Coverage for pygeodesy/latlonBase.py: 93%
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« prev ^ index » next coverage.py v7.2.2, created at 2023-10-11 16:04 -0400
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 _0_0, _0_5, _1_0, _180_0
16# from pygeodesy.datums import _spherical_datum # from .formy
17from pygeodesy.dms import F_D, F_DMS, latDMS, lonDMS, parse3llh
18# from pygeodesy.ecef import EcefKarney # _MODS
19from pygeodesy.errors import _AttributeError, _incompatible, \
20 _IsnotError, IntersectionError, \
21 _TypeError, _ValueError, _xattr, _xdatum, \
22 _xError, _xkwds, _xkwds_not
23from pygeodesy.fmath import favg, sqrt_a
24from pygeodesy.formy import antipode, compassAngle, cosineAndoyerLambert_, \
25 cosineForsytheAndoyerLambert_, cosineLaw, \
26 equirectangular, euclidean, flatLocal_, \
27 flatPolar, _hartzell, haversine, isantipode, \
28 _isequalTo, isnormal, normal, philam2n_xyz, \
29 thomas_, vincentys, _spherical_datum
30from pygeodesy.interns import NN, _COMMASPACE_, _concentric_, _height_, \
31 _intersection_, _LatLon_, _m_, _negative_, \
32 _no_, _overlap_, _too_, _point_ # PYCHOK used!
33# from pygeodesy.iters import PointsIter, points2 # from .vector3d, _MODS
34# from pygeodesy.karney import Caps # _MODS
35from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
36# from pygeodesy.ltp import Ltp, _xLtp # _MODS
37from pygeodesy.named import _NamedBase, notOverloaded, Fmt
38from pygeodesy.namedTuples import Bounds2Tuple, LatLon2Tuple, PhiLam2Tuple, \
39 Trilaterate5Tuple, Vector3Tuple
40# from pygeodesy.nvectorBase import _N_vector_ # _MODS
41from pygeodesy.props import deprecated_method, Property, Property_RO, \
42 property_RO, _update_all
43# from pygeodesy.streprs import Fmt, hstr # from .named, _MODS
44from pygeodesy.units import Distance_, Lat, Lon, Height, Radius, Radius_, \
45 Scalar, Scalar_
46from pygeodesy.utily import sincos2d, _unrollon, _unrollon3, _Wrap
47from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, circum4_, \
48 Circum3Tuple, _radii11ABC
49from pygeodesy.vector3d import nearestOn6, Vector3d, PointsIter
51from contextlib import contextmanager
52from math import asin, cos, degrees, fabs, radians
54__all__ = _ALL_LAZY.latlonBase
55__version__ = '23.10.08'
58def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__
59 '''(INTERNAL) Get 3-tuple C{(lat, lon, height)}.
60 '''
61 try:
62 lat, lon = latlonh.lat, latlonh.lon
63 height = _xattr(latlonh, height=height)
64 except AttributeError:
65 raise _IsnotError(_LatLon_, latlonh=latlonh)
66 if wrap:
67 lat, lon = _Wrap.latlon(lat, lon)
68 return lat, lon, height
71class LatLonBase(_NamedBase):
72 '''(INTERNAL) Base class for C{LatLon} points on spherical or
73 ellipsoidal earth models.
74 '''
75 _clipid = INT0 # polygonal clip, see .booleans
76 _datum = None # L{Datum}, to be overriden
77 _height = INT0 # height (C{meter}), default
78 _lat = 0 # latitude (C{degrees})
79 _lon = 0 # longitude (C{degrees})
81 def __init__(self, latlonh, lon=None, height=0, wrap=False, name=NN, datum=None):
82 '''New C{LatLon}.
84 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or
85 a previous C{LatLon} instance provided C{B{lon}=None}.
86 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or
87 C(None), indicating B{C{latlonh}} is a C{LatLon}.
88 @kwarg height: Optional height above (or below) the earth surface
89 (C{meter}, conventionally).
90 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}}
91 (C{bool}).
92 @kwarg name: Optional name (C{str}).
93 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},
94 L{a_f2Tuple} or I{scalar} radius) or C{None}.
96 @return: New instance (C{LatLon}).
98 @raise RangeError: A B{C{lon}} or C{lat} value outside the valid
99 range and L{rangerrors} set to C{True}.
101 @raise TypeError: If B{C{latlonh}} is not a C{LatLon}.
103 @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}.
105 @example:
107 >>> p = LatLon(50.06632, -5.71475)
108 >>> q = LatLon('50°03′59″N', """005°42'53"W""")
109 >>> r = LatLon(p)
110 '''
111 if name:
112 self.name = name
114 if lon is None:
115 lat, lon, height = _latlonheight3(latlonh, height, wrap)
116 elif wrap:
117 lat, lon = _Wrap.latlonDMS2(latlonh, lon)
118 else:
119 lat = latlonh
121 self._lat = Lat(lat) # parseDMS2(lat, lon)
122 self._lon = Lon(lon) # PYCHOK LatLon2Tuple
123 if height: # elevation
124 self._height = Height(height)
125 if datum:
126 self._datum = _spherical_datum(datum, name=self.name)
128 def __eq__(self, other):
129 return self.isequalTo(other)
131 def __ne__(self, other):
132 return not self.isequalTo(other)
134 def __str__(self):
135 return self.toStr(form=F_D, prec=6)
137 def antipode(self, height=None):
138 '''Return the antipode, the point diametrically opposite
139 to this point.
141 @kwarg height: Optional height of the antipode (C{meter}),
142 this point's height otherwise.
144 @return: The antipodal point (C{LatLon}).
145 '''
146 h = self._heigHt(height)
147 return self.classof(*antipode(*self.latlon), height=h)
149 @deprecated_method
150 def bounds(self, wide, tall, radius=R_M): # PYCHOK no cover
151 '''DEPRECATED, use method C{boundsOf}.'''
152 return self.boundsOf(wide, tall, radius=radius)
154 def boundsOf(self, wide, tall, radius=R_M, height=None):
155 '''Return the SW and NE lat-/longitude of a great circle
156 bounding box centered at this location.
158 @arg wide: Longitudinal box width (C{meter}, same units as
159 B{C{radius}} or C{degrees} if B{C{radius}} is C{None}).
160 @arg tall: Latitudinal box size (C{meter}, same units as
161 B{C{radius}} or C{degrees} if B{C{radius}} is C{None}).
162 @kwarg radius: Mean earth radius (C{meter}) or C{None} if I{both}
163 B{C{wide}} and B{C{tall}} are in C{degrees}.
164 @kwarg height: Height for C{latlonSW} and C{latlonNE} (C{meter}),
165 overriding the point's height.
167 @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)}, the
168 lower-left and upper-right corner (C{LatLon}).
170 @see: U{https://www.Movable-Type.co.UK/scripts/latlong-db.html}
171 '''
172 w = Scalar_(wide=wide) * _0_5
173 t = Scalar_(tall=tall) * _0_5
174 if radius is not None:
175 r = Radius_(radius)
176 c = cos(self.phi)
177 w = degrees(asin(w / r) / c) if fabs(c) > EPS0 else _0_0 # XXX
178 t = degrees(t / r)
179 y, t = self.lat, fabs(t)
180 x, w = self.lon, fabs(w)
182 h = self._heigHt(height)
183 sw = self.classof(y - t, x - w, height=h)
184 ne = self.classof(y + t, x + w, height=h)
185 return Bounds2Tuple(sw, ne, name=self.name)
187 def chordTo(self, other, height=None, wrap=False):
188 '''Compute the length of the chord through the earth between
189 this and an other point.
191 @arg other: The other point (C{LatLon}).
192 @kwarg height: Overriding height for both points (C{meter})
193 or C{None} for each point's height.
194 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{other}}
195 point (C{bool}).
197 @return: The chord length (conventionally C{meter}).
199 @raise TypeError: The B{C{other}} point is not C{LatLon}.
200 '''
201 def _v3d(ll):
202 t = ll.toEcef(height=height) # .toVector(Vector=Vector3d)
203 return Vector3d(t.x, t.y, t.z)
205 p = self.others(other)
206 if wrap:
207 p = _Wrap.point(p)
208 return _v3d(self).minus(_v3d(p)).length
210 def circin6(self, point2, point3, eps=EPS4, wrap=False):
211 '''Return the radius and center of the I{inscribed} aka I{In-}circle
212 of the (planar) triangle formed by this and two other points.
214 @arg point2: Second point (C{LatLon}).
215 @arg point3: Third point (C{LatLon}).
216 @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}.
217 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and
218 B{C{point3}} (C{bool}).
220 @return: L{Circin6Tuple}C{(radius, center, deltas, cA, cB, cC)}. The
221 C{center} and contact points C{cA}, C{cB} and C{cC}, each an
222 instance of this (sub-)class, are co-planar with this and the
223 two given points, see the B{Note} below.
225 @raise ImportError: Package C{numpy} not found, not installed or older
226 than version 1.10.
228 @raise IntersectionError: Near-coincident or -colinear points or
229 a trilateration or C{numpy} issue.
231 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
233 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted
234 back to geodetic lat-, longitude and height. The latter, conventionally
235 in C{meter} indicates whether the C{center} is above, below or on the
236 surface of the earth model. If C{deltas} is C{None}, the C{center} is
237 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon,
238 height)} representing the differences between both results from
239 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
241 @see: Function L{pygeodesy.circin6}, method L{circum3}, U{Incircle
242 <https://MathWorld.Wolfram.com/Incircle.html>} and U{Contact Triangle
243 <https://MathWorld.Wolfram.com/ContactTriangle.html>}.
244 '''
245 with _toCartesian3(self, point2, point3, wrap) as cs:
246 r, c, d, cA, cB, cC = _circin6(*cs, eps=eps, useZ=True, dLL3=True,
247 datum=self.datum) # PYCHOK unpack
248 return Circin6Tuple(r, c.toLatLon(), d, cA.toLatLon(), cB.toLatLon(), cC.toLatLon())
250 def circum3(self, point2, point3, circum=True, eps=EPS4, wrap=False):
251 '''Return the radius and center of the smallest circle I{through} or I{containing}
252 this and two other points.
254 @arg point2: Second point (C{LatLon}).
255 @arg point3: Third point (C{LatLon}).
256 @kwarg circum: If C{True} return the C{circumradius} and C{circumcenter},
257 always, ignoring the I{Meeus}' Type I case (C{bool}).
258 @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}.
259 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and
260 B{C{point3}} (C{bool}).
262 @return: A L{Circum3Tuple}C{(radius, center, deltas)}. The C{center}, an
263 instance of this (sub-)class, is co-planar with this and the two
264 given points. If C{deltas} is C{None}, the C{center} is
265 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat,
266 lon, height)} representing the difference between both results
267 from L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
269 @raise ImportError: Package C{numpy} not found, not installed or older than
270 version 1.10.
272 @raise IntersectionError: Near-concentric, -coincident or -colinear points,
273 incompatible C{Ecef} classes or a trilateration
274 or C{numpy} issue.
276 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
278 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted
279 back to geodetic lat-, longitude and height. The latter, conventionally
280 in C{meter} indicates whether the C{center} is above, below or on the
281 surface of the earth model. If C{deltas} is C{None}, the C{center} is
282 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon,
283 height)} representing the difference between both results from
284 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
286 @see: Function L{pygeodesy.circum3} and methods L{circin6} and L{circum4_}.
287 '''
288 with _toCartesian3(self, point2, point3, wrap, circum=circum) as cs:
289 r, c, d = _circum3(*cs, circum=circum, eps=eps, useZ=True, dLL3=True, # XXX -3d2
290 clas=cs[0].classof, datum=self.datum) # PYCHOK unpack
291 return Circum3Tuple(r, c.toLatLon(), d)
293 def circum4_(self, *points, **wrap):
294 '''Best-fit a sphere through this and two or more other points.
296 @arg points: The other points (each a C{LatLon}).
297 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{points}}
298 (C{bool}), default C{False}.
300 @return: L{Circum4Tuple}C{(radius, center, rank, residuals)} with C{center}
301 an instance of this (sub-)class.
303 @raise ImportError: Package C{numpy} not found, not installed or older than
304 version 1.10.
306 @raise NumPyError: Some C{numpy} issue.
308 @raise TypeError: One of the B{C{points}} invalid.
310 @raise ValueError: Too few B{C{points}}.
312 @see: Function L{pygeodesy.circum4_} and L{circum3}.
313 '''
314 def _cs(ps, C, wrap=False):
315 _wp = _Wrap.point if wrap else (lambda p: p)
316 for i, p in enumerate(ps):
317 yield C(i=i, points=_wp(p))
319 C = self._toCartesianEcef
320 c = C(point=self)
321 t = circum4_(c, Vector=c.classof, *_cs(points, C, **wrap))
322 c = t.center.toLatLon(LatLon=self.classof)
323 return t.dup(center=c)
325 @property
326 def clipid(self):
327 '''Get the (polygonal) clip (C{int}).
328 '''
329 return self._clipid
331 @clipid.setter # PYCHOK setter!
332 def clipid(self, clipid):
333 '''Get the (polygonal) clip (C{int}).
334 '''
335 self._clipid = int(clipid)
337 @deprecated_method
338 def compassAngle(self, other, **adjust_wrap): # PYCHOK no cover
339 '''DEPRECATED, use method L{compassAngleTo}.'''
340 return self.compassAngleTo(other, **adjust_wrap)
342 def compassAngleTo(self, other, **adjust_wrap):
343 '''Return the angle from North for the direction vector between
344 this and an other point.
346 Suitable only for short, non-near-polar vectors up to a few
347 hundred Km or Miles. Use method C{initialBearingTo} for
348 larger distances.
350 @arg other: The other point (C{LatLon}).
351 @kwarg adjust_wrap: Optional keyword arguments for function
352 L{pygeodesy.compassAngle}.
354 @return: Compass angle from North (C{degrees360}).
356 @raise TypeError: The B{C{other}} point is not C{LatLon}.
358 @note: Courtesy of Martin Schultz.
360 @see: U{Local, flat earth approximation
361 <https://www.EdWilliams.org/avform.htm#flat>}.
362 '''
363 p = self.others(other)
364 return compassAngle(self.lat, self.lon, p.lat, p.lon, **adjust_wrap)
366 def cosineAndoyerLambertTo(self, other, wrap=False):
367 '''Compute the distance between this and an other point using the U{Andoyer-Lambert correction<https://
368 navlib.net/wp-content/uploads/2013/10/admiralty-manual-of-navigation-vol-1-1964-english501c.pdf>}
369 of the U{Law of Cosines<https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>} formula.
371 @arg other: The other point (C{LatLon}).
372 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
373 the B{C{other}} point (C{bool}).
375 @return: Distance (C{meter}, same units as the axes of this
376 point's datum ellipsoid).
378 @raise TypeError: The B{C{other}} point is not C{LatLon}.
380 @see: Function L{pygeodesy.cosineAndoyerLambert} and methods
381 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo},
382 C{distanceTo*}, L{equirectangularTo}, L{euclideanTo},
383 L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo},
384 L{thomasTo} and L{vincentysTo}.
385 '''
386 return self._distanceTo_(cosineAndoyerLambert_, other, wrap=wrap)
388 def cosineForsytheAndoyerLambertTo(self, other, wrap=False):
389 '''Compute the distance between this and an other point using
390 the U{Forsythe-Andoyer-Lambert correction
391 <https://www2.UNB.Ca/gge/Pubs/TR77.pdf>} of the U{Law of Cosines
392 <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>}
393 formula.
395 @arg other: The other point (C{LatLon}).
396 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
397 the B{C{other}} point (C{bool}).
399 @return: Distance (C{meter}, same units as the axes of
400 this point's datum ellipsoid).
402 @raise TypeError: The B{C{other}} point is not C{LatLon}.
404 @see: Function L{pygeodesy.cosineForsytheAndoyerLambert} and methods
405 L{cosineAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
406 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
407 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}.
408 '''
409 return self._distanceTo_(cosineForsytheAndoyerLambert_, other, wrap=wrap)
411 def cosineLawTo(self, other, radius=None, wrap=False):
412 '''Compute the distance between this and an other point using the
413 U{spherical Law of Cosines
414 <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>}
415 formula.
417 @arg other: The other point (C{LatLon}).
418 @kwarg radius: Mean earth radius (C{meter}) or C{None}
419 for the mean radius of this point's datum
420 ellipsoid.
421 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
422 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(cosineLaw, other, radius, wrap=wrap)
435 @property_RO
436 def datum(self): # PYCHOK no cover
437 '''I{Must be overloaded}.'''
438 notOverloaded(self)
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) 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_RO
479 def Ecef(self):
480 '''Get the ECEF I{class} (L{EcefKarney}), I{lazily}.
481 '''
482 return _MODS.ecef.EcefKarney # default
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 @deprecated_method
497 def equals(self, other, eps=None): # PYCHOK no cover
498 '''DEPRECATED, use method L{isequalTo}.'''
499 return self.isequalTo(other, eps=eps)
501 @deprecated_method
502 def equals3(self, other, eps=None): # PYCHOK no cover
503 '''DEPRECATED, use method L{isequalTo3}.'''
504 return self.isequalTo3(other, eps=eps)
506 def equirectangularTo(self, other, **radius_adjust_limit_wrap):
507 '''Compute the distance between this and an other point
508 using the U{Equirectangular Approximation / Projection
509 <https://www.Movable-Type.co.UK/scripts/latlong.html#equirectangular>}.
511 Suitable only for short, non-near-polar distances up to a
512 few hundred Km or Miles. Use method L{haversineTo} or
513 C{distanceTo*} for more accurate and/or larger distances.
515 @arg other: The other point (C{LatLon}).
516 @kwarg radius_adjust_limit_wrap: Optional keyword arguments
517 for function L{pygeodesy.equirectangular},
518 overriding the default mean C{radius} of this
519 point's datum ellipsoid.
521 @return: Distance (C{meter}, same units as B{C{radius}}).
523 @raise TypeError: The B{C{other}} point is not C{LatLon}.
525 @see: Function L{pygeodesy.equirectangular} and methods L{cosineAndoyerLambertTo},
526 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
527 C{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},
528 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
529 '''
530 return self._distanceTo(equirectangular, other, **radius_adjust_limit_wrap)
532 def euclideanTo(self, other, **radius_adjust_wrap):
533 '''Approximate the C{Euclidian} distance between this and
534 an other point.
536 See function L{pygeodesy.euclidean} for the available B{C{options}}.
538 @arg other: The other point (C{LatLon}).
539 @kwarg radius_adjust_wrap: Optional keyword arguments for function
540 L{pygeodesy.euclidean}, overriding the default mean
541 C{radius} of this point's datum ellipsoid.
543 @return: Distance (C{meter}, same units as B{C{radius}}).
545 @raise TypeError: The B{C{other}} point is not C{LatLon}.
547 @see: Function L{pygeodesy.euclidean} and methods L{cosineAndoyerLambertTo},
548 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
549 L{equirectangularTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},
550 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
551 '''
552 return self._distanceTo(euclidean, other, **radius_adjust_wrap)
554 def flatLocalTo(self, other, radius=None, wrap=False):
555 '''Compute the distance between this and an other point using the
556 U{ellipsoidal Earth to plane projection
557 <https://WikiPedia.org/wiki/Geographical_distance#Ellipsoidal_Earth_projected_to_a_plane>}
558 aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>} formula.
560 @arg other: The other point (C{LatLon}).
561 @kwarg radius: Mean earth radius (C{meter}) or C{None} for
562 the I{equatorial radius} of this point's
563 datum ellipsoid.
564 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
565 the B{C{other}} point (C{bool}).
567 @return: Distance (C{meter}, same units as B{C{radius}}).
569 @raise TypeError: The B{C{other}} point is not C{LatLon}.
571 @raise ValueError: Invalid B{C{radius}}.
573 @see: Function L{pygeodesy.flatLocal}/L{pygeodesy.hubeny}, methods
574 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo},
575 L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo},
576 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo} and
577 U{local, flat Earth approximation<https://www.edwilliams.org/avform.htm#flat>}.
578 '''
579 return self._distanceTo_(flatLocal_, other, wrap=wrap, radius=
580 radius if radius in (None, R_M, _1_0, 1) else Radius(radius)) # PYCHOK kwargs
582 hubenyTo = flatLocalTo # for Karl Hubeny
584 def flatPolarTo(self, other, **radius_wrap):
585 '''Compute the distance between this and an other point using
586 the U{polar coordinate flat-Earth<https://WikiPedia.org/wiki/
587 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula.
589 @arg other: The other point (C{LatLon}).
590 @kwarg radius_wrap: Optional keyword arguments for function
591 L{pygeodesy.flatPolar}, overriding the
592 default mean C{radius} of this point's
593 datum ellipsoid.
595 @return: Distance (C{meter}, same units as B{C{radius}}).
597 @raise TypeError: The B{C{other}} point is not C{LatLon}.
599 @see: Function L{pygeodesy.flatPolar} and methods L{cosineAndoyerLambertTo},
600 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
601 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
602 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
603 '''
604 return self._distanceTo(flatPolar, other, **radius_wrap)
606 def hartzell(self, los=None, earth=None):
607 '''Compute the intersection of a Line-Of-Sight (los) from this Point-Of-View
608 (pov) with this point's ellipsoid surface.
610 @kwarg los: Line-Of-Sight, I{direction} to earth (L{Los}, L{Vector3d})
611 or C{None} to point to the ellipsoid's center.
612 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},
613 L{a_f2Tuple} or C{scalar} radius in C{meter}) overriding
614 this point's C{datum} ellipsoid.
616 @return: The ellipsoid intersection (C{LatLon}) with C{.height} set
617 to the distance to this C{pov}.
619 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov}
620 is inside the ellipsoid or B{C{los}} points
621 outside or away from the ellipsoid.
623 @raise TypeError: Invalid B{C{los}}.
625 @see: Function C{hartzell} for further details.
626 '''
627 return _hartzell(self, los, earth, LatLon=self.classof)
629 def haversineTo(self, other, **radius_wrap):
630 '''Compute the distance between this and an other point using the
631 U{Haversine<https://www.Movable-Type.co.UK/scripts/latlong.html>}
632 formula.
634 @arg other: The other point (C{LatLon}).
635 @kwarg radius_wrap: Optional keyword arguments for function
636 L{pygeodesy.haversine}, overriding the
637 default mean C{radius} of this point's
638 datum ellipsoid.
640 @return: Distance (C{meter}, same units as B{C{radius}}).
642 @raise TypeError: The B{C{other}} point is not C{LatLon}.
644 @see: Function L{pygeodesy.haversine} and methods L{cosineAndoyerLambertTo},
645 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
646 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
647 L{flatPolarTo}, L{thomasTo} and L{vincentysTo}.
648 '''
649 return self._distanceTo(haversine, other, **radius_wrap)
651 def _havg(self, other, f=_0_5, h=None):
652 '''(INTERNAL) Weighted, average height.
654 @arg other: An other point (C{LatLon}).
655 @kwarg f: Optional fraction (C{float}).
656 @kwarg h: Overriding height (C{meter}).
658 @return: Average, fractional height (C{float}) or
659 the overriding B{C{height}} (C{Height}).
660 '''
661 return Height(h) if h is not None else \
662 favg(self.height, other.height, f=f)
664 @Property
665 def height(self):
666 '''Get the height (C{meter}).
667 '''
668 return self._height
670 @height.setter # PYCHOK setter!
671 def height(self, height):
672 '''Set the height (C{meter}).
674 @raise TypeError: Invalid B{C{height}} C{type}.
676 @raise ValueError: Invalid B{C{height}}.
677 '''
678 h = Height(height)
679 if self._height != h:
680 _update_all(self)
681 self._height = h
683 def _heigHt(self, height):
684 '''(INTERNAL) Overriding this C{height}.
685 '''
686 return self.height if height is None else Height(height)
688 def height4(self, earth=None, normal=True, LatLon=None, **LatLon_kwds):
689 '''Compute the height above or below and the projection of this point
690 on this datum's or on an other earth's ellipsoid surface.
692 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius
693 I{overriding} this datum (L{Datum}, L{Ellipsoid},
694 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
695 L{JacobiConformal} or C{meter}, conventionally).
696 @kwarg normal: If C{True} the projection is the nearest point on the
697 ellipsoid's surface, otherwise the intersection of the
698 radial line to the center and the ellipsoid's surface.
699 @kwarg LatLon: Optional class to return the height and projection
700 (C{LatLon}) or C{None}.
701 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
702 ignored if C{B{LatLon} is None}.
704 @note: Use keyword argument C{height=0} to override C{B{LatLon}.height}
705 to {0} or any other C{scalar}, conventionally in C{meter}.
707 @return: An instance of B{C{LatLon}} or if C{B{LatLon} is None}, a
708 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
709 and C{z} coordinates and height C{h} in C{meter}, conventionally.
711 @raise TriaxialError: No convergence in triaxial root finding.
713 @raise TypeError: Invalid B{C{earth}}.
715 @see: L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
716 '''
717 c = self.toCartesian()
718 if LatLon is None:
719 r = c.height4(earth=earth, normal=normal)
720 else:
721 r = c.height4(earth=earth, normal=normal, Cartesian=c.classof, height=0)
722 r = r.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, height=r.height))
723 return r
725 def heightStr(self, prec=-2, m=_m_):
726 '''Return this point's B{C{height}} as C{str}ing.
728 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
729 @kwarg m: Optional unit of the height (C{str}).
731 @see: Function L{pygeodesy.hstr}.
732 '''
733 return _MODS.streprs.hstr(self.height, prec=prec, m=m)
735 @deprecated_method
736 def isantipode(self, other, eps=EPS): # PYCHOK no cover
737 '''DEPRECATED, use method L{isantipodeTo}.'''
738 return self.isantipodeTo(other, eps=eps)
740 def isantipodeTo(self, other, eps=EPS):
741 '''Check whether this and an other point are antipodal,
742 on diametrically opposite sides of the earth.
744 @arg other: The other point (C{LatLon}).
745 @kwarg eps: Tolerance for near-equality (C{degrees}).
747 @return: C{True} if points are antipodal within the given
748 tolerance, C{False} otherwise.
749 '''
750 p = self.others(other)
751 return isantipode(*(self.latlon + p.latlon), eps=eps)
753 @Property_RO
754 def isEllipsoidal(self):
755 '''Check whether this point is ellipsoidal (C{bool} or C{None} if unknown).
756 '''
757 return self.datum.isEllipsoidal if self._datum else None
759 @Property_RO
760 def isEllipsoidalLatLon(self):
761 '''Get C{LatLon} base.
762 '''
763 return False
765 def isequalTo(self, other, eps=None):
766 '''Compare this point with an other point, I{ignoring} height.
768 @arg other: The other point (C{LatLon}).
769 @kwarg eps: Tolerance for equality (C{degrees}).
771 @return: C{True} if both points are identical,
772 I{ignoring} height, C{False} otherwise.
774 @raise TypeError: The B{C{other}} point is not C{LatLon}
775 or mismatch of the B{C{other}} and
776 this C{class} or C{type}.
778 @raise UnitError: Invalid B{C{eps}}.
780 @see: Method L{isequalTo3}.
781 '''
782 return _isequalTo(self, self.others(other), eps=eps)
784 def isequalTo3(self, other, eps=None):
785 '''Compare this point with an other point, I{including} height.
787 @arg other: The other point (C{LatLon}).
788 @kwarg eps: Tolerance for equality (C{degrees}).
790 @return: C{True} if both points are identical
791 I{including} height, C{False} otherwise.
793 @raise TypeError: The B{C{other}} point is not C{LatLon}
794 or mismatch of the B{C{other}} and
795 this C{class} or C{type}.
797 @see: Method L{isequalTo}.
798 '''
799 return self.height == self.others(other).height and \
800 _isequalTo(self, other, eps=eps)
802 @Property_RO
803 def isnormal(self):
804 '''Return C{True} if this point is normal (C{bool}),
805 meaning C{abs(lat) <= 90} and C{abs(lon) <= 180}.
807 @see: Methods L{normal}, L{toNormal} and functions
808 L{pygeodesy.isnormal} and L{pygeodesy.normal}.
809 '''
810 return isnormal(self.lat, self.lon, eps=0)
812 @Property_RO
813 def isSpherical(self):
814 '''Check whether this point is spherical (C{bool} or C{None} if unknown).
815 '''
816 return self.datum.isSpherical if self._datum else None
818 @Property_RO
819 def lam(self):
820 '''Get the longitude (B{C{radians}}).
821 '''
822 return radians(self.lon)
824 @Property
825 def lat(self):
826 '''Get the latitude (C{degrees90}).
827 '''
828 return self._lat
830 @lat.setter # PYCHOK setter!
831 def lat(self, lat):
832 '''Set the latitude (C{str[N|S]} or C{degrees}).
834 @raise ValueError: Invalid B{C{lat}}.
835 '''
836 lat = Lat(lat) # parseDMS(lat, suffix=_NS_, clip=90)
837 if self._lat != lat:
838 _update_all(self)
839 self._lat = lat
841 @Property
842 def latlon(self):
843 '''Get the lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).
844 '''
845 return LatLon2Tuple(self._lat, self._lon, name=self.name)
847 @latlon.setter # PYCHOK setter!
848 def latlon(self, latlonh):
849 '''Set the lat- and longitude and optionally the height
850 (2- or 3-tuple or comma- or space-separated C{str}
851 of C{degrees90}, C{degrees180} and C{meter}).
853 @raise TypeError: Height of B{C{latlonh}} not C{scalar} or
854 B{C{latlonh}} not C{list} or C{tuple}.
856 @raise ValueError: Invalid B{C{latlonh}} or M{len(latlonh)}.
858 @see: Function L{pygeodesy.parse3llh} to parse a B{C{latlonh}}
859 string into a 3-tuple C{(lat, lon, h)}.
860 '''
861 if isstr(latlonh):
862 latlonh = parse3llh(latlonh, height=self.height)
863 else:
864 _xinstanceof(list, tuple, latlonh=latlonh)
865 if len(latlonh) == 3:
866 h = Height(latlonh[2], name=Fmt.SQUARE(latlonh=2))
867 elif len(latlonh) != 2:
868 raise _ValueError(latlonh=latlonh)
869 else:
870 h = self.height
872 llh = Lat(latlonh[0]), Lon(latlonh[1]), h # parseDMS2(latlonh[0], latlonh[1])
873 if (self._lat, self._lon, self._height) != llh:
874 _update_all(self)
875 self._lat, self._lon, self._height = llh
877 def latlon2(self, ndigits=0):
878 '''Return this point's lat- and longitude in C{degrees}, rounded.
880 @kwarg ndigits: Number of (decimal) digits (C{int}).
882 @return: A L{LatLon2Tuple}C{(lat, lon)}, both C{float}
883 and rounded away from zero.
885 @note: The C{round}ed values are always C{float}, also
886 if B{C{ndigits}} is omitted.
887 '''
888 return LatLon2Tuple(round(self.lat, ndigits),
889 round(self.lon, ndigits), name=self.name)
891 @deprecated_method
892 def latlon_(self, ndigits=0): # PYCHOK no cover
893 '''DEPRECATED, use method L{latlon2}.'''
894 return self.latlon2(ndigits=ndigits)
896 latlon2round = latlon_ # PYCHOK no cover
898 @Property
899 def latlonheight(self):
900 '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).
901 '''
902 return self.latlon.to3Tuple(self.height)
904 @latlonheight.setter # PYCHOK setter!
905 def latlonheight(self, latlonh):
906 '''Set the lat- and longitude and optionally the height
907 (2- or 3-tuple or comma- or space-separated C{str}
908 of C{degrees90}, C{degrees180} and C{meter}).
910 @see: Property L{latlon} for more details.
911 '''
912 self.latlon = latlonh
914 @Property
915 def lon(self):
916 '''Get the longitude (C{degrees180}).
917 '''
918 return self._lon
920 @lon.setter # PYCHOK setter!
921 def lon(self, lon):
922 '''Set the longitude (C{str[E|W]} or C{degrees}).
924 @raise ValueError: Invalid B{C{lon}}.
925 '''
926 lon = Lon(lon) # parseDMS(lon, suffix=_EW_, clip=180)
927 if self._lon != lon:
928 _update_all(self)
929 self._lon = lon
931 @Property_RO
932 def _ltp(self):
933 '''(INTERNAL) Cache for L{toLtp}.
934 '''
935 return _MODS.ltp.Ltp(self, ecef=self.Ecef(self.datum), name=self.name)
937 def nearestOn6(self, points, closed=False, height=None, wrap=False):
938 '''Locate the point on a path or polygon closest to this point.
940 Points are converted to and distances are computed in
941 I{geocentric}, cartesian space.
943 @arg points: The path or polygon points (C{LatLon}[]).
944 @kwarg closed: Optionally, close the polygon (C{bool}).
945 @kwarg height: Optional height, overriding the height of
946 this and all other points (C{meter}). If
947 C{None}, take the height of points into
948 account for distances.
949 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
950 the B{C{points}} (C{bool}).
952 @return: A L{NearestOn6Tuple}C{(closest, distance, fi, j,
953 start, end)} with the C{closest}, the C{start}
954 and the C{end} point each an instance of this
955 C{LatLon} and C{distance} in C{meter}, same
956 units as the cartesian axes.
958 @raise PointsError: Insufficient number of B{C{points}}.
960 @raise TypeError: Some B{C{points}} or some B{C{points}}'
961 C{Ecef} invalid.
963 @raise ValueError: Some B{C{points}}' C{Ecef} is incompatible.
965 @see: Function L{pygeodesy.nearestOn6}.
966 '''
967 def _cs(Ps, h, w, C):
968 p = None # not used
969 for i, q in Ps.enumerate():
970 if w and i:
971 q = _unrollon(p, q)
972 yield C(height=h, i=i, up=3, points=q)
973 p = q
975 C = self._toCartesianEcef # to verify datum and Ecef
976 Ps = self.PointsIter(points, wrap=wrap)
978 c = C(height=height, this=self) # this Cartesian
979 t = nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed)
980 c, s, e = t.closest, t.start, t.end
982 kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon
983 height=height)
984 _r = self.Ecef(self.datum).reverse
985 p = _r(c).toLatLon(**kwds)
986 s = _r(s).toLatLon(**kwds) if s is not c else p
987 e = _r(e).toLatLon(**kwds) if e is not c else p
988 return t.dup(closest=p, start=s, end=e)
990 def normal(self):
991 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and
992 C{abs(lon) <= 180}.
994 @return: C{True} if this point was I{normal}, C{False} if it
995 wasn't (but is now).
997 @see: Property L{isnormal} and method L{toNormal}.
998 '''
999 n = self.isnormal
1000 if not n:
1001 self.latlon = normal(*self.latlon)
1002 return n
1004 @Property_RO
1005 def _N_vector(self):
1006 '''(INTERNAL) Get the (C{nvectorBase._N_vector_})
1007 '''
1008 return _MODS.nvectorBase._N_vector_(*self.xyzh)
1010 @Property_RO
1011 def phi(self):
1012 '''Get the latitude (B{C{radians}}).
1013 '''
1014 return radians(self.lat)
1016 @Property_RO
1017 def philam(self):
1018 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).
1019 '''
1020 return PhiLam2Tuple(self.phi, self.lam, name=self.name)
1022 def philam2(self, ndigits=0):
1023 '''Return this point's lat- and longitude in C{radians}, rounded.
1025 @kwarg ndigits: Number of (decimal) digits (C{int}).
1027 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float}
1028 and rounded away from zero.
1030 @note: The C{round}ed values are always C{float}, also
1031 if B{C{ndigits}} is omitted.
1032 '''
1033 return PhiLam2Tuple(round(self.phi, ndigits),
1034 round(self.lam, ndigits), name=self.name)
1036 @Property_RO
1037 def philamheight(self):
1038 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
1039 '''
1040 return self.philam.to3Tuple(self.height)
1042 @deprecated_method
1043 def points(self, points, closed=True): # PYCHOK no cover
1044 '''DEPRECATED, use method L{points2}.'''
1045 return self.points2(points, closed=closed)
1047 def points2(self, points, closed=True):
1048 '''Check a path or polygon represented by points.
1050 @arg points: The path or polygon points (C{LatLon}[])
1051 @kwarg closed: Optionally, consider the polygon closed,
1052 ignoring any duplicate or closing final
1053 B{C{points}} (C{bool}).
1055 @return: A L{Points2Tuple}C{(number, points)}, an C{int}
1056 and C{list} or C{tuple}.
1058 @raise PointsError: Insufficient number of B{C{points}}.
1060 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1061 '''
1062 return _MODS.iters.points2(points, closed=closed, base=self)
1064 def PointsIter(self, points, loop=0, dedup=False, wrap=False):
1065 '''Return a C{PointsIter} iterator.
1067 @arg points: The path or polygon points (C{LatLon}[])
1068 @kwarg loop: Number of loop-back points (non-negative C{int}).
1069 @kwarg dedup: Skip duplicate points (C{bool}).
1070 @kwarg wrap: If C{True}, wrap or I{normalize} the
1071 enum-/iterated B{C{points}} (C{bool}).
1073 @return: A new C{PointsIter} iterator.
1075 @raise PointsError: Insufficient number of B{C{points}}.
1076 '''
1077 return PointsIter(points, base=self, loop=loop, dedup=dedup, wrap=wrap)
1079 def radii11(self, point2, point3, wrap=False):
1080 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent}
1081 circles of a (planar) triangle formed by this and two other points.
1083 @arg point2: Second point (C{LatLon}).
1084 @arg point3: Third point (C{LatLon}).
1085 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and
1086 B{C{point3}} (C{bool}).
1088 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.
1090 @raise IntersectionError: Near-coincident or -colinear points.
1092 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
1094 @see: Function L{pygeodesy.radii11}, U{Incircle
1095 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles
1096 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent
1097 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}.
1098 '''
1099 with _toCartesian3(self, point2, point3, wrap) as cs:
1100 return _radii11ABC(*cs, useZ=True)[0]
1102 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3
1103 '''(INTERNAL) Get the C{rhumb} for this point's datum or for
1104 the B{C{radius}}' earth model iff non-C{None}.
1105 ''' # in .ellipsoidalBase.LatLonEllipsoidalBase.intersecant2
1106 try:
1107 d = self._rhumb3dict
1108 t = d[(exact, radius)]
1109 except KeyError:
1110 D = self.datum if radius is None else _spherical_datum(radius) # ellipsoidal OK
1111 try:
1112 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical)
1113 except AttributeError as x:
1114 raise _AttributeError(datum=D, radius=radius, cause=x)
1115 t = r, D, _MODS.karney.Caps
1116 while d:
1117 d.popitem()
1118 d[(exact, radius)] = t # cache 3-tuple
1119 return t
1121 @Property_RO
1122 def _rhumb3dict(self):
1123 return {} # single-item cache
1125 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False):
1126 '''Return the azimuth (bearing) of a rhumb line (loxodrome)
1127 between this and an other (ellipsoidal) point.
1129 @arg other: The other point (C{LatLon}).
1130 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1131 see method L{Ellipsoid.rhumb_}.
1132 @kwarg radius: Optional earth radius (C{meter}) or earth model
1133 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1134 L{a_f2Tuple}), overriding this point's datum.
1135 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1136 B{C{other}} point (C{bool}).
1138 @return: Rhumb azimuth (compass C{degrees360}).
1140 @raise TypeError: The B{C{other}} point is incompatible or
1141 B{C{radius}} is invalid.
1142 '''
1143 r, _, Cs = self._rhumb3(exact, radius)
1144 return r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12
1146 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None):
1147 '''Return the destination point having travelled the given distance
1148 from this point along a rhumb line (loxodrome) at the given azimuth.
1150 @arg distance: Distance travelled (C{meter}, same units as this
1151 point's datum (ellipsoid) axes or B{C{radius}},
1152 may be negative.
1153 @arg azimuth: Azimuth (bearing) at this point (compass C{degrees}).
1154 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1155 see method L{Ellipsoid.rhumb_}.
1156 @kwarg radius: Optional earth radius (C{meter}) or earth model
1157 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1158 L{a_f2Tuple}), overriding this point's datum.
1159 @kwarg height: Optional height, overriding the default height
1160 (C{meter}).
1162 @return: The destination point (ellipsoidal C{LatLon}).
1164 @raise TypeError: Invalid B{C{radius}}.
1166 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}},
1167 B{C{radius}} or B{C{height}}.
1168 '''
1169 r, D, _ = self._rhumb3(exact, radius)
1170 d = r._Direct(self, azimuth, distance)
1171 h = self._heigHt(height)
1172 return self.classof(d.lat2, d.lon2, datum=D, height=h)
1174 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False):
1175 '''Return the distance from this to an other point along
1176 a rhumb line (loxodrome).
1178 @arg other: The other point (C{LatLon}).
1179 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1180 see method L{Ellipsoid.rhumb_}.
1181 @kwarg radius: Optional earth radius (C{meter}) or earth model
1182 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1183 L{a_f2Tuple}), overriding this point's datum.
1184 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1185 B{C{other}} point (C{bool}).
1187 @return: Distance (C{meter}, the same units as this point's
1188 datum (ellipsoid) axes or B{C{radius}}.
1190 @raise TypeError: The B{C{other}} point is incompatible or
1191 B{C{radius}} is invalid.
1193 @raise ValueError: Invalid B{C{radius}}.
1194 '''
1195 r, _, Cs = self._rhumb3(exact, radius)
1196 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12
1198 def rhumbLine(self, azimuth_other, exact=False, radius=None, wrap=False,
1199 **name_caps):
1200 '''Get a rhumb line through this point at a given azimuth or
1201 through this and an other point.
1203 @arg azimuth_other: The azimuth of the rhumb line (compass
1204 C{degrees}) or the other point (C{LatLon}).
1205 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1206 see method L{Ellipsoid.rhumb_}.
1207 @kwarg radius: Optional earth radius (C{meter}) or earth model
1208 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1209 L{a_f2Tuple}), overriding this point's datum.
1210 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1211 C{azimuth_B{other}} point (C{bool}).
1212 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see
1213 L{RhumbLine} C{B{caps}}.
1215 @return: A C{RhumbLine} instance.
1217 @raise TypeError: Invalid B{C{radius}} or BC{C{azimuth_other}}
1218 not a C{scalar} nor a C{LatLon}.
1220 @see: Modules L{rhumbaux} and L{rhumbx}.
1221 '''
1222 r, _, _ = self._rhumb3(exact, radius)
1223 a, kwds = azimuth_other, _xkwds(name_caps, name=self.name)
1224 if isscalar(a):
1225 r = r._DirectLine(self, a, **kwds)
1226 elif isinstance(a, LatLonBase): # isLatLon(a)
1227 r = r._InverseLine(self, a, wrap, **kwds)
1228 else:
1229 raise _TypeError(azimuth_other=a)
1230 return r
1232 def rhumbMidpointTo(self, other, exact=False, radius=None,
1233 height=None, fraction=_0_5, wrap=False):
1234 '''Return the (loxodromic) midpoint on the rhumb line between
1235 this and an other point.
1237 @arg other: The other point (C{LatLon}).
1238 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1239 see method L{Ellipsoid.rhumb_}.
1240 @kwarg radius: Optional earth radius (C{meter}) or earth model
1241 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1242 L{a_f2Tuple}), overriding this point's datum.
1243 @kwarg height: Optional height, overriding the mean height
1244 (C{meter}).
1245 @kwarg fraction: Midpoint location from this point (C{scalar}), 0
1246 for this, 1 for the B{C{other}}, 0.5 for halfway
1247 between this and the B{C{other}} point, may be
1248 negative or greater than 1.
1249 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1250 B{C{other}} point (C{bool}).
1252 @return: The midpoint at the given B{C{fraction}} along the
1253 rhumb line (C{LatLon}).
1255 @raise TypeError: The B{C{other}} point is incompatible or
1256 B{C{radius}} is invalid.
1258 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}.
1259 '''
1260 r, D, _ = self._rhumb3(exact, radius)
1261 f = Scalar(fraction=fraction)
1262 d = r._Inverse(self, other, wrap) # C.AZIMUTH_DISTANCE
1263 d = r._Direct( self, d.azi12, d.s12 * f)
1264 h = self._havg(other, f=f, h=height)
1265 return self.classof(d.lat2, d.lon2, datum=D, height=h)
1267 def thomasTo(self, other, wrap=False):
1268 '''Compute the distance between this and an other point using
1269 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>}
1270 formula.
1272 @arg other: The other point (C{LatLon}).
1273 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
1274 the B{C{other}} point (C{bool}).
1276 @return: Distance (C{meter}, same units as the axes of
1277 this point's datum ellipsoid).
1279 @raise TypeError: The B{C{other}} point is not C{LatLon}.
1281 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo},
1282 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
1283 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
1284 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}.
1285 '''
1286 return self._distanceTo_(thomas_, other, wrap=wrap)
1288 @deprecated_method
1289 def to2ab(self): # PYCHOK no cover
1290 '''DEPRECATED, use property L{philam}.'''
1291 return self.philam
1293 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds):
1294 '''Convert this point to cartesian, I{geocentric} coordinates,
1295 also known as I{Earth-Centered, Earth-Fixed} (ECEF).
1297 @kwarg height: Optional height, overriding this point's height
1298 (C{meter}, conventionally).
1299 @kwarg Cartesian: Optional class to return the geocentric
1300 coordinates (C{Cartesian}) or C{None}.
1301 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}}
1302 keyword arguments, ignored if
1303 C{B{Cartesian} is None}.
1305 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None},
1306 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,
1307 datum)} with C{C=0} and C{M} if available.
1309 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.
1310 '''
1311 r = self._ecef9 if height is None else self.toEcef(height=height)
1312 if Cartesian is not None: # class or .classof
1313 r = self._xnamed(Cartesian(r, **Cartesian_kwds))
1314 _xdatum(r.datum, self.datum)
1315 return r
1317 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point):
1318 '''(INTERNAL) Convert to cartesian and check Ecef's before and after.
1319 '''
1320 p = self.others(up=up, **name_point)
1321 c = p.toCartesian(height=height)
1322 E = self.Ecef
1323 if E:
1324 for p in (p, c):
1325 e = getattr(p, LatLonBase.Ecef.name, None)
1326 if e not in (None, E): # PYCHOK no cover
1327 n, _ = name_point.popitem()
1328 if i is not None:
1329 Fmt.SQUARE(n, i)
1330 raise _ValueError(n, e, txt=_incompatible(E.__name__))
1331 return c
1333 def toDatum(self, datum2, height=None, name=NN):
1334 '''I{Must be overloaded}.'''
1335 notOverloaded(self, datum2, height=height, name=name)
1337 def toEcef(self, height=None, M=False):
1338 '''Convert this point to I{geocentric} coordinates, also known as
1339 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).
1341 @kwarg height: Optional height, overriding this point's height
1342 (C{meter}, conventionally).
1343 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}).
1345 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
1346 with C{C=0} and C{M} if available.
1348 @raise EcefError: A C{.datum} or an ECEF issue.
1349 '''
1350 return self._ecef9 if height in (None, self.height) else \
1351 self._Ecef_forward(self.lat, self.lon, height=height, M=M)
1353 @deprecated_method
1354 def to3llh(self, height=None): # PYCHOK no cover
1355 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.'''
1356 return self.latlonheight if height in (None, self.height) else \
1357 self.latlon.to3Tuple(height)
1359 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):
1360 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}.
1362 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}
1363 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
1364 @kwarg ltp: The I{local tangent plane} (LTP) to use,
1365 overriding this point's LTP (L{Ltp}).
1366 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
1367 arguments, ignored if C{B{Xyz} is None}.
1369 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
1370 a L{Local9Tuple}C{(x, y, z, lat, lon, height,
1371 ltp, ecef, M)} with C{M=None}, always.
1373 @raise TypeError: Invalid B{C{ltp}}.
1374 '''
1375 p = _MODS.ltp._xLtp(ltp, self._ltp)
1376 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)
1378 def toLtp(self, Ecef=None):
1379 '''Return the I{local tangent plane} (LTP) for this point.
1381 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...
1382 L{EcefYou}), overriding this point's C{Ecef}.
1383 '''
1384 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp(
1385 self, ecef=Ecef(self.datum), name=self.name)
1387 def toNormal(self, deep=False, name=NN):
1388 '''Get this point I{normalized} to C{abs(lat) <= 90}
1389 and C{abs(lon) <= 180}.
1391 @kwarg deep: If C{True} make a deep, otherwise a
1392 shallow copy (C{bool}).
1393 @kwarg name: Optional name of the copy (C{str}).
1395 @return: A copy of this point, I{normalized} and
1396 optionally renamed (C{LatLon}).
1398 @see: Property L{isnormal}, method L{normal} and function
1399 L{pygeodesy.normal}.
1400 '''
1401 ll = self.copy(deep=deep)
1402 _ = ll.normal()
1403 if name:
1404 ll.rename(name)
1405 return ll
1407 def toNvector(self, h=None, Nvector=None, **Nvector_kwds):
1408 '''Convert this point to C{n-vector} (normal to the earth's surface)
1409 components, I{including height}.
1411 @kwarg h: Optional height, overriding this point's
1412 height (C{meter}).
1413 @kwarg Nvector: Optional class to return the C{n-vector}
1414 components (C{Nvector}) or C{None}.
1415 @kwarg Nvector_kwds_wrap: Optional, additional B{C{Nvector}}
1416 keyword arguments, ignored if C{B{Nvector}
1417 is None}.
1419 @return: A B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)}
1420 if B{C{Nvector}} is C{None}.
1422 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}.
1423 '''
1424 return self.toVector(Vector=Nvector, h=self.height if h is None else h,
1425 ll=self, **Nvector_kwds)
1427 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected
1428 '''Convert this point to a "lat, lon[, +/-height]" string, formatted
1429 in the given C{B{form}at}.
1431 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see
1432 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.
1433 @kwarg joined: Separator to join the lat-, longitude and heigth
1434 strings (C{str} or C{None} or C{NN} for non-joined).
1435 @kwarg m: Optional unit of the height (C{str}), use C{None} to
1436 exclude height from the returned string.
1437 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator},
1438 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword
1439 arguments, see function L{pygeodesy.latDMS} or
1440 L{pygeodesy.lonDMS}.
1442 @return: This point in the specified C{B{form}at}, etc. (C{str} or
1443 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if
1444 C{B{joined}=NN} or C{B{joined}=None}).
1446 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more
1447 details about keyword arguments C{B{form}at}, C{B{prec}ision},
1448 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.
1450 @example:
1452 >>> LatLon(51.4778, -0.0016).toStr() # 51°28′40″N, 000°00′06″W
1453 >>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W
1454 >>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m
1455 '''
1456 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),
1457 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))
1458 if self.height and m is not None:
1459 t += (self.heightStr(m=m),)
1460 return joined.join(t) if joined else t
1462 def toVector(self, Vector=None, **Vector_kwds):
1463 '''Convert this point to C{n-vector} (normal to the earth's
1464 surface) components, I{ignoring height}.
1466 @kwarg Vector: Optional class to return the C{n-vector}
1467 components (L{Vector3d}) or C{None}.
1468 @kwarg Vector_kwds: Optional, additional B{C{Vector}}
1469 keyword arguments, ignored if
1470 C{B{Vector} is None}.
1472 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)}
1473 if B{C{Vector}} is C{None}.
1475 @raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}.
1477 @note: These are C{n-vector} x, y and z components,
1478 I{NOT} geocentric (ECEF) x, y and z coordinates!
1479 '''
1480 r = self._vector3tuple
1481 if Vector is not None:
1482 r = Vector(*r, **_xkwds(Vector_kwds, name=self.name))
1483 return r
1485 def toVector3d(self):
1486 '''Convert this point to C{n-vector} (normal to the earth's
1487 surface) components, I{ignoring height}.
1489 @return: Unit vector (L{Vector3d}).
1491 @note: These are C{n-vector} x, y and z components,
1492 I{NOT} geocentric (ECEF) x, y and z coordinates!
1493 '''
1494 return self._vector3d # XXX .unit()
1496 def toWm(self, **toWm_kwds):
1497 '''Convert this point to a WM coordinate.
1499 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments.
1501 @return: The WM coordinate (L{Wm}).
1503 @see: Function L{pygeodesy.toWm}.
1504 '''
1505 return self._wm if not toWm_kwds else _MODS.webmercator.toWm(
1506 self, **_xkwds(toWm_kwds, name=self.name))
1508 @deprecated_method
1509 def to3xyz(self): # PYCHOK no cover
1510 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector},
1511 L{toVector3d} or perhaps (geocentric) L{toEcef}.'''
1512 return self.xyz # self.toVector()
1514 @Property_RO
1515 def _vector3d(self):
1516 '''(INTERNAL) Cache for L{toVector3d}.
1517 '''
1518 return self.toVector(Vector=Vector3d) # XXX .unit()
1520 @Property_RO
1521 def _vector3tuple(self):
1522 '''(INTERNAL) Cache for L{toVector}.
1523 '''
1524 return philam2n_xyz(self.phi, self.lam, name=self.name)
1526 def vincentysTo(self, other, **radius_wrap):
1527 '''Compute the distance between this and an other point using
1528 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>}
1529 spherical formula.
1531 @arg other: The other point (C{LatLon}).
1532 @kwarg radius_wrap: Optional keyword arguments for function
1533 L{pygeodesy.vincentys}, overriding the
1534 default mean C{radius} of this point's
1535 datum ellipsoid.
1537 @return: Distance (C{meter}, same units as B{C{radius}}).
1539 @raise TypeError: The B{C{other}} point is not C{LatLon}.
1541 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo},
1542 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
1543 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
1544 L{flatPolarTo}, L{haversineTo} and L{thomasTo}.
1545 '''
1546 return self._distanceTo(vincentys, other, **_xkwds(radius_wrap, radius=None))
1548 @Property_RO
1549 def _wm(self):
1550 '''(INTERNAL) Get this point as webmercator (L{Wm}).
1551 '''
1552 return _MODS.webmercator.toWm(self)
1554 @Property_RO
1555 def xyz(self):
1556 '''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)})
1558 @note: These are C{n-vector} x, y and z components, I{NOT}
1559 geocentric (ECEF) x, y and z coordinates!
1560 '''
1561 return self.toVector(Vector=Vector3Tuple)
1563 @Property_RO
1564 def xyzh(self):
1565 '''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)})
1567 @note: These are C{n-vector} x, y and z components, I{NOT}
1568 geocentric (ECEF) x, y and z coordinates!
1569 '''
1570 return self.xyz.to4Tuple(self.height)
1573class _toCartesian3(object): # see also .geodesicw._wargs, .vector2d._numpy
1574 '''(INTERNAL) Wrapper to convert 2 other points.
1575 '''
1576 @contextmanager # <https://www.python.org/dev/peps/pep-0343/> Examples
1577 def __call__(self, p, p2, p3, wrap, **kwds):
1578 try:
1579 if wrap:
1580 p2, p3 = map1(_Wrap.point, p2, p3)
1581 kwds = _xkwds(kwds, wrap=wrap)
1582 yield (p. toCartesian().copy(name=_point_), # copy to rename
1583 p._toCartesianEcef(up=4, point2=p2),
1584 p._toCartesianEcef(up=4, point3=p3))
1585 except (AssertionError, TypeError, ValueError) as x:
1586 raise _xError(x, point=p, point2=p2, point3=p3, **kwds)
1588_toCartesian3 = _toCartesian3() # PYCHOK singleton
1591def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13
1592 radius=R_M, wrap=False):
1593 '''(INTERNAL) Trilaterate three points by I{area overlap} or by
1594 I{perimeter intersection} of three circles.
1596 @note: The B{C{radius}} is only needed for both the n-vectorial
1597 and C{sphericalTrigonometry.LatLon.distanceTo} methods and
1598 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve},
1599 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods.
1600 '''
1601 p2, p3, w = _unrollon3(p1, p2, p3, wrap)
1603 r1 = Distance_(distance1=d1)
1604 r2 = Distance_(distance2=d2)
1605 r3 = Distance_(distance3=d3)
1606 m = 0 if area else (r1 + r2 + r3)
1607 pc = 0
1608 t = []
1609 for _ in range(3):
1610 try: # intersection of circle (p1, r1) and (p2, r2)
1611 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w)
1613 if area: # check overlap
1614 if c1 is c2: # abutting
1615 c = c1
1616 else: # nearest point on radical
1617 c = p3.nearestOn(c1, c2, within=True, wrap=w)
1618 d = r3 - p3.distanceTo(c, radius=radius, wrap=w)
1619 if d > eps: # sufficient overlap
1620 t.append((d, c))
1621 m = max(m, d)
1623 else: # check intersection
1624 for c in ((c1,) if c1 is c2 else (c1, c2)):
1625 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w))
1626 if d < eps: # below margin
1627 t.append((d, c))
1628 m = min(m, d)
1630 except IntersectionError as x:
1631 if _concentric_ in str(x): # XXX ConcentricError?
1632 pc += 1
1634 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate
1636 if t: # get min, max, points and count ...
1637 t = tuple(sorted(t))
1638 n = len(t), # as 1-tuple
1639 # ... or for a single trilaterated result,
1640 # min *is* max, min- *is* maxPoint and n=1, 2 or 3
1641 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...)
1643 elif area and pc == 3: # all pairwise concentric ...
1644 r, p = min((r1, p1), (r2, p2), (r3, p3))
1645 m = max(r1, r2, r3)
1646 # ... return "smallest" point twice, the smallest
1647 # and largest distance and n=0 for concentric
1648 return Trilaterate5Tuple(float(r), p, float(m), p, 0)
1650 n, f = (_overlap_, max) if area else (_intersection_, min)
1651 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m))
1652 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t)
1655def _intersecend2(p, d, a, b, r, radius, height, exact): # in .ellipsoidalBas, .sphericalBase
1656 '''(INTERNAL) Compute the intersecant2 end-result.
1657 '''
1658 if d > EPS:
1659 s, c = sincos2d(b - a)
1660 s = sqrt_a(r, fabs(s * d))
1661 if s > r:
1662 raise IntersectionError(_too_(Fmt.distant(s)))
1663 elif (r - s) < EPS:
1664 return p, p # tangent
1665 c *= d
1666 else: # p and c coincide
1667 s, c = r, 0
1668 t = ()
1669 for d, b in ((s + c, b), (s - c, b + _180_0)): # bearing direction first
1670 t += (p.destination(d, b, radius=radius, height=height) if exact is None else
1671 p.rhumbDestination(d, b, radius=radius, height=height, exact=exact)),
1672 return t
1675__all__ += _ALL_DOCS(LatLonBase)
1677# **) MIT License
1678#
1679# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1680#
1681# Permission is hereby granted, free of charge, to any person obtaining a
1682# copy of this software and associated documentation files (the "Software"),
1683# to deal in the Software without restriction, including without limitation
1684# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1685# and/or sell copies of the Software, and to permit persons to whom the
1686# Software is furnished to do so, subject to the following conditions:
1687#
1688# The above copyright notice and this permission notice shall be included
1689# in all copies or substantial portions of the Software.
1690#
1691# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1692# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1693# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1694# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1695# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1696# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1697# OTHER DEALINGS IN THE SOFTWARE.