, h)})
1526 '''
1527 return self.xyz.to4Tuple(self.height)
1530class _toCartesian3(object): # see also .formy._idllmn6, .geodesicw._wargs, .vector2d._numpy
1531 '''(INTERNAL) Wrapper to convert 2 other points.
1532 '''
1533 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples
1534 def __call__(self, p, p2, p3, wrap, **kwds):
1535 try:
1536 if wrap:
1537 p2, p3 = map1(_Wrap.point, p2, p3)
1538 kwds = _xkwds(kwds, wrap=wrap)
1539 yield (p. toCartesian().copy(name=_point_), # copy to rename
1540 p._toCartesianEcef(up=4, point2=p2),
1541 p._toCartesianEcef(up=4, point3=p3))
1542 except (AssertionError, TypeError, ValueError) as x: # Exception?
1543 raise _xError(x, point=p, point2=p2, point3=p3, **kwds)
1545_toCartesian3 = _toCartesian3() # PYCHOK singleton
1548def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__
1549 '''(INTERNAL) Get 3-tuple C{(lat, lon, height)}.
1550 '''
1551 try:
1552 lat, lon = latlonh.lat, latlonh.lon
1553 height = _xattr(latlonh, height=height)
1554 except AttributeError:
1555 raise _IsnotError(_LatLon_, latlonh=latlonh)
1556 if wrap:
1557 lat, lon = _Wrap.latlon(lat, lon)
1558 return lat, lon, height
1561def latlon2n_xyz(lat_ll, lon=None, **name):
1562 '''Convert lat-, longitude to C{n-vector} (I{normal} to the earth's surface) X, Y and Z components.
1564 @arg lat_ll: Latitude (C{degrees}) or a C{LatLon} instance, L{LatLon2Tuple} or other C{LatLon*Tuple}.
1565 @kwarg lon: Longitude (C{degrees}), required if C{B{lon_ll} is degrees}, ignored otherwise.
1566 @kwarg name: Optional C{B{name}=NN} (C{str}).
1568 @return: A L{Vector3Tuple}C{(x, y, z)}.
1570 @see: Function L{philam2n_xyz}.
1572 @note: These are C{n-vector} x, y and z components, I{NOT geocentric} x, y and z (ECEF) coordinates!
1573 '''
1574 lat = lat_ll
1575 if lon is None:
1576 try:
1577 lat, lon = lat_ll.latlon
1578 except AttributeError:
1579 lat = lat_ll.lat
1580 lon = lat_ll.lon
1581 # Kenneth Gade eqn 3, but using right-handed
1582 # vector x -> 0°E,0°N, y -> 90°E,0°N, z -> 90°N
1583 sa, ca, sb, cb = sincos2d_(lat, lon)
1584 return Vector3Tuple(ca * cb, ca * sb, sa, **name)
1587def philam2n_xyz(phi_ll, lam=None, **name):
1588 '''Convert lat-, longitude to C{n-vector} (I{normal} to the earth's surface) X, Y and Z components.
1590 @arg phi_ll: Latitude (C{radians}) or a C{LatLon} instance with C{phi}, C{lam} or C{philam} attributes.
1591 @kwarg lam: Longitude (C{radians}), required if C{B{phi_ll} is radians}, ignored otherwise.
1592 @kwarg name: Optional name (C{str}).
1594 @return: A L{Vector3Tuple}C{(x, y, z)}.
1596 @see: Function L{latlon2n_xyz}.
1598 @note: These are C{n-vector} x, y and z components, I{NOT geocentric} x, y and z (ECEF) coordinates!
1599 '''
1600 phi = phi_ll
1601 if lam is None:
1602 try:
1603 phi, lam = phi_ll.philam
1604 except AttributeError:
1605 phi = phi_ll.phi
1606 lam = phi_ll.lam
1607 return latlon2n_xyz(degrees(phi), degrees(lam), **name)
1610def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, radius=R_M, wrap=False): # MCCABE 13
1611 '''(INTERNAL) Trilaterate three points by I{area overlap} or by I{perimeter intersection} of three circles.
1613 @note: The B{C{radius}} is needed only for C{n-vectorial} and C{sphericalTrigonometry.LatLon.distanceTo}
1614 methods and silently ignored by the C{ellipsoidalExact}, C{-GeodSolve}, C{-Karney} and
1615 C{-Vincenty.LatLon.distanceTo} methods.
1616 '''
1617 p2, p3, w = _unrollon3(p1, p2, p3, wrap)
1618 rw = dict(radius=radius, wrap=w)
1620 r1 = Distance_(distance1=d1)
1621 r2 = Distance_(distance2=d2)
1622 r3 = Distance_(distance3=d3)
1623 m = 0 if area else (r1 + r2 + r3)
1624 pc = 0
1625 t = []
1626 for _ in range(3):
1627 try: # intersection of circle (p1, r1) and (p2, r2)
1628 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w)
1630 if area: # check overlap
1631 if c1 is c2: # abutting
1632 c = c1
1633 else: # nearest point on radical
1634 c = p3.nearestOn(c1, c2, within=True, wrap=w)
1635 d = r3 - p3.distanceTo(c, **rw)
1636 if d > eps: # sufficient overlap
1637 t.append((d, c))
1638 m = max(m, d)
1640 else: # check intersection
1641 for c in ((c1,) if c1 is c2 else (c1, c2)):
1642 d = fabs(r3 - p3.distanceTo(c, **rw))
1643 if d < eps: # below margin
1644 t.append((d, c))
1645 m = min(m, d)
1647 except IntersectionError as x:
1648 if _concentric_ in str(x): # XXX ConcentricError?
1649 pc += 1
1651 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate
1653 if t: # get min, max, points and count ...
1654 t = tuple(sorted(t))
1655 n = len(t), # as 1-tuple
1656 # ... or for a single trilaterated result,
1657 # min *is* max, min- *is* maxPoint and n=1, 2 or 3
1658 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...)
1660 elif area and pc == 3: # all pairwise concentric ...
1661 r, p = min((r1, p1), (r2, p2), (r3, p3))
1662 m = max(r1, r2, r3)
1663 # ... return "smallest" point twice, the smallest
1664 # and largest distance and n=0 for concentric
1665 return Trilaterate5Tuple(float(r), p, float(m), p, 0)
1667 n, f = (_overlap_, max) if area else (_intersection_, min)
1668 t = _COMMASPACE_(_no_(n), '%s %.3g' % (typename(f), m))
1669 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t)
1672__all__ += _ALL_DOCS(LatLonBase)
1674# **) MIT License
1675#
1676# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
1677#
1678# Permission is hereby granted, free of charge, to any person obtaining a
1679# copy of this software and associated documentation files (the "Software"),
1680# to deal in the Software without restriction, including without limitation
1681# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1682# and/or sell copies of the Software, and to permit persons to whom the
1683# Software is furnished to do so, subject to the following conditions:
1684#
1685# The above copyright notice and this permission notice shall be included
1686# in all copies or substantial portions of the Software.
1687#
1688# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1689# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1690# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1691# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1692# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1693# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1694# OTHER DEALINGS IN THE SOFTWARE.