Coverage for pygeodesy/latlonBase.py: 93%
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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 isstr, map1, _xinstanceof, _passarg
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.errors import _AttributeError, IntersectionError, \
21 _incompatible, _IsnotError, _TypeError, \
22 _ValueError, _xattr, _xdatum, _xError, \
23 _xkwds, _xkwds_item2, _xkwds_not
24# from pygeodesy.fmath import favg # _MODS
25# from 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 # as _formy
31# from pygeodesy.internals import _passarg # from .basics
32from pygeodesy.interns import NN, _COMMASPACE_, _concentric_, _height_, \
33 _intersection_, _LatLon_, _m_, _negative_, \
34 _no_, _overlap_, _too_, _point_ # PYCHOK used!
35# from pygeodesy.iters import PointsIter, points2 # _MODS
36# from pygeodesy.karney import Caps # _MODS
37from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
38# from pygeodesy.ltp import Ltp, _xLtp # _MODS
39from pygeodesy.named import _name2__, _NamedBase, Fmt
40from pygeodesy.namedTuples import Bounds2Tuple, LatLon2Tuple, PhiLam2Tuple, \
41 Trilaterate5Tuple
42# from pygeodesy.nvectorBase import _N_vector_ # _MODS
43from pygeodesy.props import deprecated_method, Property, Property_RO, \
44 property_RO, property_ROnce, _update_all
45# from pygeodesy.streprs import Fmt, hstr # from .named, _MODS
46from pygeodesy.units import _isDegrees, _isRadius, Distance_, Lat, Lon, \
47 Height, Radius, Radius_, Scalar, Scalar_
48from pygeodesy.utily import _unrollon, _unrollon3, _Wrap
49# from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, circum4_, \
50# Circum3Tuple, _radii11ABC4 # _MODS
51# from pygeodesy.vector3d import nearestOn6, Vector3d # _MODS
53from contextlib import contextmanager
54from math import asin, cos, degrees, fabs, radians
56__all__ = _ALL_LAZY.latlonBase
57__version__ = '24.11.10'
59_formy = _MODS.into(formy=__name__)
62class LatLonBase(_NamedBase):
63 '''(INTERNAL) Base class for C{LatLon} points on spherical or
64 ellipsoidal earth models.
65 '''
66 _clipid = INT0 # polygonal clip, see .booleans
67 _datum = None # L{Datum}, to be overriden
68 _height = INT0 # height (C{meter}), default
69 _lat = 0 # latitude (C{degrees})
70 _lon = 0 # longitude (C{degrees})
72 def __init__(self, latlonh, lon=None, height=0, datum=None, **wrap_name):
73 '''New C{LatLon}.
75 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or
76 a previous C{LatLon} instance provided C{B{lon}=None}.
77 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or
78 C(None), indicating B{C{latlonh}} is a C{LatLon}.
79 @kwarg height: Optional height above (or below) the earth surface
80 (C{meter}, conventionally).
81 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},
82 L{a_f2Tuple} or I{scalar} radius) or C{None}.
83 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword
84 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}
85 B{C{lat}} and B{C{lon}} (C{bool}).
87 @return: New instance (C{LatLon}).
89 @raise RangeError: A B{C{lon}} or C{lat} value outside the valid
90 range and L{rangerrors} set to C{True}.
92 @raise TypeError: If B{C{latlonh}} is not a C{LatLon}.
94 @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}.
95 '''
96 w, n = self._wrap_name2(**wrap_name)
97 if n:
98 self.name = n
100 if lon is None:
101 lat, lon, height = _latlonheight3(latlonh, height, w)
102 elif w:
103 lat, lon = _Wrap.latlonDMS2(latlonh, lon)
104 else:
105 lat = latlonh
107 self._lat = Lat(lat) # parseDMS2(lat, lon)
108 self._lon = Lon(lon) # PYCHOK LatLon2Tuple
109 if height: # elevation
110 self._height = Height(height)
111 if datum is not None:
112 self._datum = _spherical_datum(datum, name=self.name)
114 def __eq__(self, other):
115 return self.isequalTo(other)
117 def __ne__(self, other):
118 return not self.isequalTo(other)
120 def __str__(self):
121 return self.toStr(form=F_D, prec=6)
123 def antipode(self, height=None):
124 '''Return the antipode, the point diametrically opposite to
125 this point.
127 @kwarg height: Optional height of the antipode (C{meter}),
128 this point's height otherwise.
130 @return: The antipodal point (C{LatLon}).
131 '''
132 a = _formy.antipode(*self.latlon)
133 h = self._heigHt(height)
134 return self.classof(*a, height=h)
136 @deprecated_method
137 def bounds(self, wide, tall, radius=R_M): # PYCHOK no cover
138 '''DEPRECATED, use method C{boundsOf}.'''
139 return self.boundsOf(wide, tall, radius=radius)
141 def boundsOf(self, wide, tall, radius=R_M, height=None, **name):
142 '''Return the SW and NE lat-/longitude of a great circle
143 bounding box centered at this location.
145 @arg wide: Longitudinal box width (C{meter}, same units as
146 B{C{radius}} or C{degrees} if C{B{radius} is None}).
147 @arg tall: Latitudinal box size (C{meter}, same units as
148 B{C{radius}} or C{degrees} if C{B{radius} is None}).
149 @kwarg radius: Mean earth radius (C{meter}) or C{None} if I{both}
150 B{C{wide}} and B{C{tall}} are in C{degrees}.
151 @kwarg height: Height for C{latlonSW} and C{latlonNE} (C{meter}),
152 overriding the point's height.
153 @kwarg name: Optional C{B{name}=NN} (C{str}).
155 @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)}, the lower-left
156 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__(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 if C{None}, use 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, V3d=_MODS.vector3d.Vector3d):
190 t = ll.toEcef(height=height) # .toVector(Vector=V3d)
191 return V3d(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_name):
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_name: Optional C{B{name}=NN} (C{str}) and optional keyword
206 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}
207 the B{C{points}} (C{bool}).
209 @return: L{Circin6Tuple}C{(radius, center, deltas, cA, cB, cC)}. The
210 C{center} and contact points C{cA}, C{cB} and C{cC}, each an
211 instance of this (sub-)class, are co-planar with this and the
212 two given points, see the B{Note} below.
214 @raise ImportError: Package C{numpy} not found, not installed or older
215 than version 1.10.
217 @raise IntersectionError: Near-coincident or -colinear points or
218 a trilateration or C{numpy} issue.
220 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
222 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted
223 back to geodetic lat-, longitude and height. The latter, conventionally
224 in C{meter} indicates whether the C{center} is above, below or on the
225 surface of the earth model. If C{deltas} is C{None}, the C{center} is
226 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon,
227 height)} representing the differences between both results from
228 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
230 @see: Function L{pygeodesy.circin6}, method L{circum3}, U{Incircle
231 <https://MathWorld.Wolfram.com/Incircle.html>} and U{Contact Triangle
232 <https://MathWorld.Wolfram.com/ContactTriangle.html>}.
233 '''
234 w, n = self._wrap_name2(**wrap_name)
236 with _toCartesian3(self, point2, point3, w) as cs:
237 m = _MODS.vector2d
238 r, c, d, A, B, C = m._circin6(*cs, eps=eps, useZ=True, dLL3=True,
239 datum=self.datum) # PYCHOK unpack
240 return m.Circin6Tuple(r, c.toLatLon(), d, A.toLatLon(),
241 B.toLatLon(),
242 C.toLatLon(), name=n)
244 def circum3(self, point2, point3, circum=True, eps=EPS4, **wrap_name):
245 '''Return the radius and center of the smallest circle I{through} or I{containing}
246 this and two other points.
248 @arg point2: Second point (C{LatLon}).
249 @arg point3: Third point (C{LatLon}).
250 @kwarg circum: If C{True}, return the C{circumradius} and C{circumcenter},
251 always, ignoring the I{Meeus}' Type I case (C{bool}).
252 @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}.
253 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword
254 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}
255 the B{C{points}} (C{bool}).
257 @return: A L{Circum3Tuple}C{(radius, center, deltas)}. The C{center}, an
258 instance of this (sub-)class, is co-planar with this and the two
259 given points. If C{deltas} is C{None}, the C{center} is
260 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat,
261 lon, height)} representing the difference between both results
262 from L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
264 @raise ImportError: Package C{numpy} not found, not installed or older than
265 version 1.10.
267 @raise IntersectionError: Near-concentric, -coincident or -colinear points,
268 incompatible C{Ecef} classes or a trilateration
269 or C{numpy} issue.
271 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
273 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted
274 back to geodetic lat-, longitude and height. The latter, conventionally
275 in C{meter} indicates whether the C{center} is above, below or on the
276 surface of the earth model. If C{deltas} is C{None}, the C{center} is
277 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon,
278 height)} representing the difference between both results from
279 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
281 @see: Function L{pygeodesy.circum3} and methods L{circin6} and L{circum4_}.
282 '''
283 w, n = self._wrap_name2(**wrap_name)
285 with _toCartesian3(self, point2, point3, w, circum=circum) as cs:
286 m = _MODS.vector2d
287 r, c, d = m._circum3(*cs, circum=circum, eps=eps, useZ=True, dLL3=True, # XXX -3d2
288 clas=cs[0].classof, datum=self.datum) # PYCHOK unpack
289 return m.Circum3Tuple(r, c.toLatLon(), d, name=n)
291 def circum4_(self, *points, **wrap_name):
292 '''Best-fit a sphere through this and two or more other points.
294 @arg points: The other points (each a C{LatLon}).
295 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument
296 C{B{wrap}=False}, if C{True}, wrap or I{normalize} the B{C{points}}
297 (C{bool}).
299 @return: L{Circum4Tuple}C{(radius, center, rank, residuals)} with C{center} an
300 instance of this (sub-)class.
302 @raise ImportError: Package C{numpy} not found, not installed or older than
303 version 1.10.
305 @raise NumPyError: Some C{numpy} issue.
307 @raise TypeError: One of the B{C{points}} invalid.
309 @raise ValueError: Too few B{C{points}}.
311 @see: Function L{pygeodesy.circum4_} and L{circum3}.
312 '''
313 w, n = self._wrap_name2(**wrap_name)
315 def _cs(ps, C, w):
316 _wp = _Wrap.point if w else _passarg
317 for i, p in enumerate(ps):
318 yield C(i=i, points=_wp(p))
320 C = self._toCartesianEcef
321 c = C(point=self)
322 t = _MODS.vector2d.circum4_(c, Vector=c.classof, *_cs(points, C, w))
323 c = t.center.toLatLon(LatLon=self.classof)
324 return t.dup(center=c, name=n)
326 @property
327 def clipid(self):
328 '''Get the (polygonal) clip (C{int}).
329 '''
330 return self._clipid
332 @clipid.setter # PYCHOK setter!
333 def clipid(self, clipid):
334 '''Get the (polygonal) clip (C{int}).
335 '''
336 self._clipid = int(clipid)
338 @deprecated_method
339 def compassAngle(self, other, **adjust_wrap): # PYCHOK no cover
340 '''DEPRECATED, use method L{compassAngleTo}.'''
341 return self.compassAngleTo(other, **adjust_wrap)
343 def compassAngleTo(self, other, **adjust_wrap):
344 '''Return the angle from North for the direction vector between
345 this and an other point.
347 Suitable only for short, non-near-polar vectors up to a few
348 hundred Km or Miles. Use method C{initialBearingTo} for
349 larger distances.
351 @arg other: The other point (C{LatLon}).
352 @kwarg adjust_wrap: Optional keyword arguments for function
353 L{pygeodesy.compassAngle}.
355 @return: Compass angle from North (C{degrees360}).
357 @raise TypeError: The B{C{other}} point is not C{LatLon}.
359 @note: Courtesy of Martin Schultz.
361 @see: U{Local, flat earth approximation
362 <https://www.EdWilliams.org/avform.htm#flat>}.
363 '''
364 p = self.others(other)
365 return _formy.compassAngle(self.lat, self.lon, p.lat, p.lon, **adjust_wrap)
367 def cosineAndoyerLambertTo(self, other, **wrap):
368 '''Compute the distance between this and an other point using the U{Andoyer-Lambert correction<https://
369 navlib.net/wp-content/uploads/2013/10/admiralty-manual-of-navigation-vol-1-1964-english501c.pdf>}
370 of the U{Law of Cosines<https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>} formula.
372 @arg other: The other point (C{LatLon}).
373 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap
374 or I{normalize} and unroll the B{C{other}} point (C{bool}).
376 @return: Distance (C{meter}, same units as the axes of this point's datum
377 ellipsoid).
379 @raise TypeError: The B{C{other}} point is not C{LatLon}.
381 @see: Function L{pygeodesy.cosineAndoyerLambert} and methods
382 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo},
383 C{distanceTo*}, L{equirectangularTo}, L{euclideanTo},
384 L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo},
385 L{thomasTo} and L{vincentysTo}.
386 '''
387 return self._distanceTo_(_formy.cosineAndoyerLambert_, other, **wrap)
389 def cosineForsytheAndoyerLambertTo(self, other, **wrap):
390 '''Compute the distance between this and an other point using
391 the U{Forsythe-Andoyer-Lambert correction
392 <https://www2.UNB.Ca/gge/Pubs/TR77.pdf>} of the U{Law of Cosines
393 <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>}
394 formula.
396 @arg other: The other point (C{LatLon}).
397 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap
398 or I{normalize} and unroll the B{C{other}} point (C{bool}).
400 @return: Distance (C{meter}, same units as the axes of this point's datum
401 ellipsoid).
403 @raise TypeError: The B{C{other}} point is not C{LatLon}.
405 @see: Function L{pygeodesy.cosineForsytheAndoyerLambert} and methods
406 L{cosineAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
407 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
408 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}.
409 '''
410 return self._distanceTo_(_formy.cosineForsytheAndoyerLambert_, other, **wrap)
412 def cosineLawTo(self, other, radius=None, **wrap):
413 '''Compute the distance between this and an other point using the
414 U{spherical Law of Cosines
415 <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>}
416 formula.
418 @arg other: The other point (C{LatLon}).
419 @kwarg radius: Mean earth radius (C{meter}) or C{None} for the mean radius
420 of this point's datum ellipsoid.
421 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap
422 or I{normalize} and unroll the B{C{other}} point (C{bool}).
424 @return: Distance (C{meter}, same units as B{C{radius}}).
426 @raise TypeError: The B{C{other}} point is not C{LatLon}.
428 @see: Function L{pygeodesy.cosineLaw} and methods L{cosineAndoyerLambertTo},
429 L{cosineForsytheAndoyerLambertTo}, C{distanceTo*}, L{equirectangularTo},
430 L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},
431 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
432 '''
433 return self._distanceTo(_formy.cosineLaw, other, radius, **wrap)
435 @property_RO
436 def datum(self): # PYCHOK no cover
437 '''I{Must be overloaded}.'''
438 self._notOverloaded()
440 def destinationXyz(self, delta, LatLon=None, **LatLon_kwds):
441 '''Calculate the destination using a I{local} delta from this point.
443 @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu},
444 L{Ned} or L{Local9Tuple}).
445 @kwarg LatLon: Optional (geodetic) class to return the destination
446 or C{None}.
447 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
448 arguments, ignored if C{B{LatLon} is None}.
450 @return: Destination as a C{B{LatLon}(lat, lon, **B{LatLon_kwds})}
451 instance or if C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat,
452 lon, height)} respectively L{LatLon4Tuple}C{(lat, lon,
453 height, datum)} depending on whether a C{datum} keyword
454 is un-/specified.
456 @raise TypeError: Invalid B{C{delta}}, B{C{LatLon}} or B{C{LatLon_kwds}}.
457 '''
458 t = self._Ltp._local2ecef(delta, nine=True)
459 return t.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, name=self.name))
461 def _distanceTo(self, func, other, radius=None, **kwds):
462 '''(INTERNAL) Helper for distance methods C{<func>To}.
463 '''
464 p, r = self.others(other, up=2), radius
465 if r is None:
466 r = self._datum.ellipsoid.R1 if self._datum else R_M
467 return func(self.lat, self.lon, p.lat, p.lon, radius=r, **kwds)
469 def _distanceTo_(self, func_, other, wrap=False, radius=None):
470 '''(INTERNAL) Helper for (ellipsoidal) distance methods C{<func>To}.
471 '''
472 p = self.others(other, up=2)
473 D = self.datum
474 lam21, phi2, _ = _Wrap.philam3(self.lam, p.phi, p.lam, wrap)
475 r = func_(phi2, self.phi, lam21, datum=D)
476 return r * (D.ellipsoid.a if radius is None else radius)
478 @property_ROnce
479 def Ecef(self):
480 '''Get the ECEF I{class} (L{EcefKarney}), I{once}.
481 '''
482 return _MODS.ecef.EcefKarney
484 @Property_RO
485 def _Ecef_forward(self):
486 '''(INTERNAL) Helper for L{_ecef9} and L{toEcef} (C{callable}).
487 '''
488 return self.Ecef(self.datum, name=self.name).forward
490 @Property_RO
491 def _ecef9(self):
492 '''(INTERNAL) Helper for L{toCartesian}, L{toEcef} and L{toCartesian} (L{Ecef9Tuple}).
493 '''
494 return self._Ecef_forward(self, M=True)
496 @property_RO
497 def ellipsoidalLatLon(self):
498 '''Get the C{LatLon type} iff ellipsoidal, overloaded in L{LatLonEllipsoidalBase}.
499 '''
500 return False
502 @deprecated_method
503 def equals(self, other, eps=None): # PYCHOK no cover
504 '''DEPRECATED, use method L{isequalTo}.'''
505 return self.isequalTo(other, eps=eps)
507 @deprecated_method
508 def equals3(self, other, eps=None): # PYCHOK no cover
509 '''DEPRECATED, use method L{isequalTo3}.'''
510 return self.isequalTo3(other, eps=eps)
512 def equirectangularTo(self, other, **radius_adjust_limit_wrap):
513 '''Compute the distance between this and an other point
514 using the U{Equirectangular Approximation / Projection
515 <https://www.Movable-Type.co.UK/scripts/latlong.html#equirectangular>}.
517 Suitable only for short, non-near-polar distances up to a
518 few hundred Km or Miles. Use method L{haversineTo} or
519 C{distanceTo*} for more accurate and/or larger distances.
521 @arg other: The other point (C{LatLon}).
522 @kwarg radius_adjust_limit_wrap: Optional keyword arguments
523 for function L{pygeodesy.equirectangular},
524 overriding the default mean C{radius} of this
525 point's datum ellipsoid.
527 @return: Distance (C{meter}, same units as B{C{radius}}).
529 @raise TypeError: The B{C{other}} point is not C{LatLon}.
531 @see: Function L{pygeodesy.equirectangular} and methods L{cosineAndoyerLambertTo},
532 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
533 C{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},
534 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
535 '''
536 return self._distanceTo(_formy.equirectangular, other, **radius_adjust_limit_wrap)
538 def euclideanTo(self, other, **radius_adjust_wrap):
539 '''Approximate the C{Euclidian} distance between this and
540 an other point.
542 See function L{pygeodesy.euclidean} for the available B{C{options}}.
544 @arg other: The other point (C{LatLon}).
545 @kwarg radius_adjust_wrap: Optional keyword arguments for function
546 L{pygeodesy.euclidean}, overriding the default mean
547 C{radius} of this point's datum ellipsoid.
549 @return: Distance (C{meter}, same units as B{C{radius}}).
551 @raise TypeError: The B{C{other}} point is not C{LatLon}.
553 @see: Function L{pygeodesy.euclidean} and methods L{cosineAndoyerLambertTo},
554 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
555 L{equirectangularTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},
556 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
557 '''
558 return self._distanceTo(_formy.euclidean, other, **radius_adjust_wrap)
560 def flatLocalTo(self, other, radius=None, **wrap):
561 '''Compute the distance between this and an other point using the
562 U{ellipsoidal Earth to plane projection
563 <https://WikiPedia.org/wiki/Geographical_distance#Ellipsoidal_Earth_projected_to_a_plane>}
564 aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>} formula.
566 @arg other: The other point (C{LatLon}).
567 @kwarg radius: Mean earth radius (C{meter}) or C{None} for the I{equatorial
568 radius} of this point's datum ellipsoid.
569 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap
570 or I{normalize} and unroll the B{C{other}} point (C{bool}).
572 @return: Distance (C{meter}, same units as B{C{radius}}).
574 @raise TypeError: The B{C{other}} point is not C{LatLon}.
576 @raise ValueError: Invalid B{C{radius}}.
578 @see: Function L{pygeodesy.flatLocal}/L{pygeodesy.hubeny}, methods
579 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo},
580 L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo},
581 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo} and
582 U{local, flat Earth approximation<https://www.edwilliams.org/avform.htm#flat>}.
583 '''
584 r = radius if radius in (None, R_M, _1_0, 1) else Radius(radius)
585 return self._distanceTo_(_formy.flatLocal_, other, radius=r, **wrap) # PYCHOK kwargs
587 hubenyTo = flatLocalTo # for Karl Hubeny
589 def flatPolarTo(self, other, **radius_wrap):
590 '''Compute the distance between this and an other point using
591 the U{polar coordinate flat-Earth<https://WikiPedia.org/wiki/
592 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula.
594 @arg other: The other point (C{LatLon}).
595 @kwarg radius_wrap: Optional keyword arguments for function
596 L{pygeodesy.flatPolar}, overriding the
597 default mean C{radius} of this point's
598 datum ellipsoid.
600 @return: Distance (C{meter}, same units as B{C{radius}}).
602 @raise TypeError: The B{C{other}} point is not C{LatLon}.
604 @see: Function L{pygeodesy.flatPolar} and methods L{cosineAndoyerLambertTo},
605 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
606 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
607 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
608 '''
609 return self._distanceTo(_formy.flatPolar, other, **radius_wrap)
611 def hartzell(self, los=False, earth=None):
612 '''Compute the intersection of a Line-Of-Sight from this (geodetic) Point-Of-View
613 (pov) with this point's ellipsoid surface.
615 @kwarg los: Line-Of-Sight, I{direction} to the ellipsoid (L{Los}, L{Vector3d}),
616 C{True} for the I{normal, plumb} onto the surface or I{False} or
617 C{None} to point to the center of the ellipsoid.
618 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple}
619 or C{scalar} radius in C{meter}), overriding this point's C{datum}
620 ellipsoid.
622 @return: The intersection (C{LatLon}) with C{.height} set to the distance to
623 this C{pov}.
625 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov} is inside
626 the ellipsoid or B{C{los}} points outside or away from
627 the ellipsoid.
629 @raise TypeError: Invalid B{C{los}} or invalid or undefined B{C{earth}} or C{datum}.
631 @see: Function L{hartzell<pygeodesy.formy.hartzell>} for further details.
632 '''
633 return _formy._hartzell(self, los, earth, LatLon=self.classof)
635 def haversineTo(self, other, **radius_wrap):
636 '''Compute the distance between this and an other point using the
637 U{Haversine<https://www.Movable-Type.co.UK/scripts/latlong.html>}
638 formula.
640 @arg other: The other point (C{LatLon}).
641 @kwarg radius_wrap: Optional keyword arguments for function
642 L{pygeodesy.haversine}, overriding the
643 default mean C{radius} of this point's
644 datum ellipsoid.
646 @return: Distance (C{meter}, same units as B{C{radius}}).
648 @raise TypeError: The B{C{other}} point is not C{LatLon}.
650 @see: Function L{pygeodesy.haversine} and methods L{cosineAndoyerLambertTo},
651 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
652 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
653 L{flatPolarTo}, L{thomasTo} and L{vincentysTo}.
654 '''
655 return self._distanceTo(_formy.haversine, other, **radius_wrap)
657 def _havg(self, other, f=_0_5, h=None):
658 '''(INTERNAL) Weighted, average height.
660 @arg other: An other point (C{LatLon}).
661 @kwarg f: Optional fraction (C{float}).
662 @kwarg h: Overriding height (C{meter}).
664 @return: Average, fractional height (C{float}) or
665 the overriding height B{C{h}} (C{Height}).
666 '''
667 return Height(h) if h is not None else \
668 _MODS.fmath.favg(self.height, other.height, f=f)
670 @Property
671 def height(self):
672 '''Get the height (C{meter}).
673 '''
674 return self._height
676 @height.setter # PYCHOK setter!
677 def height(self, height):
678 '''Set the height (C{meter}).
680 @raise TypeError: Invalid B{C{height}} C{type}.
682 @raise ValueError: Invalid B{C{height}}.
683 '''
684 h = Height(height)
685 if self._height != h:
686 _update_all(self)
687 self._height = h
689 def _heigHt(self, height):
690 '''(INTERNAL) Overriding this C{height}.
691 '''
692 return self.height if height is None else Height(height)
694 def height4(self, earth=None, normal=True, LatLon=None, **LatLon_kwds):
695 '''Compute the projection of this point on and the height above or below
696 this datum's ellipsoid surface.
698 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius,
699 I{overriding} this datum (L{Datum}, L{Ellipsoid},
700 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
701 L{JacobiConformal} or C{meter}, conventionally).
702 @kwarg normal: If C{True}, the projection is the normal to this ellipsoid's
703 surface, otherwise the intersection of the I{radial} line to
704 this ellipsoid's center (C{bool}).
705 @kwarg LatLon: Optional class to return the projection, height and
706 datum (C{LatLon}) or C{None}.
707 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
708 ignored if C{B{LatLon} is None}.
710 @note: Use keyword argument C{height=0} to override C{B{LatLon}.height}
711 to {0} or any other C{scalar}, conventionally in C{meter}.
713 @return: An instance of class B{C{LatLon}} or if C{B{LatLon} is None}, a
714 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
715 and C{z} coordinates and height C{h} in C{meter}, conventionally.
717 @raise TriaxialError: No convergence in triaxial root finding.
719 @raise TypeError: Invalid B{C{earth}} or triaxial B{C{earth}} couldn't be
720 converted to biaxial B{C{LatLon}} datum.
722 @see: Methods L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
723 '''
724 c = self.toCartesian()
725 if LatLon is None:
726 r = c.height4(earth=earth, normal=normal)
727 else:
728 c = c.height4(earth=earth, normal=normal, Cartesian=c.classof, height=0)
729 r = c.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, datum=c.datum, height=c.height))
730 if r.datum != c.datum:
731 raise _TypeError(earth=earth, datum=r.datum)
732 return r
734 def heightStr(self, prec=-2, m=_m_):
735 '''Return this point's B{C{height}} as C{str}ing.
737 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
738 @kwarg m: Optional unit of the height (C{str}).
740 @see: Function L{pygeodesy.hstr}.
741 '''
742 return _MODS.streprs.hstr(self.height, prec=prec, m=m)
744 def intersecant2(self, *args, **kwds): # PYCHOK no cover
745 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
746 self._notImplemented(*args, **kwds)
748 def _intersecend2(self, p, q, wrap, height, g_or_r, P, Q, unused): # in .LatLonEllipsoidalBaseDI.intersecant2
749 '''(INTERNAL) Interpolate 2 heights along a geodesic or rhumb
750 line and return the 2 intercant points accordingly.
751 '''
752 if height is None:
753 hp = hq = _xattr(p, height=INT0)
754 h = _xattr(q, height=hp) # if isLatLon(q) else hp
755 if h != hp:
756 s = g_or_r._Inverse(p, q, wrap).s12
757 if s: # fmath.fidw?
758 s = (h - hp) / s # slope
759 hq += s * Q.s12
760 hp += s * P.s12
761 else:
762 hp = hq = _MODS.fmath.favg(hp, h)
763 else:
764 hp = hq = Height(height)
766# n = self.name or unused.__name__
767 p = q = self.classof(P.lat2, P.lon2, datum=g_or_r.datum, height=hp) # name=n
768 p._iteration = P.iteration
769 if P is not Q:
770 q = self.classof(Q.lat2, Q.lon2, datum=g_or_r.datum, height=hq) # name=n
771 q._iteration = Q.iteration
772 return p, q
774 @deprecated_method
775 def isantipode(self, other, eps=EPS): # PYCHOK no cover
776 '''DEPRECATED, use method L{isantipodeTo}.'''
777 return self.isantipodeTo(other, eps=eps)
779 def isantipodeTo(self, other, eps=EPS):
780 '''Check whether this and an other point are antipodal,
781 on diametrically opposite sides of the earth.
783 @arg other: The other point (C{LatLon}).
784 @kwarg eps: Tolerance for near-equality (C{degrees}).
786 @return: C{True} if points are antipodal within the given
787 tolerance, C{False} otherwise.
788 '''
789 p = self.others(other)
790 return _formy.isantipode(*(self.latlon + p.latlon), eps=eps)
792 @Property_RO
793 def isEllipsoidal(self):
794 '''Check whether this point is ellipsoidal (C{bool} or C{None} if unknown).
795 '''
796 return _xattr(self.datum, isEllipsoidal=None)
798 def isequalTo(self, other, eps=None):
799 '''Compare this point with an other point, I{ignoring} height.
801 @arg other: The other point (C{LatLon}).
802 @kwarg eps: Tolerance for equality (C{degrees}).
804 @return: C{True} if both points are identical,
805 I{ignoring} height, C{False} otherwise.
807 @raise TypeError: The B{C{other}} point is not C{LatLon}
808 or mismatch of the B{C{other}} and
809 this C{class} or C{type}.
811 @raise UnitError: Invalid B{C{eps}}.
813 @see: Method L{isequalTo3}.
814 '''
815 return _formy._isequalTo(self, self.others(other), eps=eps)
817 def isequalTo3(self, other, eps=None):
818 '''Compare this point with an other point, I{including} height.
820 @arg other: The other point (C{LatLon}).
821 @kwarg eps: Tolerance for equality (C{degrees}).
823 @return: C{True} if both points are identical I{including}
824 height, C{False} otherwise.
826 @raise TypeError: The B{C{other}} point is not C{LatLon}
827 or mismatch of the B{C{other}} and this
828 C{class} or C{type}.
830 @see: Method L{isequalTo}.
831 '''
832 return self.height == self.others(other).height and \
833 _formy._isequalTo(self, other, eps=eps)
835 @Property_RO
836 def isnormal(self):
837 '''Return C{True} if this point is normal (C{bool}),
838 meaning C{abs(lat) <= 90} and C{abs(lon) <= 180}.
840 @see: Methods L{normal}, L{toNormal} and functions L{isnormal
841 <pygeodesy.isnormal>} and L{normal<pygeodesy.normal>}.
842 '''
843 return _formy.isnormal(self.lat, self.lon, eps=0)
845 @Property_RO
846 def isSpherical(self):
847 '''Check whether this point is spherical (C{bool} or C{None} if unknown).
848 '''
849 return _xattr(self.datum, isSpherical=None)
851 @Property_RO
852 def lam(self):
853 '''Get the longitude (B{C{radians}}).
854 '''
855 return radians(self.lon)
857 @Property
858 def lat(self):
859 '''Get the latitude (C{degrees90}).
860 '''
861 return self._lat
863 @lat.setter # PYCHOK setter!
864 def lat(self, lat):
865 '''Set the latitude (C{str[N|S]} or C{degrees}).
867 @raise ValueError: Invalid B{C{lat}}.
868 '''
869 lat = Lat(lat) # parseDMS(lat, suffix=_NS_, clip=90)
870 if self._lat != lat:
871 _update_all(self)
872 self._lat = lat
874 @Property
875 def latlon(self):
876 '''Get the lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).
877 '''
878 return LatLon2Tuple(self._lat, self._lon, name=self.name)
880 @latlon.setter # PYCHOK setter!
881 def latlon(self, latlonh):
882 '''Set the lat- and longitude and optionally the height
883 (2- or 3-tuple or comma- or space-separated C{str}
884 of C{degrees90}, C{degrees180} and C{meter}).
886 @raise TypeError: Height of B{C{latlonh}} not C{scalar} or
887 B{C{latlonh}} not C{list} or C{tuple}.
889 @raise ValueError: Invalid B{C{latlonh}} or M{len(latlonh)}.
891 @see: Function L{pygeodesy.parse3llh} to parse a B{C{latlonh}}
892 string into a 3-tuple C{(lat, lon, h)}.
893 '''
894 if isstr(latlonh):
895 latlonh = parse3llh(latlonh, height=self.height)
896 else:
897 _xinstanceof(list, tuple, latlonh=latlonh)
898 if len(latlonh) == 3:
899 h = Height(latlonh[2], name=Fmt.SQUARE(latlonh=2))
900 elif len(latlonh) != 2:
901 raise _ValueError(latlonh=latlonh)
902 else:
903 h = self.height
905 llh = Lat(latlonh[0]), Lon(latlonh[1]), h # parseDMS2(latlonh[0], latlonh[1])
906 if (self._lat, self._lon, self._height) != llh:
907 _update_all(self)
908 self._lat, self._lon, self._height = llh
910 def latlon2(self, ndigits=0):
911 '''Return this point's lat- and longitude in C{degrees}, rounded.
913 @kwarg ndigits: Number of (decimal) digits (C{int}).
915 @return: A L{LatLon2Tuple}C{(lat, lon)}, both C{float}
916 and rounded away from zero.
918 @note: The C{round}ed values are always C{float}, also
919 if B{C{ndigits}} is omitted.
920 '''
921 return LatLon2Tuple(round(self.lat, ndigits),
922 round(self.lon, ndigits), name=self.name)
924 @deprecated_method
925 def latlon_(self, ndigits=0): # PYCHOK no cover
926 '''DEPRECATED, use method L{latlon2}.'''
927 return self.latlon2(ndigits=ndigits)
929 latlon2round = latlon_ # PYCHOK no cover
931 @Property
932 def latlonheight(self):
933 '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).
934 '''
935 return self.latlon.to3Tuple(self.height)
937 @latlonheight.setter # PYCHOK setter!
938 def latlonheight(self, latlonh):
939 '''Set the lat- and longitude and optionally the height
940 (2- or 3-tuple or comma- or space-separated C{str} of
941 C{degrees90}, C{degrees180} and C{meter}).
943 @see: Property L{latlon} for more details.
944 '''
945 self.latlon = latlonh
947 @Property
948 def lon(self):
949 '''Get the longitude (C{degrees180}).
950 '''
951 return self._lon
953 @lon.setter # PYCHOK setter!
954 def lon(self, lon):
955 '''Set the longitude (C{str[E|W]} or C{degrees}).
957 @raise ValueError: Invalid B{C{lon}}.
958 '''
959 lon = Lon(lon) # parseDMS(lon, suffix=_EW_, clip=180)
960 if self._lon != lon:
961 _update_all(self)
962 self._lon = lon
964 @Property_RO
965 def _Ltp(self):
966 '''(INTERNAL) Cache for L{toLtp}.
967 '''
968 return _MODS.ltp.Ltp(self, ecef=self.Ecef(self.datum), name=self.name)
970 def nearestOn6(self, points, closed=False, height=None, wrap=False):
971 '''Locate the point on a path or polygon closest to this point.
973 Points are converted to and distances are computed in
974 I{geocentric}, cartesian space.
976 @arg points: The path or polygon points (C{LatLon}[]).
977 @kwarg closed: Optionally, close the polygon (C{bool}).
978 @kwarg height: Optional height, overriding the height of
979 this and all other points (C{meter}). If
980 C{None}, take the height of points into
981 account for distances.
982 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
983 the B{C{points}} (C{bool}).
985 @return: A L{NearestOn6Tuple}C{(closest, distance, fi, j,
986 start, end)} with the C{closest}, the C{start}
987 and the C{end} point each an instance of this
988 C{LatLon} and C{distance} in C{meter}, same
989 units as the cartesian axes.
991 @raise PointsError: Insufficient number of B{C{points}}.
993 @raise TypeError: Some B{C{points}} or some B{C{points}}'
994 C{Ecef} invalid.
996 @raise ValueError: Some B{C{points}}' C{Ecef} is incompatible.
998 @see: Function L{nearestOn6<pygeodesy.nearestOn6>}.
999 '''
1000 def _cs(Ps, h, w, C):
1001 p = None # not used
1002 for i, q in Ps.enumerate():
1003 if w and i:
1004 q = _unrollon(p, q)
1005 yield C(height=h, i=i, up=3, points=q)
1006 p = q
1008 C = self._toCartesianEcef # to verify datum and Ecef
1009 Ps = self.PointsIter(points, wrap=wrap)
1011 c = C(height=height, this=self) # this Cartesian
1012 t = _MODS.vector3d.nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed)
1013 c, s, e = t.closest, t.start, t.end
1015 kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon
1016 height=height)
1017 _r = self.Ecef(self.datum).reverse
1018 p = _r(c).toLatLon(**kwds)
1019 s = _r(s).toLatLon(**kwds) if s is not c else p
1020 e = _r(e).toLatLon(**kwds) if e is not c else p
1021 return t.dup(closest=p, start=s, end=e)
1023 def nearestTo(self, *args, **kwds): # PYCHOK no cover
1024 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
1025 self._notImplemented(*args, **kwds)
1027 def normal(self):
1028 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and
1029 C{abs(lon) <= 180}.
1031 @return: C{True} if this point was I{normal}, C{False} if it
1032 wasn't (but is now).
1034 @see: Property L{isnormal} and method L{toNormal}.
1035 '''
1036 n = self.isnormal
1037 if not n:
1038 self.latlon = _formy.normal(*self.latlon)
1039 return n
1041 @property_RO
1042 def _N_vector(self):
1043 '''(INTERNAL) Get the C{Nvector} (C{nvectorBase._N_vector_})
1044 '''
1045 _N = _MODS.nvectorBase._N_vector_
1046 return _N(*self._n_xyz3, h=self.height, name=self.name)
1048 @Property_RO
1049 def _n_xyz3(self):
1050 '''(INTERNAL) Get the n-vector components as L{Vector3Tuple}.
1051 '''
1052 return _formy.philam2n_xyz(self.phi, self.lam, name=self.name)
1054 @Property_RO
1055 def phi(self):
1056 '''Get the latitude (B{C{radians}}).
1057 '''
1058 return radians(self.lat)
1060 @Property_RO
1061 def philam(self):
1062 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).
1063 '''
1064 return PhiLam2Tuple(self.phi, self.lam, name=self.name)
1066 def philam2(self, ndigits=0):
1067 '''Return this point's lat- and longitude in C{radians}, rounded.
1069 @kwarg ndigits: Number of (decimal) digits (C{int}).
1071 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float}
1072 and rounded away from zero.
1074 @note: The C{round}ed values are always C{float}, also
1075 if B{C{ndigits}} is omitted.
1076 '''
1077 return PhiLam2Tuple(round(self.phi, ndigits),
1078 round(self.lam, ndigits), name=self.name)
1080 @Property_RO
1081 def philamheight(self):
1082 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
1083 '''
1084 return self.philam.to3Tuple(self.height)
1086 @deprecated_method
1087 def points(self, points, **closed): # PYCHOK no cover
1088 '''DEPRECATED, use method L{points2}.'''
1089 return self.points2(points, **closed)
1091 def points2(self, points, closed=True):
1092 '''Check a path or polygon represented by points.
1094 @arg points: The path or polygon points (C{LatLon}[])
1095 @kwarg closed: Optionally, consider the polygon closed,
1096 ignoring any duplicate or closing final
1097 B{C{points}} (C{bool}).
1099 @return: A L{Points2Tuple}C{(number, points)}, an C{int}
1100 and C{list} or C{tuple}.
1102 @raise PointsError: Insufficient number of B{C{points}}.
1104 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1105 '''
1106 return _MODS.iters.points2(points, closed=closed, base=self)
1108 def PointsIter(self, points, loop=0, dedup=False, wrap=False):
1109 '''Return a C{PointsIter} iterator.
1111 @arg points: The path or polygon points (C{LatLon}[])
1112 @kwarg loop: Number of loop-back points (non-negative C{int}).
1113 @kwarg dedup: If C{True}, skip duplicate points (C{bool}).
1114 @kwarg wrap: If C{True}, wrap or I{normalize} the
1115 enum-/iterated B{C{points}} (C{bool}).
1117 @return: A new C{PointsIter} iterator.
1119 @raise PointsError: Insufficient number of B{C{points}}.
1120 '''
1121 return _MODS.iters.PointsIter(points, base=self, loop=loop,
1122 dedup=dedup, wrap=wrap)
1124 def radii11(self, point2, point3, wrap=False):
1125 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent}
1126 circles of a (planar) triangle formed by this and two other points.
1128 @arg point2: Second point (C{LatLon}).
1129 @arg point3: Third point (C{LatLon}).
1130 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and
1131 B{C{point3}} (C{bool}).
1133 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.
1135 @raise IntersectionError: Near-coincident or -colinear points.
1137 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
1139 @see: Function L{pygeodesy.radii11}, U{Incircle
1140 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles
1141 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent
1142 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}.
1143 '''
1144 with _toCartesian3(self, point2, point3, wrap) as cs:
1145 return _MODS.vector2d._radii11ABC4(*cs, useZ=True)[0]
1147 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3
1148 '''(INTERNAL) Get the C{rhumb} for this point's datum or for
1149 the B{C{radius}}' earth model iff non-C{None}.
1150 '''
1151 try:
1152 d = self._rhumb3dict
1153 t = d[(exact, radius)]
1154 except KeyError:
1155 D = self.datum if radius is None else \
1156 _spherical_datum(radius) # ellipsoidal OK
1157 try:
1158 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical
1159 except AttributeError as x:
1160 raise _AttributeError(datum=D, radius=radius, cause=x)
1161 t = r, D, _MODS.karney.Caps
1162 if len(d) > 2:
1163 d.clear() # d[:] = {}
1164 d[(exact, radius)] = t # cache 3-tuple
1165 return t
1167 @Property_RO
1168 def _rhumb3dict(self): # in ._update
1169 return {} # 3-item cache
1171 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False, b360=False):
1172 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between this
1173 and an other (ellipsoidal) point.
1175 @arg other: The other point (C{LatLon}).
1176 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see
1177 method L{Ellipsoid.rhumb_}.
1178 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},
1179 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding
1180 this point's datum.
1181 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}
1182 point (C{bool}).
1183 @kwarg b360: If C{True}, return the azimuth as bearing in compass
1184 degrees (C{bool}).
1186 @return: Rhumb azimuth (C{degrees180} or compass C{degrees360}).
1188 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}
1189 is invalid.
1190 '''
1191 r, _, Cs = self._rhumb3(exact, radius)
1192 z = r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12
1193 return _umod_360(z + _360_0) if b360 else z
1195 def rhumbDestination(self, distance, azimuth, radius=None, height=None,
1196 exact=False, **name):
1197 '''Return the destination point having travelled the given distance from
1198 this point along a rhumb line (loxodrome) of the given azimuth.
1200 @arg distance: Distance travelled (C{meter}, same units as this point's
1201 datum (ellipsoid) axes or B{C{radius}}, may be negative.
1202 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}).
1203 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},
1204 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding
1205 this point's datum.
1206 @kwarg height: Optional height, overriding the default height (C{meter}).
1207 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see
1208 method L{Ellipsoid.rhumb_}.
1209 @kwarg name: Optional C{B{name}=NN} (C{str}).
1211 @return: The destination point (ellipsoidal C{LatLon}).
1213 @raise TypeError: Invalid B{C{radius}}.
1215 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}}
1216 or B{C{height}}.
1217 '''
1218 r, D, _ = self._rhumb3(exact, radius)
1219 d = r._Direct(self, azimuth, distance)
1220 h = self._heigHt(height)
1221 return self.classof(d.lat2, d.lon2, datum=D, height=h, **name)
1223 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False):
1224 '''Return the distance from this to an other point along a rhumb line
1225 (loxodrome).
1227 @arg other: The other point (C{LatLon}).
1228 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see
1229 method L{Ellipsoid.rhumb_}.
1230 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},
1231 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding
1232 this point's datum.
1233 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}
1234 point (C{bool}).
1236 @return: Distance (C{meter}, the same units as this point's datum
1237 (ellipsoid) axes or B{C{radius}}.
1239 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}
1240 is invalid.
1242 @raise ValueError: Invalid B{C{radius}}.
1243 '''
1244 r, _, Cs = self._rhumb3(exact, radius)
1245 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12
1247 def rhumbIntersecant2(self, circle, point, other, height=None,
1248 **exact_radius_wrap_eps_tol):
1249 '''Compute the intersections of a circle and a rhumb line given as two
1250 points or as a point and azimuth.
1252 @arg circle: Radius of the circle centered at this location (C{meter}),
1253 or a point on the circle (same C{LatLon} class).
1254 @arg point: The start point of the rhumb line (same C{LatLon} class).
1255 @arg other: An other point I{on} (same C{LatLon} class) or the azimuth
1256 I{of} (compass C{degrees}) the rhumb line.
1257 @kwarg height: Optional height for the intersection points (C{meter},
1258 conventionally) or C{None} for interpolated heights.
1259 @kwarg exact_radius_wrap_eps_tol: Optional keyword arguments, see
1260 methods L{rhumbLine} and L{RhumbLineAux.Intersecant2}
1261 or L{RhumbLine.Intersecant2}.
1263 @return: 2-Tuple of the intersection points (representing a chord),
1264 each an instance of this class. Both points are the same
1265 instance if the rhumb line is tangent to the circle.
1267 @raise IntersectionError: The circle and rhumb line do not intersect.
1269 @raise TypeError: Invalid B{C{point}}, B{C{circle}} or B{C{other}}.
1271 @raise ValueError: Invalid B{C{circle}}, B{C{other}}, B{C{height}}
1272 or B{C{exact_radius_wrap}}.
1274 @see: Methods L{RhumbLineAux.Intersecant2} and L{RhumbLine.Intersecant2}.
1275 '''
1276 def _kwds3(eps=EPS, tol=_TOL, wrap=False, **kwds):
1277 return kwds, wrap, dict(eps=eps, tol=tol)
1279 exact_radius, w, eps_tol = _kwds3(**exact_radius_wrap_eps_tol)
1281 p = _unrollon(self, self.others(point=point), wrap=w)
1282 try:
1283 r = Radius_(circle=circle) if _isRadius(circle) else \
1284 self.rhumbDistanceTo(self.others(circle=circle), wrap=w, **exact_radius)
1285 rl = p.rhumbLine(other, wrap=w, **exact_radius)
1286 P, Q = rl.Intersecant2(self.lat, self.lon, r, **eps_tol)
1288 return self._intersecend2(p, other, w, height, rl.rhumb, P, Q,
1289 self.rhumbIntersecant2)
1290 except (TypeError, ValueError) as x:
1291 raise _xError(x, center=self, circle=circle, point=point, other=other,
1292 **exact_radius_wrap_eps_tol)
1294 def rhumbLine(self, other, exact=False, radius=None, wrap=False, **name_caps):
1295 '''Get a rhumb line through this point at a given azimuth or through
1296 this and an other point.
1298 @arg other: The azimuth I{of} (compass C{degrees}) or an other point
1299 I{on} (same C{LatLon} class) the rhumb line.
1300 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see
1301 method L{Ellipsoid.rhumb_}.
1302 @kwarg radius: Optional earth radius (C{meter}) or earth model
1303 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}),
1304 overriding this point's datum.
1305 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}
1306 point (C{bool}).
1307 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see L{RhumbLine}
1308 or L{RhumbLineAux} C{B{caps}}.
1310 @return: A C{RhumbLine} instance.
1312 @raise TypeError: Invalid B{C{radius}} or B{C{other}} not C{scalar} nor
1313 same C{LatLon} class.
1315 @see: Modules L{rhumb.aux_} and L{rhumb.ekx}.
1316 '''
1317 r, _, Cs = self._rhumb3(exact, radius)
1318 kwds = _xkwds(name_caps, name=self.name, caps=Cs.LINE_OFF)
1319 rl = r._DirectLine( self, other, **kwds) if _isDegrees(other) else \
1320 r._InverseLine(self, self.others(other), wrap, **kwds)
1321 return rl
1323 def rhumbMidpointTo(self, other, exact=False, radius=None,
1324 height=None, fraction=_0_5, **wrap_name):
1325 '''Return the (loxodromic) midpoint on the rhumb line between this and
1326 an other point.
1328 @arg other: The other point (same C{LatLon} class).
1329 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see
1330 method L{Ellipsoid.rhumb_}.
1331 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},
1332 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding
1333 this point's datum.
1334 @kwarg height: Optional height, overriding the mean height (C{meter}).
1335 @kwarg fraction: Midpoint location from this point (C{scalar}), 0 for this,
1336 1 for the B{C{other}}, 0.5 for halfway between this and
1337 the B{C{other}} point, may be negative or greater than 1.
1338 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword
1339 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}
1340 and unroll the B{C{other}} point (C{bool}).
1342 @return: The midpoint at the given B{C{fraction}} along the rhumb line
1343 (same C{LatLon} class).
1345 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}
1346 is invalid.
1348 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}.
1349 '''
1350 w, n = self._wrap_name2(**wrap_name)
1351 r, D, _ = self._rhumb3(exact, radius)
1352 f = Scalar(fraction=fraction)
1353 d = r._Inverse(self, self.others(other), w) # C.AZIMUTH_DISTANCE
1354 d = r._Direct( self, d.azi12, d.s12 * f)
1355 h = self._havg(other, f=f, h=height)
1356 return self.classof(d.lat2, d.lon2, datum=D, height=h, name=n)
1358 @property_RO
1359 def sphericalLatLon(self):
1360 '''Get the C{LatLon type} iff spherical, overloaded in L{LatLonSphericalBase}.
1361 '''
1362 return False
1364 def thomasTo(self, other, **wrap):
1365 '''Compute the distance between this and an other point using U{Thomas'
1366 <https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>} formula.
1368 @arg other: The other point (C{LatLon}).
1369 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap
1370 or I{normalize} and unroll the B{C{other}} point (C{bool}).
1372 @return: Distance (C{meter}, same units as the axes of this point's datum
1373 ellipsoid).
1375 @raise TypeError: The B{C{other}} point is not C{LatLon}.
1377 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo},
1378 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
1379 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
1380 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}.
1381 '''
1382 return self._distanceTo_(_formy.thomas_, other, **wrap)
1384 @deprecated_method
1385 def to2ab(self): # PYCHOK no cover
1386 '''DEPRECATED, use property L{philam}.'''
1387 return self.philam
1389 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds):
1390 '''Convert this point to cartesian, I{geocentric} coordinates,
1391 also known as I{Earth-Centered, Earth-Fixed} (ECEF).
1393 @kwarg height: Optional height, overriding this point's height
1394 (C{meter}, conventionally).
1395 @kwarg Cartesian: Optional class to return the geocentric
1396 coordinates (C{Cartesian}) or C{None}.
1397 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
1398 arguments, ignored if C{B{Cartesian} is None}.
1400 @return: A B{C{Cartesian}} or if B{C{Cartesian} is None}, an
1401 L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
1402 with C{C=0} and C{M} if available.
1404 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.
1406 @see: Methods C{toNvector}, C{toVector} and C{toVector3d}.
1407 '''
1408 r = self._ecef9 if height is None else self.toEcef(height=height)
1409 if Cartesian is not None: # class or .classof
1410 r = Cartesian(r, **self._name1__(Cartesian_kwds))
1411 _xdatum(r.datum, self.datum)
1412 return r
1414 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point):
1415 '''(INTERNAL) Convert to cartesian and check Ecef's before and after.
1416 '''
1417 p = self.others(up=up, **name_point)
1418 c = p.toCartesian(height=height)
1419 E = self.Ecef
1420 if E:
1421 for p in (p, c):
1422 e = _xattr(p, Ecef=None)
1423 if e not in (None, E): # PYCHOK no cover
1424 n, _ = _xkwds_item2(name_point)
1425 n = Fmt.INDEX(n, i)
1426 raise _ValueError(n, e, txt=_incompatible(E.__name__)) # txt__
1427 return c
1429 def toDatum(self, datum2, height=None, **name):
1430 '''I{Must be overloaded}.'''
1431 self._notOverloaded(datum2, height=height, **name)
1433 def toEcef(self, height=None, M=False):
1434 '''Convert this point to I{geocentric} coordinates, also known as
1435 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).
1437 @kwarg height: Optional height, overriding this point's height
1438 (C{meter}, conventionally).
1439 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}).
1441 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
1442 with C{C=0} and C{M} if available.
1444 @raise EcefError: A C{.datum} or an ECEF issue.
1445 '''
1446 return self._ecef9 if height in (None, self.height) else \
1447 self._Ecef_forward(self.lat, self.lon, height=height, M=M)
1449 @deprecated_method
1450 def to3llh(self, height=None): # PYCHOK no cover
1451 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.'''
1452 return self.latlonheight if height in (None, self.height) else \
1453 self.latlon.to3Tuple(height)
1455 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):
1456 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}.
1458 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} (L{XyzLocal},
1459 L{Enu}, L{Ned}) or C{None}.
1460 @kwarg ltp: The I{local tangent plane} (LTP) to use, overriding this
1461 point's LTP (L{Ltp}).
1462 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword arguments,
1463 ignored if C{B{Xyz} is None}.
1465 @return: An B{C{Xyz}} instance or a L{Local9Tuple}C{(x, y, z, lat, lon,
1466 height, ltp, ecef, M)} if C{B{Xyz} is None} (with C{M=None}).
1468 @raise TypeError: Invalid B{C{ltp}}.
1469 '''
1470 return _MODS.ltp._toLocal(self, ltp, Xyz, Xyz_kwds) # self._ecef9
1472 def toLtp(self, Ecef=None, **name):
1473 '''Return the I{local tangent plane} (LTP) for this point.
1475 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...
1476 L{EcefYou}), overriding this point's C{Ecef}.
1477 @kwarg name: Optional C{B{name}=NN} (C{str}).
1478 '''
1479 return _MODS.ltp._toLtp(self, Ecef, self, name) # self._Ltp
1481 def toNormal(self, deep=False, **name):
1482 '''Get this point I{normalized} to C{abs(lat) <= 90}
1483 and C{abs(lon) <= 180}.
1485 @kwarg deep: If C{True}, make a deep, otherwise a shallow
1486 copy (C{bool}).
1487 @kwarg name: Optional C{B{name}=NN} (C{str}).
1489 @return: A copy of this point, I{normalized} (C{LatLon}),
1490 optionally renamed.
1492 @see: Property L{isnormal}, method L{normal} and function
1493 L{pygeodesy.normal}.
1494 '''
1495 ll = self.copy(deep=deep)
1496 _ = ll.normal()
1497 if name:
1498 ll.rename(name)
1499 return ll
1501 def toNvector(self, h=None, Nvector=None, **name_Nvector_kwds):
1502 '''Convert this point to C{n-vector} (normal to the earth's surface)
1503 components, I{including height}.
1505 @kwarg h: Optional height, overriding this point's height (C{meter}).
1506 @kwarg Nvector: Optional class to return the C{n-vector} components
1507 (C{Nvector}) or C{None}.
1508 @kwarg name_Nvector_kwds: Optional C{B{name}=NN} (C{str}) and optionally,
1509 additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector}
1510 is None}.
1512 @return: An named B{C{Nvector}} or if C{B{Nvector} is None} a named
1513 L{Vector4Tuple}C{(x, y, z, h)}.
1515 @raise TypeError: Invalid B{C{h}}, B{C{Nvector}} or B{C{name_Nvector_kwds}}.
1517 @see: Methods C{toCartesian}, C{toVector} and C{toVector3d}.
1518 '''
1519 h = self._heigHt(h)
1520 if Nvector is None:
1521 r = self._n_xyz3.to4Tuple(h)
1522 n, _ = _name2__(name_Nvector_kwds, _or_nameof=self)
1523 if n:
1524 r.rename(n)
1525 else:
1526 x, y, z = self._n_xyz3
1527 r = Nvector(x, y, z, h=h, ll=self, **self._name1__(name_Nvector_kwds))
1528 return r
1530 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected
1531 '''Convert this point to a "lat, lon[, +/-height]" string, formatted
1532 in the given C{B{form}at}.
1534 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see
1535 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.
1536 @kwarg joined: Separator to join the lat-, longitude and height
1537 strings (C{str} or C{None} or C{NN} for non-joined).
1538 @kwarg m: Optional unit of the height (C{str}), use C{None} to
1539 exclude height from the returned string.
1540 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator},
1541 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword
1542 arguments, see function L{pygeodesy.toDMS} for details.
1544 @return: This point in the specified C{B{form}at}, etc. (C{str} or
1545 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if
1546 B{C{joined}} is C{NN} or C{None}).
1548 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more
1549 details about keyword arguments C{B{form}at}, C{B{prec}ision},
1550 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.
1551 '''
1552 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),
1553 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))
1554 if self.height and m is not None:
1555 t += (self.heightStr(m=m),)
1556 return joined.join(t) if joined else t
1558 def toVector(self, Vector=None, **Vector_kwds):
1559 '''Convert this point to a C{Vector} with the I{geocentric} C{(x,
1560 y, z)} (ECEF) coordinates, I{ignoring height}.
1562 @kwarg Vector: Optional class to return the I{geocentric}
1563 components (L{Vector3d}) or C{None}.
1564 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
1565 arguments, ignored if C{B{Vector} is None}.
1567 @return: A named B{C{Vector}} or if C{B{Vector} is None} a
1568 named L{Vector3Tuple}C{(x, y, z)}.
1570 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}.
1572 @see: Methods C{toCartesian}, C{toNvector} and C{toVector3d}.
1573 '''
1574 return self._ecef9.toVector(Vector=Vector, **self._name1__(Vector_kwds))
1576 def toVector3d(self, norm=True, **Vector3d_kwds):
1577 '''Convert this point to a L{Vector3d} with the I{geocentric} C{(x, y,
1578 z)} (ECEF) coordinates, I{ignoring height}.
1580 @kwarg norm: If C{False}, don't normalize the coordinates (C{bool}).
1581 @kwarg Vector3d_kwds: Optional L{Vector3d} keyword arguments.
1583 @return: Named, unit vector or vector (L{Vector3d}).
1585 @raise TypeError: Invalid B{C{Vector3d_kwds}}.
1587 @see: Methods C{toCartesian}, C{toNvector} and C{toVector}.
1588 '''
1589 r = self.toVector(Vector=_MODS.vector3d.Vector3d, **Vector3d_kwds)
1590 if norm:
1591 r = r.unit(ll=self)
1592 return r
1594 def toWm(self, **toWm_kwds):
1595 '''Convert this point to a WM coordinate.
1597 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments.
1599 @return: The WM coordinate (L{Wm}).
1601 @see: Function L{pygeodesy.toWm}.
1602 '''
1603 return _MODS.webmercator.toWm(self, **self._name1__(toWm_kwds))
1605 @deprecated_method
1606 def to3xyz(self): # PYCHOK no cover
1607 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector},
1608 L{toVector3d} or perhaps (geocentric) L{toEcef}.'''
1609 return self.xyz # self.toVector()
1611# def _update(self, updated, *attrs, **setters):
1612# '''(INTERNAL) See C{_NamedBase._update}.
1613# '''
1614# if updated:
1615# self._rhumb3dict.clear()
1616# return _NamedBase._update(self, updated, *attrs, **setters)
1618 def vincentysTo(self, other, **radius_wrap):
1619 '''Compute the distance between this and an other point using
1620 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>}
1621 spherical formula.
1623 @arg other: The other point (C{LatLon}).
1624 @kwarg radius_wrap: Optional keyword arguments for function
1625 L{pygeodesy.vincentys}, overriding the
1626 default mean C{radius} of this point's
1627 datum ellipsoid.
1629 @return: Distance (C{meter}, same units as B{C{radius}}).
1631 @raise TypeError: The B{C{other}} point is not C{LatLon}.
1633 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo},
1634 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
1635 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
1636 L{flatPolarTo}, L{haversineTo} and L{thomasTo}.
1637 '''
1638 return self._distanceTo(_formy.vincentys, other, **_xkwds(radius_wrap, radius=None))
1640 def _wrap_name2(self, wrap=False, **name):
1641 '''(INTERNAL) Return the C{wrap} and C{name} value.
1642 '''
1643 return wrap, (self._name__(name) if name else NN)
1645 @property_RO
1646 def xyz(self):
1647 '''Get the I{geocentric} C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)})
1648 '''
1649 return self._ecef9.xyz
1651 @property_RO
1652 def xyz3(self):
1653 '''Get the I{geocentric} C{(x, y, z)} coordinates as C{3-tuple}.
1654 '''
1655 return tuple(self.xyz)
1657 @Property_RO
1658 def xyzh(self):
1659 '''Get the I{geocentric} C{(x, y, z)} coordinates and height (L{Vector4Tuple}C{(x, y, z, h)})
1660 '''
1661 return self.xyz.to4Tuple(self.height)
1664class _toCartesian3(object): # see also .formy._idllmn6, .geodesicw._wargs, .vector2d._numpy
1665 '''(INTERNAL) Wrapper to convert 2 other points.
1666 '''
1667 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples
1668 def __call__(self, p, p2, p3, wrap, **kwds):
1669 try:
1670 if wrap:
1671 p2, p3 = map1(_Wrap.point, p2, p3)
1672 kwds = _xkwds(kwds, wrap=wrap)
1673 yield (p. toCartesian().copy(name=_point_), # copy to rename
1674 p._toCartesianEcef(up=4, point2=p2),
1675 p._toCartesianEcef(up=4, point3=p3))
1676 except (AssertionError, TypeError, ValueError) as x: # Exception?
1677 raise _xError(x, point=p, point2=p2, point3=p3, **kwds)
1679_toCartesian3 = _toCartesian3() # PYCHOK singleton
1682def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__
1683 '''(INTERNAL) Get 3-tuple C{(lat, lon, height)}.
1684 '''
1685 try:
1686 lat, lon = latlonh.lat, latlonh.lon
1687 height = _xattr(latlonh, height=height)
1688 except AttributeError:
1689 raise _IsnotError(_LatLon_, latlonh=latlonh)
1690 if wrap:
1691 lat, lon = _Wrap.latlon(lat, lon)
1692 return lat, lon, height
1695def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13
1696 radius=R_M, wrap=False):
1697 '''(INTERNAL) Trilaterate three points by I{area overlap} or by
1698 I{perimeter intersection} of three circles.
1700 @note: The B{C{radius}} is only needed for the n-vectorial and
1701 C{sphericalTrigonometry.LatLon.distanceTo} methods and
1702 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve},
1703 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods.
1704 '''
1705 p2, p3, w = _unrollon3(p1, p2, p3, wrap)
1707 r1 = Distance_(distance1=d1)
1708 r2 = Distance_(distance2=d2)
1709 r3 = Distance_(distance3=d3)
1710 m = 0 if area else (r1 + r2 + r3)
1711 pc = 0
1712 t = []
1713 for _ in range(3):
1714 try: # intersection of circle (p1, r1) and (p2, r2)
1715 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w)
1717 if area: # check overlap
1718 if c1 is c2: # abutting
1719 c = c1
1720 else: # nearest point on radical
1721 c = p3.nearestOn(c1, c2, within=True, wrap=w)
1722 d = r3 - p3.distanceTo(c, radius=radius, wrap=w)
1723 if d > eps: # sufficient overlap
1724 t.append((d, c))
1725 m = max(m, d)
1727 else: # check intersection
1728 for c in ((c1,) if c1 is c2 else (c1, c2)):
1729 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w))
1730 if d < eps: # below margin
1731 t.append((d, c))
1732 m = min(m, d)
1734 except IntersectionError as x:
1735 if _concentric_ in str(x): # XXX ConcentricError?
1736 pc += 1
1738 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate
1740 if t: # get min, max, points and count ...
1741 t = tuple(sorted(t))
1742 n = len(t), # as 1-tuple
1743 # ... or for a single trilaterated result,
1744 # min *is* max, min- *is* maxPoint and n=1, 2 or 3
1745 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...)
1747 elif area and pc == 3: # all pairwise concentric ...
1748 r, p = min((r1, p1), (r2, p2), (r3, p3))
1749 m = max(r1, r2, r3)
1750 # ... return "smallest" point twice, the smallest
1751 # and largest distance and n=0 for concentric
1752 return Trilaterate5Tuple(float(r), p, float(m), p, 0)
1754 n, f = (_overlap_, max) if area else (_intersection_, min)
1755 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m))
1756 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t)
1759__all__ += _ALL_DOCS(LatLonBase)
1761# **) MIT License
1762#
1763# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1764#
1765# Permission is hereby granted, free of charge, to any person obtaining a
1766# copy of this software and associated documentation files (the "Software"),
1767# to deal in the Software without restriction, including without limitation
1768# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1769# and/or sell copies of the Software, and to permit persons to whom the
1770# Software is furnished to do so, subject to the following conditions:
1771#
1772# The above copyright notice and this permission notice shall be included
1773# in all copies or substantial portions of the Software.
1774#
1775# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1776# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1777# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1778# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1779# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1780# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1781# OTHER DEALINGS IN THE SOFTWARE.