Coverage for pygeodesy/latlonBase.py: 92%
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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}' 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 isscalar, 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
17# from pygeodesy.datums import _spherical_datum # from .formy
18from pygeodesy.dms import F_D, F_DMS, latDMS, lonDMS, parse3llh
19# from pygeodesy.ecef import EcefKarney # _MODS
20from pygeodesy.errors import _AttributeError, _incompatible, \
21 _IsnotError, IntersectionError, \
22 _ValueError, _xattr, _xdatum, \
23 _xError, _xkwds, _xkwds_not
24# from pygeodesy.fmath import favg # _MODS
25from pygeodesy.formy import antipode, compassAngle, cosineAndoyerLambert_, \
26 cosineForsytheAndoyerLambert_, cosineLaw, \
27 equirectangular, euclidean, flatLocal_, \
28 flatPolar, _hartzell, haversine, isantipode, \
29 _isequalTo, isnormal, normal, philam2n_xyz, \
30 thomas_, vincentys, _spherical_datum
31from pygeodesy.interns import NN, _COMMASPACE_, _concentric_, _height_, \
32 _intersection_, _LatLon_, _m_, _negative_, \
33 _no_, _overlap_, _too_, _point_ # PYCHOK used!
34# from pygeodesy.iters import PointsIter, points2 # from .vector3d, _MODS
35# from pygeodesy.karney import Caps # _MODS
36from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
37# from pygeodesy.ltp import Ltp, _xLtp # _MODS
38from pygeodesy.named import _NamedBase, notImplemented, notOverloaded, Fmt
39from pygeodesy.namedTuples import Bounds2Tuple, LatLon2Tuple, PhiLam2Tuple, \
40 Trilaterate5Tuple, Vector3Tuple
41# from pygeodesy.nvectorBase import _N_vector_ # _MODS
42from pygeodesy.props import deprecated_method, Property, Property_RO, \
43 property_RO, _update_all
44# from pygeodesy.streprs import Fmt, hstr # from .named, _MODS
45from pygeodesy.units import Distance_, Lat, Lon, Height, Radius, Radius_, \
46 Scalar, Scalar_
47from pygeodesy.utily import _unrollon, _unrollon3, _Wrap
48from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, circum4_, \
49 Circum3Tuple, _radii11ABC
50from pygeodesy.vector3d import nearestOn6, Vector3d, PointsIter
52from contextlib import contextmanager
53from math import asin, cos, degrees, fabs, radians
55__all__ = _ALL_LAZY.latlonBase
56__version__ = '23.11.08'
59class LatLonBase(_NamedBase):
60 '''(INTERNAL) Base class for C{LatLon} points on spherical or
61 ellipsoidal earth models.
62 '''
63 _clipid = INT0 # polygonal clip, see .booleans
64 _datum = None # L{Datum}, to be overriden
65 _height = INT0 # height (C{meter}), default
66 _lat = 0 # latitude (C{degrees})
67 _lon = 0 # longitude (C{degrees})
69 def __init__(self, latlonh, lon=None, height=0, wrap=False, name=NN, datum=None):
70 '''New C{LatLon}.
72 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or
73 a previous C{LatLon} instance provided C{B{lon}=None}.
74 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or
75 C(None), indicating B{C{latlonh}} is a C{LatLon}.
76 @kwarg height: Optional height above (or below) the earth surface
77 (C{meter}, conventionally).
78 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}}
79 (C{bool}).
80 @kwarg name: Optional name (C{str}).
81 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},
82 L{a_f2Tuple} or I{scalar} radius) or C{None}.
84 @return: New instance (C{LatLon}).
86 @raise RangeError: A B{C{lon}} or C{lat} value outside the valid
87 range and L{rangerrors} set to C{True}.
89 @raise TypeError: If B{C{latlonh}} is not a C{LatLon}.
91 @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}.
93 @example:
95 >>> p = LatLon(50.06632, -5.71475)
96 >>> q = LatLon('50°03′59″N', """005°42'53"W""")
97 >>> r = LatLon(p)
98 '''
99 if name:
100 self.name = name
102 if lon is None:
103 lat, lon, height = _latlonheight3(latlonh, height, wrap)
104 elif wrap:
105 lat, lon = _Wrap.latlonDMS2(latlonh, lon)
106 else:
107 lat = latlonh
109 self._lat = Lat(lat) # parseDMS2(lat, lon)
110 self._lon = Lon(lon) # PYCHOK LatLon2Tuple
111 if height: # elevation
112 self._height = Height(height)
113 if datum:
114 self._datum = _spherical_datum(datum, name=self.name)
116 def __eq__(self, other):
117 return self.isequalTo(other)
119 def __ne__(self, other):
120 return not self.isequalTo(other)
122 def __str__(self):
123 return self.toStr(form=F_D, prec=6)
125 def antipode(self, height=None):
126 '''Return the antipode, the point diametrically opposite
127 to this point.
129 @kwarg height: Optional height of the antipode (C{meter}),
130 this point's height otherwise.
132 @return: The antipodal point (C{LatLon}).
133 '''
134 h = self._heigHt(height)
135 return self.classof(*antipode(*self.latlon), height=h)
137 @deprecated_method
138 def bounds(self, wide, tall, radius=R_M): # PYCHOK no cover
139 '''DEPRECATED, use method C{boundsOf}.'''
140 return self.boundsOf(wide, tall, radius=radius)
142 def boundsOf(self, wide, tall, radius=R_M, height=None):
143 '''Return the SW and NE lat-/longitude of a great circle
144 bounding box centered at this location.
146 @arg wide: Longitudinal box width (C{meter}, same units as
147 B{C{radius}} or C{degrees} if B{C{radius}} is C{None}).
148 @arg tall: Latitudinal box size (C{meter}, same units as
149 B{C{radius}} or C{degrees} if B{C{radius}} is C{None}).
150 @kwarg radius: Mean earth radius (C{meter}) or C{None} if I{both}
151 B{C{wide}} and B{C{tall}} are in C{degrees}.
152 @kwarg height: Height for C{latlonSW} and C{latlonNE} (C{meter}),
153 overriding the point's height.
155 @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)}, the
156 lower-left and upper-right corner (C{LatLon}).
158 @see: U{https://www.Movable-Type.co.UK/scripts/latlong-db.html}
159 '''
160 w = Scalar_(wide=wide) * _0_5
161 t = Scalar_(tall=tall) * _0_5
162 if radius is not None:
163 r = Radius_(radius)
164 c = cos(self.phi)
165 w = degrees(asin(w / r) / c) if fabs(c) > EPS0 else _0_0 # XXX
166 t = degrees(t / r)
167 y, t = self.lat, fabs(t)
168 x, w = self.lon, fabs(w)
170 h = self._heigHt(height)
171 sw = self.classof(y - t, x - w, height=h)
172 ne = self.classof(y + t, x + w, height=h)
173 return Bounds2Tuple(sw, ne, name=self.name)
175 def chordTo(self, other, height=None, wrap=False):
176 '''Compute the length of the chord through the earth between
177 this and an other point.
179 @arg other: The other point (C{LatLon}).
180 @kwarg height: Overriding height for both points (C{meter})
181 or C{None} for each point's height.
182 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{other}}
183 point (C{bool}).
185 @return: The chord length (conventionally C{meter}).
187 @raise TypeError: The B{C{other}} point is not C{LatLon}.
188 '''
189 def _v3d(ll):
190 t = ll.toEcef(height=height) # .toVector(Vector=Vector3d)
191 return Vector3d(t.x, t.y, t.z)
193 p = self.others(other)
194 if wrap:
195 p = _Wrap.point(p)
196 return _v3d(self).minus(_v3d(p)).length
198 def circin6(self, point2, point3, eps=EPS4, wrap=False):
199 '''Return the radius and center of the I{inscribed} aka I{In-}circle
200 of the (planar) triangle formed by this and two other points.
202 @arg point2: Second point (C{LatLon}).
203 @arg point3: Third point (C{LatLon}).
204 @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}.
205 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and
206 B{C{point3}} (C{bool}).
208 @return: L{Circin6Tuple}C{(radius, center, deltas, cA, cB, cC)}. The
209 C{center} and contact points C{cA}, C{cB} and C{cC}, each an
210 instance of this (sub-)class, are co-planar with this and the
211 two given points, see the B{Note} below.
213 @raise ImportError: Package C{numpy} not found, not installed or older
214 than version 1.10.
216 @raise IntersectionError: Near-coincident or -colinear points or
217 a trilateration or C{numpy} issue.
219 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
221 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted
222 back to geodetic lat-, longitude and height. The latter, conventionally
223 in C{meter} indicates whether the C{center} is above, below or on the
224 surface of the earth model. If C{deltas} is C{None}, the C{center} is
225 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon,
226 height)} representing the differences between both results from
227 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
229 @see: Function L{pygeodesy.circin6}, method L{circum3}, U{Incircle
230 <https://MathWorld.Wolfram.com/Incircle.html>} and U{Contact Triangle
231 <https://MathWorld.Wolfram.com/ContactTriangle.html>}.
232 '''
233 with _toCartesian3(self, point2, point3, wrap) as cs:
234 r, c, d, cA, cB, cC = _circin6(*cs, eps=eps, useZ=True, dLL3=True,
235 datum=self.datum) # PYCHOK unpack
236 return Circin6Tuple(r, c.toLatLon(), d, cA.toLatLon(), cB.toLatLon(), cC.toLatLon())
238 def circum3(self, point2, point3, circum=True, eps=EPS4, wrap=False):
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: If C{True}, wrap or I{normalize} B{C{point2}} and
248 B{C{point3}} (C{bool}).
250 @return: A L{Circum3Tuple}C{(radius, center, deltas)}. The C{center}, an
251 instance of this (sub-)class, is co-planar with this and the two
252 given points. If C{deltas} is C{None}, the C{center} is
253 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat,
254 lon, height)} representing the difference between both results
255 from L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
257 @raise ImportError: Package C{numpy} not found, not installed or older than
258 version 1.10.
260 @raise IntersectionError: Near-concentric, -coincident or -colinear points,
261 incompatible C{Ecef} classes or a trilateration
262 or C{numpy} issue.
264 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
266 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted
267 back to geodetic lat-, longitude and height. The latter, conventionally
268 in C{meter} indicates whether the C{center} is above, below or on the
269 surface of the earth model. If C{deltas} is C{None}, the C{center} is
270 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon,
271 height)} representing the difference between both results from
272 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
274 @see: Function L{pygeodesy.circum3} and methods L{circin6} and L{circum4_}.
275 '''
276 with _toCartesian3(self, point2, point3, wrap, circum=circum) as cs:
277 r, c, d = _circum3(*cs, circum=circum, eps=eps, useZ=True, dLL3=True, # XXX -3d2
278 clas=cs[0].classof, datum=self.datum) # PYCHOK unpack
279 return Circum3Tuple(r, c.toLatLon(), d)
281 def circum4_(self, *points, **wrap):
282 '''Best-fit a sphere through this and two or more other points.
284 @arg points: The other points (each a C{LatLon}).
285 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{points}}
286 (C{bool}), default C{False}.
288 @return: L{Circum4Tuple}C{(radius, center, rank, residuals)} with C{center}
289 an instance of this (sub-)class.
291 @raise ImportError: Package C{numpy} not found, not installed or older than
292 version 1.10.
294 @raise NumPyError: Some C{numpy} issue.
296 @raise TypeError: One of the B{C{points}} invalid.
298 @raise ValueError: Too few B{C{points}}.
300 @see: Function L{pygeodesy.circum4_} and L{circum3}.
301 '''
302 def _cs(ps, C, wrap=False):
303 _wp = _Wrap.point if wrap else (lambda p: p)
304 for i, p in enumerate(ps):
305 yield C(i=i, points=_wp(p))
307 C = self._toCartesianEcef
308 c = C(point=self)
309 t = circum4_(c, Vector=c.classof, *_cs(points, C, **wrap))
310 c = t.center.toLatLon(LatLon=self.classof)
311 return t.dup(center=c)
313 @property
314 def clipid(self):
315 '''Get the (polygonal) clip (C{int}).
316 '''
317 return self._clipid
319 @clipid.setter # PYCHOK setter!
320 def clipid(self, clipid):
321 '''Get the (polygonal) clip (C{int}).
322 '''
323 self._clipid = int(clipid)
325 @deprecated_method
326 def compassAngle(self, other, **adjust_wrap): # PYCHOK no cover
327 '''DEPRECATED, use method L{compassAngleTo}.'''
328 return self.compassAngleTo(other, **adjust_wrap)
330 def compassAngleTo(self, other, **adjust_wrap):
331 '''Return the angle from North for the direction vector between
332 this and an other point.
334 Suitable only for short, non-near-polar vectors up to a few
335 hundred Km or Miles. Use method C{initialBearingTo} for
336 larger distances.
338 @arg other: The other point (C{LatLon}).
339 @kwarg adjust_wrap: Optional keyword arguments for function
340 L{pygeodesy.compassAngle}.
342 @return: Compass angle from North (C{degrees360}).
344 @raise TypeError: The B{C{other}} point is not C{LatLon}.
346 @note: Courtesy of Martin Schultz.
348 @see: U{Local, flat earth approximation
349 <https://www.EdWilliams.org/avform.htm#flat>}.
350 '''
351 p = self.others(other)
352 return compassAngle(self.lat, self.lon, p.lat, p.lon, **adjust_wrap)
354 def cosineAndoyerLambertTo(self, other, wrap=False):
355 '''Compute the distance between this and an other point using the U{Andoyer-Lambert correction<https://
356 navlib.net/wp-content/uploads/2013/10/admiralty-manual-of-navigation-vol-1-1964-english501c.pdf>}
357 of the U{Law of Cosines<https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>} formula.
359 @arg other: The other point (C{LatLon}).
360 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
361 the B{C{other}} point (C{bool}).
363 @return: Distance (C{meter}, same units as the axes of this
364 point's datum ellipsoid).
366 @raise TypeError: The B{C{other}} point is not C{LatLon}.
368 @see: Function L{pygeodesy.cosineAndoyerLambert} and methods
369 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo},
370 C{distanceTo*}, L{equirectangularTo}, L{euclideanTo},
371 L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo},
372 L{thomasTo} and L{vincentysTo}.
373 '''
374 return self._distanceTo_(cosineAndoyerLambert_, other, wrap=wrap)
376 def cosineForsytheAndoyerLambertTo(self, other, wrap=False):
377 '''Compute the distance between this and an other point using
378 the U{Forsythe-Andoyer-Lambert correction
379 <https://www2.UNB.Ca/gge/Pubs/TR77.pdf>} of the U{Law of Cosines
380 <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>}
381 formula.
383 @arg other: The other point (C{LatLon}).
384 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
385 the B{C{other}} point (C{bool}).
387 @return: Distance (C{meter}, same units as the axes of
388 this point's datum ellipsoid).
390 @raise TypeError: The B{C{other}} point is not C{LatLon}.
392 @see: Function L{pygeodesy.cosineForsytheAndoyerLambert} and methods
393 L{cosineAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
394 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
395 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}.
396 '''
397 return self._distanceTo_(cosineForsytheAndoyerLambert_, other, wrap=wrap)
399 def cosineLawTo(self, other, radius=None, wrap=False):
400 '''Compute the distance between this and an other point using the
401 U{spherical Law of Cosines
402 <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>}
403 formula.
405 @arg other: The other point (C{LatLon}).
406 @kwarg radius: Mean earth radius (C{meter}) or C{None}
407 for the mean radius of this point's datum
408 ellipsoid.
409 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
410 the B{C{other}} point (C{bool}).
412 @return: Distance (C{meter}, same units as B{C{radius}}).
414 @raise TypeError: The B{C{other}} point is not C{LatLon}.
416 @see: Function L{pygeodesy.cosineLaw} and methods L{cosineAndoyerLambertTo},
417 L{cosineForsytheAndoyerLambertTo}, C{distanceTo*}, L{equirectangularTo},
418 L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},
419 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
420 '''
421 return self._distanceTo(cosineLaw, other, radius, wrap=wrap)
423 @property_RO
424 def datum(self): # PYCHOK no cover
425 '''I{Must be overloaded}.'''
426 notOverloaded(self)
428 def destinationXyz(self, delta, LatLon=None, **LatLon_kwds):
429 '''Calculate the destination using a I{local} delta from this point.
431 @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu},
432 L{Ned} or L{Local9Tuple}).
433 @kwarg LatLon: Optional (geodetic) class to return the destination
434 or C{None}.
435 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
436 arguments, ignored if C{B{LatLon} is None}.
438 @return: Destination as a C{B{LatLon}(lat, lon, **B{LatLon_kwds})}
439 instance or if C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat,
440 lon, height)} respectively L{LatLon4Tuple}C{(lat, lon,
441 height, datum)} depending on whether a C{datum} keyword
442 is un-/specified.
444 @raise TypeError: Invalid B{C{delta}}, B{C{LatLon}} or B{C{LatLon_kwds}}.
445 '''
446 t = self._ltp._local2ecef(delta, nine=True)
447 return t.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, name=self.name))
449 def _distanceTo(self, func, other, radius=None, **kwds):
450 '''(INTERNAL) Helper for distance methods C{<func>To}.
451 '''
452 p, r = self.others(other, up=2), radius
453 if r is None:
454 r = self._datum.ellipsoid.R1 if self._datum else R_M
455 return func(self.lat, self.lon, p.lat, p.lon, radius=r, **kwds)
457 def _distanceTo_(self, func_, other, wrap=False, radius=None):
458 '''(INTERNAL) Helper for (ellipsoidal) methods C{<func>To}.
459 '''
460 p = self.others(other, up=2)
461 D = self.datum
462 lam21, phi2, _ = _Wrap.philam3(self.lam, p.phi, p.lam, wrap)
463 r = func_(phi2, self.phi, lam21, datum=D)
464 return r * (D.ellipsoid.a if radius is None else radius)
466 @Property_RO
467 def Ecef(self):
468 '''Get the ECEF I{class} (L{EcefKarney}), I{lazily}.
469 '''
470 return _MODS.ecef.EcefKarney # default
472 @Property_RO
473 def _Ecef_forward(self):
474 '''(INTERNAL) Helper for L{_ecef9} and L{toEcef} (C{callable}).
475 '''
476 return self.Ecef(self.datum, name=self.name).forward
478 @Property_RO
479 def _ecef9(self):
480 '''(INTERNAL) Helper for L{toCartesian}, L{toEcef} and L{toCartesian} (L{Ecef9Tuple}).
481 '''
482 return self._Ecef_forward(self, M=True)
484 @property_RO
485 def ellipsoidalLatLon(self):
486 '''Get the C{LatLon type} iff ellipsoidal, overloaded in L{LatLonEllipsoidalBase}.
487 '''
488 return False
490 @deprecated_method
491 def equals(self, other, eps=None): # PYCHOK no cover
492 '''DEPRECATED, use method L{isequalTo}.'''
493 return self.isequalTo(other, eps=eps)
495 @deprecated_method
496 def equals3(self, other, eps=None): # PYCHOK no cover
497 '''DEPRECATED, use method L{isequalTo3}.'''
498 return self.isequalTo3(other, eps=eps)
500 def equirectangularTo(self, other, **radius_adjust_limit_wrap):
501 '''Compute the distance between this and an other point
502 using the U{Equirectangular Approximation / Projection
503 <https://www.Movable-Type.co.UK/scripts/latlong.html#equirectangular>}.
505 Suitable only for short, non-near-polar distances up to a
506 few hundred Km or Miles. Use method L{haversineTo} or
507 C{distanceTo*} for more accurate and/or larger distances.
509 @arg other: The other point (C{LatLon}).
510 @kwarg radius_adjust_limit_wrap: Optional keyword arguments
511 for function L{pygeodesy.equirectangular},
512 overriding the default mean C{radius} of this
513 point's datum ellipsoid.
515 @return: Distance (C{meter}, same units as B{C{radius}}).
517 @raise TypeError: The B{C{other}} point is not C{LatLon}.
519 @see: Function L{pygeodesy.equirectangular} and methods L{cosineAndoyerLambertTo},
520 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
521 C{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},
522 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
523 '''
524 return self._distanceTo(equirectangular, other, **radius_adjust_limit_wrap)
526 def euclideanTo(self, other, **radius_adjust_wrap):
527 '''Approximate the C{Euclidian} distance between this and
528 an other point.
530 See function L{pygeodesy.euclidean} for the available B{C{options}}.
532 @arg other: The other point (C{LatLon}).
533 @kwarg radius_adjust_wrap: Optional keyword arguments for function
534 L{pygeodesy.euclidean}, overriding the default mean
535 C{radius} of this point's datum ellipsoid.
537 @return: Distance (C{meter}, same units as B{C{radius}}).
539 @raise TypeError: The B{C{other}} point is not C{LatLon}.
541 @see: Function L{pygeodesy.euclidean} and methods L{cosineAndoyerLambertTo},
542 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
543 L{equirectangularTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},
544 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
545 '''
546 return self._distanceTo(euclidean, other, **radius_adjust_wrap)
548 def flatLocalTo(self, other, radius=None, wrap=False):
549 '''Compute the distance between this and an other point using the
550 U{ellipsoidal Earth to plane projection
551 <https://WikiPedia.org/wiki/Geographical_distance#Ellipsoidal_Earth_projected_to_a_plane>}
552 aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>} formula.
554 @arg other: The other point (C{LatLon}).
555 @kwarg radius: Mean earth radius (C{meter}) or C{None} for
556 the I{equatorial radius} of this point's
557 datum ellipsoid.
558 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
559 the B{C{other}} point (C{bool}).
561 @return: Distance (C{meter}, same units as B{C{radius}}).
563 @raise TypeError: The B{C{other}} point is not C{LatLon}.
565 @raise ValueError: Invalid B{C{radius}}.
567 @see: Function L{pygeodesy.flatLocal}/L{pygeodesy.hubeny}, methods
568 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo},
569 L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo},
570 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo} and
571 U{local, flat Earth approximation<https://www.edwilliams.org/avform.htm#flat>}.
572 '''
573 return self._distanceTo_(flatLocal_, other, wrap=wrap, radius=
574 radius if radius in (None, R_M, _1_0, 1) else Radius(radius)) # PYCHOK kwargs
576 hubenyTo = flatLocalTo # for Karl Hubeny
578 def flatPolarTo(self, other, **radius_wrap):
579 '''Compute the distance between this and an other point using
580 the U{polar coordinate flat-Earth<https://WikiPedia.org/wiki/
581 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula.
583 @arg other: The other point (C{LatLon}).
584 @kwarg radius_wrap: Optional keyword arguments for function
585 L{pygeodesy.flatPolar}, overriding the
586 default mean C{radius} of this point's
587 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.flatPolar} and methods L{cosineAndoyerLambertTo},
594 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
595 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
596 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
597 '''
598 return self._distanceTo(flatPolar, other, **radius_wrap)
600 def hartzell(self, los=None, earth=None):
601 '''Compute the intersection of a Line-Of-Sight (los) from this Point-Of-View
602 (pov) with this point's ellipsoid surface.
604 @kwarg los: Line-Of-Sight, I{direction} to earth (L{Los}, L{Vector3d})
605 or C{None} to point to the ellipsoid's center.
606 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},
607 L{a_f2Tuple} or C{scalar} radius in C{meter}) overriding
608 this point's C{datum} ellipsoid.
610 @return: The ellipsoid intersection (C{LatLon}) with C{.height} set
611 to the distance to this C{pov}.
613 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov}
614 is inside the ellipsoid or B{C{los}} points
615 outside or away from the ellipsoid.
617 @raise TypeError: Invalid B{C{los}}.
619 @see: Function C{hartzell} for further details.
620 '''
621 return _hartzell(self, los, earth, LatLon=self.classof)
623 def haversineTo(self, other, **radius_wrap):
624 '''Compute the distance between this and an other point using the
625 U{Haversine<https://www.Movable-Type.co.UK/scripts/latlong.html>}
626 formula.
628 @arg other: The other point (C{LatLon}).
629 @kwarg radius_wrap: Optional keyword arguments for function
630 L{pygeodesy.haversine}, overriding the
631 default mean C{radius} of this point's
632 datum ellipsoid.
634 @return: Distance (C{meter}, same units as B{C{radius}}).
636 @raise TypeError: The B{C{other}} point is not C{LatLon}.
638 @see: Function L{pygeodesy.haversine} and methods L{cosineAndoyerLambertTo},
639 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
640 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
641 L{flatPolarTo}, L{thomasTo} and L{vincentysTo}.
642 '''
643 return self._distanceTo(haversine, other, **radius_wrap)
645 def _havg(self, other, f=_0_5, h=None):
646 '''(INTERNAL) Weighted, average height.
648 @arg other: An other point (C{LatLon}).
649 @kwarg f: Optional fraction (C{float}).
650 @kwarg h: Overriding height (C{meter}).
652 @return: Average, fractional height (C{float}) or
653 the overriding B{C{height}} (C{Height}).
654 '''
655 return Height(h) if h is not None else \
656 _MODS.fmath.favg(self.height, other.height, f=f)
658 @Property
659 def height(self):
660 '''Get the height (C{meter}).
661 '''
662 return self._height
664 @height.setter # PYCHOK setter!
665 def height(self, height):
666 '''Set the height (C{meter}).
668 @raise TypeError: Invalid B{C{height}} C{type}.
670 @raise ValueError: Invalid B{C{height}}.
671 '''
672 h = Height(height)
673 if self._height != h:
674 _update_all(self)
675 self._height = h
677 def _heigHt(self, height):
678 '''(INTERNAL) Overriding this C{height}.
679 '''
680 return self.height if height is None else Height(height)
682 def height4(self, earth=None, normal=True, LatLon=None, **LatLon_kwds):
683 '''Compute the height above or below and the projection of this point
684 on this datum's or on an other earth's ellipsoid surface.
686 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius
687 I{overriding} this datum (L{Datum}, L{Ellipsoid},
688 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
689 L{JacobiConformal} or C{meter}, conventionally).
690 @kwarg normal: If C{True} the projection is the nearest point on the
691 ellipsoid's surface, otherwise the intersection of the
692 radial line to the center and the ellipsoid's surface.
693 @kwarg LatLon: Optional class to return the height and projection
694 (C{LatLon}) or C{None}.
695 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
696 ignored if C{B{LatLon} is None}.
698 @note: Use keyword argument C{height=0} to override C{B{LatLon}.height}
699 to {0} or any other C{scalar}, conventionally in C{meter}.
701 @return: An instance of B{C{LatLon}} or if C{B{LatLon} is None}, a
702 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
703 and C{z} coordinates and height C{h} in C{meter}, conventionally.
705 @raise TriaxialError: No convergence in triaxial root finding.
707 @raise TypeError: Invalid B{C{earth}}.
709 @see: L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
710 '''
711 c = self.toCartesian()
712 if LatLon is None:
713 r = c.height4(earth=earth, normal=normal)
714 else:
715 r = c.height4(earth=earth, normal=normal, Cartesian=c.classof, height=0)
716 r = r.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, height=r.height))
717 return r
719 def heightStr(self, prec=-2, m=_m_):
720 '''Return this point's B{C{height}} as C{str}ing.
722 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
723 @kwarg m: Optional unit of the height (C{str}).
725 @see: Function L{pygeodesy.hstr}.
726 '''
727 return _MODS.streprs.hstr(self.height, prec=prec, m=m)
729 def intersecant2(self, *args, **kwds): # PYCHOK no cover
730 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
731 notImplemented(self, *args, **kwds)
733 def _intersecend2(self, p, q, wrap, height, g_or_r, P, Q, unused): # in .LatLonEllipsoidalBaseDI.intersecant2
734 '''(INTERNAL) Interpolate 2 heights along a geodesic or rhumb
735 line and return the 2 intercant points accordingly.
736 '''
737 if height is None:
738 hp = hq = _xattr(p, height=INT0)
739 h = _xattr(q, height=hp) # if isLatLon(q) else hp
740 if h != hp:
741 s = g_or_r._Inverse(p, q, wrap).s12
742 if s: # fmath.fidw?
743 s = (h - hp) / s # slope
744 hq += s * Q.s12
745 hp += s * P.s12
746 else:
747 hp = hq = _MODS.fmath.favg(hp, h)
748 else:
749 hp = hq = Height(height)
751# n = self.name or unused.__name__
752 p = q = self.classof(P.lat2, P.lon2, datum=g_or_r.datum, height=hp) # name=n
753 p._iteration = P.iteration
754 if P is not Q:
755 q = self.classof(Q.lat2, Q.lon2, datum=g_or_r.datum, height=hq) # name=n
756 q._iteration = Q.iteration
757 return p, q
759 @deprecated_method
760 def isantipode(self, other, eps=EPS): # PYCHOK no cover
761 '''DEPRECATED, use method L{isantipodeTo}.'''
762 return self.isantipodeTo(other, eps=eps)
764 def isantipodeTo(self, other, eps=EPS):
765 '''Check whether this and an other point are antipodal,
766 on diametrically opposite sides of the earth.
768 @arg other: The other point (C{LatLon}).
769 @kwarg eps: Tolerance for near-equality (C{degrees}).
771 @return: C{True} if points are antipodal within the given
772 tolerance, C{False} otherwise.
773 '''
774 p = self.others(other)
775 return isantipode(*(self.latlon + p.latlon), eps=eps)
777 @Property_RO
778 def isEllipsoidal(self):
779 '''Check whether this point is ellipsoidal (C{bool} or C{None} if unknown).
780 '''
781 return self.datum.isEllipsoidal if self._datum else None
783 def isequalTo(self, other, eps=None):
784 '''Compare this point with an other point, I{ignoring} height.
786 @arg other: The other point (C{LatLon}).
787 @kwarg eps: Tolerance for equality (C{degrees}).
789 @return: C{True} if both points are identical,
790 I{ignoring} height, C{False} otherwise.
792 @raise TypeError: The B{C{other}} point is not C{LatLon}
793 or mismatch of the B{C{other}} and
794 this C{class} or C{type}.
796 @raise UnitError: Invalid B{C{eps}}.
798 @see: Method L{isequalTo3}.
799 '''
800 return _isequalTo(self, self.others(other), eps=eps)
802 def isequalTo3(self, other, eps=None):
803 '''Compare this point with an other point, I{including} height.
805 @arg other: The other point (C{LatLon}).
806 @kwarg eps: Tolerance for equality (C{degrees}).
808 @return: C{True} if both points are identical
809 I{including} height, C{False} otherwise.
811 @raise TypeError: The B{C{other}} point is not C{LatLon}
812 or mismatch of the B{C{other}} and
813 this C{class} or C{type}.
815 @see: Method L{isequalTo}.
816 '''
817 return self.height == self.others(other).height and \
818 _isequalTo(self, other, eps=eps)
820 @Property_RO
821 def isnormal(self):
822 '''Return C{True} if this point is normal (C{bool}),
823 meaning C{abs(lat) <= 90} and C{abs(lon) <= 180}.
825 @see: Methods L{normal}, L{toNormal} and functions
826 L{pygeodesy.isnormal} and L{pygeodesy.normal}.
827 '''
828 return isnormal(self.lat, self.lon, eps=0)
830 @Property_RO
831 def isSpherical(self):
832 '''Check whether this point is spherical (C{bool} or C{None} if unknown).
833 '''
834 return self.datum.isSpherical if self._datum else None
836 @Property_RO
837 def lam(self):
838 '''Get the longitude (B{C{radians}}).
839 '''
840 return radians(self.lon)
842 @Property
843 def lat(self):
844 '''Get the latitude (C{degrees90}).
845 '''
846 return self._lat
848 @lat.setter # PYCHOK setter!
849 def lat(self, lat):
850 '''Set the latitude (C{str[N|S]} or C{degrees}).
852 @raise ValueError: Invalid B{C{lat}}.
853 '''
854 lat = Lat(lat) # parseDMS(lat, suffix=_NS_, clip=90)
855 if self._lat != lat:
856 _update_all(self)
857 self._lat = lat
859 @Property
860 def latlon(self):
861 '''Get the lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).
862 '''
863 return LatLon2Tuple(self._lat, self._lon, name=self.name)
865 @latlon.setter # PYCHOK setter!
866 def latlon(self, latlonh):
867 '''Set the lat- and longitude and optionally the height
868 (2- or 3-tuple or comma- or space-separated C{str}
869 of C{degrees90}, C{degrees180} and C{meter}).
871 @raise TypeError: Height of B{C{latlonh}} not C{scalar} or
872 B{C{latlonh}} not C{list} or C{tuple}.
874 @raise ValueError: Invalid B{C{latlonh}} or M{len(latlonh)}.
876 @see: Function L{pygeodesy.parse3llh} to parse a B{C{latlonh}}
877 string into a 3-tuple C{(lat, lon, h)}.
878 '''
879 if isstr(latlonh):
880 latlonh = parse3llh(latlonh, height=self.height)
881 else:
882 _xinstanceof(list, tuple, latlonh=latlonh)
883 if len(latlonh) == 3:
884 h = Height(latlonh[2], name=Fmt.SQUARE(latlonh=2))
885 elif len(latlonh) != 2:
886 raise _ValueError(latlonh=latlonh)
887 else:
888 h = self.height
890 llh = Lat(latlonh[0]), Lon(latlonh[1]), h # parseDMS2(latlonh[0], latlonh[1])
891 if (self._lat, self._lon, self._height) != llh:
892 _update_all(self)
893 self._lat, self._lon, self._height = llh
895 def latlon2(self, ndigits=0):
896 '''Return this point's lat- and longitude in C{degrees}, rounded.
898 @kwarg ndigits: Number of (decimal) digits (C{int}).
900 @return: A L{LatLon2Tuple}C{(lat, lon)}, both C{float}
901 and rounded away from zero.
903 @note: The C{round}ed values are always C{float}, also
904 if B{C{ndigits}} is omitted.
905 '''
906 return LatLon2Tuple(round(self.lat, ndigits),
907 round(self.lon, ndigits), name=self.name)
909 @deprecated_method
910 def latlon_(self, ndigits=0): # PYCHOK no cover
911 '''DEPRECATED, use method L{latlon2}.'''
912 return self.latlon2(ndigits=ndigits)
914 latlon2round = latlon_ # PYCHOK no cover
916 @Property
917 def latlonheight(self):
918 '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).
919 '''
920 return self.latlon.to3Tuple(self.height)
922 @latlonheight.setter # PYCHOK setter!
923 def latlonheight(self, latlonh):
924 '''Set the lat- and longitude and optionally the height
925 (2- or 3-tuple or comma- or space-separated C{str}
926 of C{degrees90}, C{degrees180} and C{meter}).
928 @see: Property L{latlon} for more details.
929 '''
930 self.latlon = latlonh
932 @Property
933 def lon(self):
934 '''Get the longitude (C{degrees180}).
935 '''
936 return self._lon
938 @lon.setter # PYCHOK setter!
939 def lon(self, lon):
940 '''Set the longitude (C{str[E|W]} or C{degrees}).
942 @raise ValueError: Invalid B{C{lon}}.
943 '''
944 lon = Lon(lon) # parseDMS(lon, suffix=_EW_, clip=180)
945 if self._lon != lon:
946 _update_all(self)
947 self._lon = lon
949 @Property_RO
950 def _ltp(self):
951 '''(INTERNAL) Cache for L{toLtp}.
952 '''
953 return _MODS.ltp.Ltp(self, ecef=self.Ecef(self.datum), name=self.name)
955 def nearestOn6(self, points, closed=False, height=None, wrap=False):
956 '''Locate the point on a path or polygon closest to this point.
958 Points are converted to and distances are computed in
959 I{geocentric}, cartesian space.
961 @arg points: The path or polygon points (C{LatLon}[]).
962 @kwarg closed: Optionally, close the polygon (C{bool}).
963 @kwarg height: Optional height, overriding the height of
964 this and all other points (C{meter}). If
965 C{None}, take the height of points into
966 account for distances.
967 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
968 the B{C{points}} (C{bool}).
970 @return: A L{NearestOn6Tuple}C{(closest, distance, fi, j,
971 start, end)} with the C{closest}, the C{start}
972 and the C{end} point each an instance of this
973 C{LatLon} and C{distance} in C{meter}, same
974 units as the cartesian axes.
976 @raise PointsError: Insufficient number of B{C{points}}.
978 @raise TypeError: Some B{C{points}} or some B{C{points}}'
979 C{Ecef} invalid.
981 @raise ValueError: Some B{C{points}}' C{Ecef} is incompatible.
983 @see: Function L{pygeodesy.nearestOn6}.
984 '''
985 def _cs(Ps, h, w, C):
986 p = None # not used
987 for i, q in Ps.enumerate():
988 if w and i:
989 q = _unrollon(p, q)
990 yield C(height=h, i=i, up=3, points=q)
991 p = q
993 C = self._toCartesianEcef # to verify datum and Ecef
994 Ps = self.PointsIter(points, wrap=wrap)
996 c = C(height=height, this=self) # this Cartesian
997 t = nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed)
998 c, s, e = t.closest, t.start, t.end
1000 kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon
1001 height=height)
1002 _r = self.Ecef(self.datum).reverse
1003 p = _r(c).toLatLon(**kwds)
1004 s = _r(s).toLatLon(**kwds) if s is not c else p
1005 e = _r(e).toLatLon(**kwds) if e is not c else p
1006 return t.dup(closest=p, start=s, end=e)
1008 def nearestTo(self, *args, **kwds): # PYCHOK no cover
1009 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
1010 notImplemented(self, *args, **kwds)
1012 def normal(self):
1013 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and
1014 C{abs(lon) <= 180}.
1016 @return: C{True} if this point was I{normal}, C{False} if it
1017 wasn't (but is now).
1019 @see: Property L{isnormal} and method L{toNormal}.
1020 '''
1021 n = self.isnormal
1022 if not n:
1023 self.latlon = normal(*self.latlon)
1024 return n
1026 @Property_RO
1027 def _N_vector(self):
1028 '''(INTERNAL) Get the (C{nvectorBase._N_vector_})
1029 '''
1030 return _MODS.nvectorBase._N_vector_(*self.xyzh)
1032 @Property_RO
1033 def phi(self):
1034 '''Get the latitude (B{C{radians}}).
1035 '''
1036 return radians(self.lat)
1038 @Property_RO
1039 def philam(self):
1040 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).
1041 '''
1042 return PhiLam2Tuple(self.phi, self.lam, name=self.name)
1044 def philam2(self, ndigits=0):
1045 '''Return this point's lat- and longitude in C{radians}, rounded.
1047 @kwarg ndigits: Number of (decimal) digits (C{int}).
1049 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float}
1050 and rounded away from zero.
1052 @note: The C{round}ed values are always C{float}, also
1053 if B{C{ndigits}} is omitted.
1054 '''
1055 return PhiLam2Tuple(round(self.phi, ndigits),
1056 round(self.lam, ndigits), name=self.name)
1058 @Property_RO
1059 def philamheight(self):
1060 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
1061 '''
1062 return self.philam.to3Tuple(self.height)
1064 @deprecated_method
1065 def points(self, points, closed=True): # PYCHOK no cover
1066 '''DEPRECATED, use method L{points2}.'''
1067 return self.points2(points, closed=closed)
1069 def points2(self, points, closed=True):
1070 '''Check a path or polygon represented by points.
1072 @arg points: The path or polygon points (C{LatLon}[])
1073 @kwarg closed: Optionally, consider the polygon closed,
1074 ignoring any duplicate or closing final
1075 B{C{points}} (C{bool}).
1077 @return: A L{Points2Tuple}C{(number, points)}, an C{int}
1078 and C{list} or C{tuple}.
1080 @raise PointsError: Insufficient number of B{C{points}}.
1082 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1083 '''
1084 return _MODS.iters.points2(points, closed=closed, base=self)
1086 def PointsIter(self, points, loop=0, dedup=False, wrap=False):
1087 '''Return a C{PointsIter} iterator.
1089 @arg points: The path or polygon points (C{LatLon}[])
1090 @kwarg loop: Number of loop-back points (non-negative C{int}).
1091 @kwarg dedup: Skip duplicate points (C{bool}).
1092 @kwarg wrap: If C{True}, wrap or I{normalize} the
1093 enum-/iterated B{C{points}} (C{bool}).
1095 @return: A new C{PointsIter} iterator.
1097 @raise PointsError: Insufficient number of B{C{points}}.
1098 '''
1099 return PointsIter(points, base=self, loop=loop, dedup=dedup, wrap=wrap)
1101 def radii11(self, point2, point3, wrap=False):
1102 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent}
1103 circles of a (planar) triangle formed by this and two other points.
1105 @arg point2: Second point (C{LatLon}).
1106 @arg point3: Third point (C{LatLon}).
1107 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and
1108 B{C{point3}} (C{bool}).
1110 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.
1112 @raise IntersectionError: Near-coincident or -colinear points.
1114 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
1116 @see: Function L{pygeodesy.radii11}, U{Incircle
1117 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles
1118 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent
1119 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}.
1120 '''
1121 with _toCartesian3(self, point2, point3, wrap) as cs:
1122 return _radii11ABC(*cs, useZ=True)[0]
1124 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3
1125 '''(INTERNAL) Get the C{rhumb} for this point's datum or for
1126 the B{C{radius}}' earth model iff non-C{None}.
1127 '''
1128 try:
1129 d = self._rhumb3dict
1130 t = d[(exact, radius)]
1131 except KeyError:
1132 D = self.datum if radius is None else _spherical_datum(radius) # ellipsoidal OK
1133 try:
1134 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical
1135 except AttributeError as x:
1136 raise _AttributeError(datum=D, radius=radius, cause=x)
1137 t = r, D, _MODS.karney.Caps
1138 while d:
1139 d.popitem()
1140 d[(exact, radius)] = t # cache 3-tuple
1141 return t
1143 @Property_RO
1144 def _rhumb3dict(self): # in rhumbIntersecant2 below
1145 return {} # single-item cache
1147 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False, b360=False):
1148 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between
1149 this and an other (ellipsoidal) point.
1151 @arg other: The other point (C{LatLon}).
1152 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1153 see method L{Ellipsoid.rhumb_}.
1154 @kwarg radius: Optional earth radius (C{meter}) or earth model
1155 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1156 L{a_f2Tuple}), overriding this point's datum.
1157 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1158 B{C{other}} point (C{bool}).
1159 @kwarg b360: If C{True}, return the azimuth in the bearing range.
1161 @return: Rhumb azimuth (compass C{degrees180} or C{degrees360}).
1163 @raise TypeError: The B{C{other}} point is incompatible or
1164 B{C{radius}} is invalid.
1165 '''
1166 r, _, Cs = self._rhumb3(exact, radius)
1167 z = r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12
1168 return _umod_360(z + _360_0) if b360 else z
1170 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None):
1171 '''Return the destination point having travelled the given distance from
1172 this point along a rhumb line (loxodrome) of the given azimuth.
1174 @arg distance: Distance travelled (C{meter}, same units as this
1175 point's datum (ellipsoid) axes or B{C{radius}},
1176 may be negative.
1177 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}).
1178 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see
1179 method L{Ellipsoid.rhumb_}.
1180 @kwarg radius: Optional earth radius (C{meter}) or earth model
1181 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1182 L{a_f2Tuple}), overriding this point's datum.
1183 @kwarg height: Optional height, overriding the default height (C{meter}).
1185 @return: The destination point (ellipsoidal C{LatLon}).
1187 @raise TypeError: Invalid B{C{radius}}.
1189 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}}
1190 or B{C{height}}.
1191 '''
1192 r, D, _ = self._rhumb3(exact, radius)
1193 d = r._Direct(self, azimuth, distance)
1194 h = self._heigHt(height)
1195 return self.classof(d.lat2, d.lon2, datum=D, height=h)
1197 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False):
1198 '''Return the distance from this to an other point along
1199 a rhumb line (loxodrome).
1201 @arg other: The other point (C{LatLon}).
1202 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1203 see method L{Ellipsoid.rhumb_}.
1204 @kwarg radius: Optional earth radius (C{meter}) or earth model
1205 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1206 L{a_f2Tuple}), overriding this point's datum.
1207 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1208 B{C{other}} point (C{bool}).
1210 @return: Distance (C{meter}, the same units as this point's
1211 datum (ellipsoid) axes or B{C{radius}}.
1213 @raise TypeError: The B{C{other}} point is incompatible or
1214 B{C{radius}} is invalid.
1216 @raise ValueError: Invalid B{C{radius}}.
1217 '''
1218 r, _, Cs = self._rhumb3(exact, radius)
1219 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12
1221 def rhumbIntersecant2(self, circle, point, other, height=None,
1222 **exact_radius_wrap_eps_tol):
1223 '''Compute the intersections of a circle and a rhumb line given as two
1224 points or as a point and azimuth.
1226 @arg circle: Radius of the circle centered at this location (C{meter}),
1227 or a point on the circle (this C{LatLon}).
1228 @arg point: The start point of the rhumb line (this C{LatLon}).
1229 @arg other: An other point I{on} (this C{LatLon}) or the azimuth I{of}
1230 (compass C{degrees}) the rhumb line.
1231 @kwarg height: Optional height for the intersection points (C{meter},
1232 conventionally) or C{None} for interpolated heights.
1233 @kwarg exact_radius_wrap_eps_tol: Optional keyword arguments, see
1234 methods L{rhumbLine} and L{RhumbLineAux.Intersecant2}
1235 or L{RhumbLine.Intersecant2}.
1237 @return: 2-Tuple of the intersection points (representing a chord),
1238 each an instance of this class. Both points are the same
1239 instance if the rhumb line is tangent to the circle.
1241 @raise IntersectionError: The circle and rhumb line do not intersect.
1243 @raise TypeError: If B{C{point}} is not this C{LatLon} or B{C{circle}}
1244 or B{C{other}} invalid.
1246 @raise ValueError: Invalid B{C{circle}}, B{C{other}}, B{C{height}}
1247 or B{C{exact_radius_wrap}}.
1249 @see: Methods L{RhumbLineAux.Intersecant2} and L{RhumbLine.Intersecant2}.
1250 '''
1251 def _kwds3(eps=EPS, tol=_TOL, wrap=False, **kwds):
1252 return kwds, wrap, dict(eps=eps, tol=tol)
1254 exact_radius, w, eps_tol = _kwds3(**exact_radius_wrap_eps_tol)
1256 p = _unrollon(self, self.others(point=point), wrap=w)
1257 try:
1258 r = Radius_(circle=circle) if isscalar(circle) else \
1259 self.rhumbDistanceTo(self.others(circle=circle), wrap=w, **exact_radius)
1260 rl = p.rhumbLine(other, wrap=w, **exact_radius)
1261 P, Q = rl.Intersecant2(self.lat, self.lon, r, **eps_tol)
1263 return self._intersecend2(p, other, w, height, rl.rhumb, P, Q,
1264 self.rhumbIntersecant2)
1266 except (TypeError, ValueError) as x:
1267 raise _xError(x, center=self, circle=circle, point=point, other=other,
1268 **exact_radius_wrap_eps_tol)
1270 def rhumbLine(self, other, exact=False, radius=None, wrap=False, **name_caps):
1271 '''Get a rhumb line through this point at a given azimuth or through
1272 this and an other point.
1274 @arg other: The azimuth I{of} (compass C{degrees}) or an other point
1275 I{on} (this C{LatLon}) the rhumb line.
1276 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see
1277 method L{Ellipsoid.rhumb_}.
1278 @kwarg radius: Optional earth radius (C{meter}) or earth model
1279 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}),
1280 overriding this point's datum.
1281 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}
1282 point (C{bool}).
1283 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see L{RhumbLine}
1284 or L{RhumbLineAux} C{B{caps}}.
1286 @return: A C{RhumbLine} instance.
1288 @raise TypeError: Invalid B{C{radius}} or B{C{other}} not C{scalar} nor
1289 this C{LatLon}.
1291 @see: Modules L{rhumbaux} and L{rhumbx}.
1292 '''
1293 r, _, Cs = self._rhumb3(exact, radius)
1294 kwds = _xkwds(name_caps, name=self.name, caps=Cs.LINE_OFF)
1295 rl = r._DirectLine( self, other, **kwds) if isscalar(other) else \
1296 r._InverseLine(self, self.others(other), wrap, **kwds)
1297 return rl
1299 def rhumbMidpointTo(self, other, exact=False, radius=None,
1300 height=None, fraction=_0_5, wrap=False):
1301 '''Return the (loxodromic) midpoint on the rhumb line between
1302 this and an other point.
1304 @arg other: The other point (this C{LatLon}).
1305 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1306 see method L{Ellipsoid.rhumb_}.
1307 @kwarg radius: Optional earth radius (C{meter}) or earth model
1308 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1309 L{a_f2Tuple}), overriding this point's datum.
1310 @kwarg height: Optional height, overriding the mean height
1311 (C{meter}).
1312 @kwarg fraction: Midpoint location from this point (C{scalar}), 0
1313 for this, 1 for the B{C{other}}, 0.5 for halfway
1314 between this and the B{C{other}} point, may be
1315 negative or greater than 1.
1316 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1317 B{C{other}} point (C{bool}).
1319 @return: The midpoint at the given B{C{fraction}} along the
1320 rhumb line (this C{LatLon}).
1322 @raise TypeError: The B{C{other}} point is incompatible or
1323 B{C{radius}} is invalid.
1325 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}.
1326 '''
1327 r, D, _ = self._rhumb3(exact, radius)
1328 f = Scalar(fraction=fraction)
1329 d = r._Inverse(self, self.others(other), wrap) # C.AZIMUTH_DISTANCE
1330 d = r._Direct( self, d.azi12, d.s12 * f)
1331 h = self._havg(other, f=f, h=height)
1332 return self.classof(d.lat2, d.lon2, datum=D, height=h)
1334 @property_RO
1335 def sphericalLatLon(self):
1336 '''Get the C{LatLon type} iff spherical, overloaded in L{LatLonSphericalBase}.
1337 '''
1338 return False
1340 def thomasTo(self, other, wrap=False):
1341 '''Compute the distance between this and an other point using
1342 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>}
1343 formula.
1345 @arg other: The other point (C{LatLon}).
1346 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
1347 the B{C{other}} point (C{bool}).
1349 @return: Distance (C{meter}, same units as the axes of
1350 this point's datum ellipsoid).
1352 @raise TypeError: The B{C{other}} point is not C{LatLon}.
1354 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo},
1355 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
1356 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
1357 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}.
1358 '''
1359 return self._distanceTo_(thomas_, other, wrap=wrap)
1361 @deprecated_method
1362 def to2ab(self): # PYCHOK no cover
1363 '''DEPRECATED, use property L{philam}.'''
1364 return self.philam
1366 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds):
1367 '''Convert this point to cartesian, I{geocentric} coordinates,
1368 also known as I{Earth-Centered, Earth-Fixed} (ECEF).
1370 @kwarg height: Optional height, overriding this point's height
1371 (C{meter}, conventionally).
1372 @kwarg Cartesian: Optional class to return the geocentric
1373 coordinates (C{Cartesian}) or C{None}.
1374 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}}
1375 keyword arguments, ignored if
1376 C{B{Cartesian} is None}.
1378 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None},
1379 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,
1380 datum)} with C{C=0} and C{M} if available.
1382 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.
1383 '''
1384 r = self._ecef9 if height is None else self.toEcef(height=height)
1385 if Cartesian is not None: # class or .classof
1386 r = self._xnamed(Cartesian(r, **Cartesian_kwds))
1387 _xdatum(r.datum, self.datum)
1388 return r
1390 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point):
1391 '''(INTERNAL) Convert to cartesian and check Ecef's before and after.
1392 '''
1393 p = self.others(up=up, **name_point)
1394 c = p.toCartesian(height=height)
1395 E = self.Ecef
1396 if E:
1397 for p in (p, c):
1398 e = getattr(p, LatLonBase.Ecef.name, None)
1399 if e not in (None, E): # PYCHOK no cover
1400 n, _ = name_point.popitem()
1401 if i is not None:
1402 Fmt.SQUARE(n, i)
1403 raise _ValueError(n, e, txt=_incompatible(E.__name__))
1404 return c
1406 def toDatum(self, datum2, height=None, name=NN):
1407 '''I{Must be overloaded}.'''
1408 notOverloaded(self, datum2, height=height, name=name)
1410 def toEcef(self, height=None, M=False):
1411 '''Convert this point to I{geocentric} coordinates, also known as
1412 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).
1414 @kwarg height: Optional height, overriding this point's height
1415 (C{meter}, conventionally).
1416 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}).
1418 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
1419 with C{C=0} and C{M} if available.
1421 @raise EcefError: A C{.datum} or an ECEF issue.
1422 '''
1423 return self._ecef9 if height in (None, self.height) else \
1424 self._Ecef_forward(self.lat, self.lon, height=height, M=M)
1426 @deprecated_method
1427 def to3llh(self, height=None): # PYCHOK no cover
1428 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.'''
1429 return self.latlonheight if height in (None, self.height) else \
1430 self.latlon.to3Tuple(height)
1432 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):
1433 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}.
1435 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}
1436 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
1437 @kwarg ltp: The I{local tangent plane} (LTP) to use,
1438 overriding this point's LTP (L{Ltp}).
1439 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
1440 arguments, ignored if C{B{Xyz} is None}.
1442 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
1443 a L{Local9Tuple}C{(x, y, z, lat, lon, height,
1444 ltp, ecef, M)} with C{M=None}, always.
1446 @raise TypeError: Invalid B{C{ltp}}.
1447 '''
1448 p = _MODS.ltp._xLtp(ltp, self._ltp)
1449 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)
1451 def toLtp(self, Ecef=None):
1452 '''Return the I{local tangent plane} (LTP) for this point.
1454 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...
1455 L{EcefYou}), overriding this point's C{Ecef}.
1456 '''
1457 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp(
1458 self, ecef=Ecef(self.datum), name=self.name)
1460 def toNormal(self, deep=False, name=NN):
1461 '''Get this point I{normalized} to C{abs(lat) <= 90}
1462 and C{abs(lon) <= 180}.
1464 @kwarg deep: If C{True} make a deep, otherwise a
1465 shallow copy (C{bool}).
1466 @kwarg name: Optional name of the copy (C{str}).
1468 @return: A copy of this point, I{normalized} and
1469 optionally renamed (C{LatLon}).
1471 @see: Property L{isnormal}, method L{normal} and function
1472 L{pygeodesy.normal}.
1473 '''
1474 ll = self.copy(deep=deep)
1475 _ = ll.normal()
1476 if name:
1477 ll.rename(name)
1478 return ll
1480 def toNvector(self, h=None, Nvector=None, **Nvector_kwds):
1481 '''Convert this point to C{n-vector} (normal to the earth's surface)
1482 components, I{including height}.
1484 @kwarg h: Optional height, overriding this point's
1485 height (C{meter}).
1486 @kwarg Nvector: Optional class to return the C{n-vector}
1487 components (C{Nvector}) or C{None}.
1488 @kwarg Nvector_kwds_wrap: Optional, additional B{C{Nvector}}
1489 keyword arguments, ignored if C{B{Nvector}
1490 is None}.
1492 @return: A B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)}
1493 if B{C{Nvector}} is C{None}.
1495 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}.
1496 '''
1497 return self.toVector(Vector=Nvector, h=self.height if h is None else h,
1498 ll=self, **Nvector_kwds)
1500 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected
1501 '''Convert this point to a "lat, lon[, +/-height]" string, formatted
1502 in the given C{B{form}at}.
1504 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see
1505 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.
1506 @kwarg joined: Separator to join the lat-, longitude and heigth
1507 strings (C{str} or C{None} or C{NN} for non-joined).
1508 @kwarg m: Optional unit of the height (C{str}), use C{None} to
1509 exclude height from the returned string.
1510 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator},
1511 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword
1512 arguments, see function L{pygeodesy.latDMS} or
1513 L{pygeodesy.lonDMS}.
1515 @return: This point in the specified C{B{form}at}, etc. (C{str} or
1516 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if
1517 C{B{joined}=NN} or C{B{joined}=None}).
1519 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more
1520 details about keyword arguments C{B{form}at}, C{B{prec}ision},
1521 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.
1523 @example:
1525 >>> LatLon(51.4778, -0.0016).toStr() # 51°28′40″N, 000°00′06″W
1526 >>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W
1527 >>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m
1528 '''
1529 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),
1530 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))
1531 if self.height and m is not None:
1532 t += (self.heightStr(m=m),)
1533 return joined.join(t) if joined else t
1535 def toVector(self, Vector=None, **Vector_kwds):
1536 '''Convert this point to C{n-vector} (normal to the earth's
1537 surface) components, I{ignoring height}.
1539 @kwarg Vector: Optional class to return the C{n-vector}
1540 components (L{Vector3d}) or C{None}.
1541 @kwarg Vector_kwds: Optional, additional B{C{Vector}}
1542 keyword arguments, ignored if
1543 C{B{Vector} is None}.
1545 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)}
1546 if B{C{Vector}} is C{None}.
1548 @raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}.
1550 @note: These are C{n-vector} x, y and z components,
1551 I{NOT} geocentric (ECEF) x, y and z coordinates!
1552 '''
1553 r = self._vector3tuple
1554 if Vector is not None:
1555 r = Vector(*r, **_xkwds(Vector_kwds, name=self.name))
1556 return r
1558 def toVector3d(self):
1559 '''Convert this point to C{n-vector} (normal to the earth's
1560 surface) components, I{ignoring height}.
1562 @return: Unit vector (L{Vector3d}).
1564 @note: These are C{n-vector} x, y and z components,
1565 I{NOT} geocentric (ECEF) x, y and z coordinates!
1566 '''
1567 return self._vector3d # XXX .unit()
1569 def toWm(self, **toWm_kwds):
1570 '''Convert this point to a WM coordinate.
1572 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments.
1574 @return: The WM coordinate (L{Wm}).
1576 @see: Function L{pygeodesy.toWm}.
1577 '''
1578 return self._wm if not toWm_kwds else _MODS.webmercator.toWm(
1579 self, **_xkwds(toWm_kwds, name=self.name))
1581 @deprecated_method
1582 def to3xyz(self): # PYCHOK no cover
1583 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector},
1584 L{toVector3d} or perhaps (geocentric) L{toEcef}.'''
1585 return self.xyz # self.toVector()
1587 @Property_RO
1588 def _vector3d(self):
1589 '''(INTERNAL) Cache for L{toVector3d}.
1590 '''
1591 return self.toVector(Vector=Vector3d) # XXX .unit()
1593 @Property_RO
1594 def _vector3tuple(self):
1595 '''(INTERNAL) Cache for L{toVector}.
1596 '''
1597 return philam2n_xyz(self.phi, self.lam, name=self.name)
1599 def vincentysTo(self, other, **radius_wrap):
1600 '''Compute the distance between this and an other point using
1601 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>}
1602 spherical formula.
1604 @arg other: The other point (C{LatLon}).
1605 @kwarg radius_wrap: Optional keyword arguments for function
1606 L{pygeodesy.vincentys}, overriding the
1607 default mean C{radius} of this point's
1608 datum ellipsoid.
1610 @return: Distance (C{meter}, same units as B{C{radius}}).
1612 @raise TypeError: The B{C{other}} point is not C{LatLon}.
1614 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo},
1615 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
1616 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
1617 L{flatPolarTo}, L{haversineTo} and L{thomasTo}.
1618 '''
1619 return self._distanceTo(vincentys, other, **_xkwds(radius_wrap, radius=None))
1621 @Property_RO
1622 def _wm(self):
1623 '''(INTERNAL) Get this point as webmercator (L{Wm}).
1624 '''
1625 return _MODS.webmercator.toWm(self)
1627 @Property_RO
1628 def xyz(self):
1629 '''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)})
1631 @note: These are C{n-vector} x, y and z components, I{NOT}
1632 geocentric (ECEF) x, y and z coordinates!
1633 '''
1634 return self.toVector(Vector=Vector3Tuple)
1636 @Property_RO
1637 def xyzh(self):
1638 '''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)})
1640 @note: These are C{n-vector} x, y and z components, I{NOT}
1641 geocentric (ECEF) x, y and z coordinates!
1642 '''
1643 return self.xyz.to4Tuple(self.height)
1646class _toCartesian3(object): # see also .formy._idllmn6, .geodesicw._wargs, .vector2d._numpy
1647 '''(INTERNAL) Wrapper to convert 2 other points.
1648 '''
1649 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples
1650 def __call__(self, p, p2, p3, wrap, **kwds):
1651 try:
1652 if wrap:
1653 p2, p3 = map1(_Wrap.point, p2, p3)
1654 kwds = _xkwds(kwds, wrap=wrap)
1655 yield (p. toCartesian().copy(name=_point_), # copy to rename
1656 p._toCartesianEcef(up=4, point2=p2),
1657 p._toCartesianEcef(up=4, point3=p3))
1658 except (AssertionError, TypeError, ValueError) as x: # Exception?
1659 raise _xError(x, point=p, point2=p2, point3=p3, **kwds)
1661_toCartesian3 = _toCartesian3() # PYCHOK singleton
1664def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__
1665 '''(INTERNAL) Get 3-tuple C{(lat, lon, height)}.
1666 '''
1667 try:
1668 lat, lon = latlonh.lat, latlonh.lon
1669 height = _xattr(latlonh, height=height)
1670 except AttributeError:
1671 raise _IsnotError(_LatLon_, latlonh=latlonh)
1672 if wrap:
1673 lat, lon = _Wrap.latlon(lat, lon)
1674 return lat, lon, height
1677def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13
1678 radius=R_M, wrap=False):
1679 '''(INTERNAL) Trilaterate three points by I{area overlap} or by
1680 I{perimeter intersection} of three circles.
1682 @note: The B{C{radius}} is only needed for both the n-vectorial
1683 and C{sphericalTrigonometry.LatLon.distanceTo} methods and
1684 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve},
1685 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods.
1686 '''
1687 p2, p3, w = _unrollon3(p1, p2, p3, wrap)
1689 r1 = Distance_(distance1=d1)
1690 r2 = Distance_(distance2=d2)
1691 r3 = Distance_(distance3=d3)
1692 m = 0 if area else (r1 + r2 + r3)
1693 pc = 0
1694 t = []
1695 for _ in range(3):
1696 try: # intersection of circle (p1, r1) and (p2, r2)
1697 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w)
1699 if area: # check overlap
1700 if c1 is c2: # abutting
1701 c = c1
1702 else: # nearest point on radical
1703 c = p3.nearestOn(c1, c2, within=True, wrap=w)
1704 d = r3 - p3.distanceTo(c, radius=radius, wrap=w)
1705 if d > eps: # sufficient overlap
1706 t.append((d, c))
1707 m = max(m, d)
1709 else: # check intersection
1710 for c in ((c1,) if c1 is c2 else (c1, c2)):
1711 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w))
1712 if d < eps: # below margin
1713 t.append((d, c))
1714 m = min(m, d)
1716 except IntersectionError as x:
1717 if _concentric_ in str(x): # XXX ConcentricError?
1718 pc += 1
1720 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate
1722 if t: # get min, max, points and count ...
1723 t = tuple(sorted(t))
1724 n = len(t), # as 1-tuple
1725 # ... or for a single trilaterated result,
1726 # min *is* max, min- *is* maxPoint and n=1, 2 or 3
1727 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...)
1729 elif area and pc == 3: # all pairwise concentric ...
1730 r, p = min((r1, p1), (r2, p2), (r3, p3))
1731 m = max(r1, r2, r3)
1732 # ... return "smallest" point twice, the smallest
1733 # and largest distance and n=0 for concentric
1734 return Trilaterate5Tuple(float(r), p, float(m), p, 0)
1736 n, f = (_overlap_, max) if area else (_intersection_, min)
1737 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m))
1738 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t)
1741__all__ += _ALL_DOCS(LatLonBase)
1743# **) MIT License
1744#
1745# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1746#
1747# Permission is hereby granted, free of charge, to any person obtaining a
1748# copy of this software and associated documentation files (the "Software"),
1749# to deal in the Software without restriction, including without limitation
1750# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1751# and/or sell copies of the Software, and to permit persons to whom the
1752# Software is furnished to do so, subject to the following conditions:
1753#
1754# The above copyright notice and this permission notice shall be included
1755# in all copies or substantial portions of the Software.
1756#
1757# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1758# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1759# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1760# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1761# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1762# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1763# OTHER DEALINGS IN THE SOFTWARE.