Coverage for pygeodesy/latlonBase.py: 93%
429 statements
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2# -*- coding: utf-8 -*-
4u'''(INTERNAL) Base class L{LatLonBase} for all elliposiodal, spherical and N-vectorial C{LatLon} classes.
6@see: I{(C) Chris Veness}' 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
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 _incompatible, IntersectionError, _IsnotError, \
20 _TypeError, _ValueError, _xdatum, _xError, \
21 _xkwds, _xkwds_not
22# from pygeodesy.fmath import favg # _MODS
23from pygeodesy.formy import antipode, compassAngle, cosineAndoyerLambert_, \
24 cosineForsytheAndoyerLambert_, cosineLaw, \
25 equirectangular, euclidean, flatLocal_, \
26 flatPolar, _hartzell, haversine, isantipode, \
27 _isequalTo, isnormal, normal, philam2n_xyz, \
28 thomas_, vincentys, _spherical_datum
29from pygeodesy.interns import NN, _COMMASPACE_, _concentric_, _height_, \
30 _intersection_, _LatLon_, _m_, _negative_, \
31 _no_, _overlap_, _point_ # PYCHOK used!
32# from pygeodesy.iters import PointsIter, points2 # from .vector3d, _MODS
33# from pygeodesy.karney import Caps # _MODS
34from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
35# from pygeodesy.ltp import Ltp, _xLtp # _MODS
36from pygeodesy.named import _NamedBase, notOverloaded, Fmt
37from pygeodesy.namedTuples import Bounds2Tuple, LatLon2Tuple, PhiLam2Tuple, \
38 Trilaterate5Tuple, Vector3Tuple
39# from pygeodesy.nvectorBase import _N_vector_ # _MODS
40from pygeodesy.props import deprecated_method, Property, Property_RO, \
41 property_RO, _update_all
42# from pygeodesy.streprs import Fmt, hstr # from .named, _MODS
43from pygeodesy.units import Distance_, Lat, Lon, Height, Radius, Radius_, \
44 Scalar, Scalar_
45from pygeodesy.utily import _unrollon, _unrollon3, _Wrap
46from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, circum4_, \
47 Circum3Tuple, _radii11ABC
48from pygeodesy.vector3d import nearestOn6, Vector3d, PointsIter
50from contextlib import contextmanager
51from math import asin, cos, degrees, fabs, radians
53__all__ = _ALL_LAZY.latlonBase
54__version__ = '23.10.04'
57class LatLonBase(_NamedBase):
58 '''(INTERNAL) Base class for C{LatLon} points on spherical or
59 ellipsoidal earth models.
60 '''
61 _clipid = INT0 # polygonal clip, see .booleans
62 _datum = None # L{Datum}, to be overriden
63 _height = INT0 # height (C{meter}), default
64 _lat = 0 # latitude (C{degrees})
65 _lon = 0 # longitude (C{degrees})
67 def __init__(self, latlonh, lon=None, height=0, wrap=False, name=NN):
68 '''New C{LatLon}.
70 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or
71 a previous C{LatLon} instance provided C{B{lon}=None}.
72 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or
73 C(None), indicating B{C{latlonh}} is a C{LatLon}.
74 @kwarg height: Optional height above (or below) the earth surface
75 (C{meter}, conventionally).
76 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}}
77 (C{bool}).
78 @kwarg name: Optional name (C{str}).
80 @return: New instance (C{LatLon}).
82 @raise RangeError: A B{C{lon}} or C{lat} value outside the valid
83 range and L{rangerrors} set to C{True}.
85 @raise TypeError: If B{C{latlonh}} is not a C{LatLon}.
87 @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}.
89 @example:
91 >>> p = LatLon(50.06632, -5.71475)
92 >>> q = LatLon('50°03′59″N', """005°42'53"W""")
93 >>> r = LatLon(p)
94 '''
95 if name:
96 self.name = name
98 if lon is None:
99 try:
100 lat, lon = latlonh.lat, latlonh.lon
101 height = latlonh.get(_height_, height)
102 except AttributeError:
103 raise _IsnotError(_LatLon_, latlonh=latlonh)
104 if wrap:
105 lat, lon = _Wrap.latlon(lat, lon)
106 elif wrap:
107 lat, lon = _Wrap.latlonDMS2(latlonh, lon)
108 else:
109 lat = latlonh
111 self._lat = Lat(lat) # parseDMS2(lat, lon)
112 self._lon = Lon(lon) # PYCHOK LatLon2Tuple
113 if height: # elevation
114 self._height = Height(height)
116 def __eq__(self, other):
117 return self.isequalTo(other)
119 def __ne__(self, other):
120 return not self.isequalTo(other)
122 def __str__(self):
123 return self.toStr(form=F_D, prec=6)
125 def antipode(self, height=None):
126 '''Return the antipode, the point diametrically opposite
127 to this point.
129 @kwarg height: Optional height of the antipode (C{meter}),
130 this point's height otherwise.
132 @return: The antipodal point (C{LatLon}).
133 '''
134 h = self._heigHt(height)
135 return self.classof(*antipode(*self.latlon), height=h)
137 @deprecated_method
138 def bounds(self, wide, tall, radius=R_M): # PYCHOK no cover
139 '''DEPRECATED, use method C{boundsOf}.'''
140 return self.boundsOf(wide, tall, radius=radius)
142 def boundsOf(self, wide, tall, radius=R_M, height=None):
143 '''Return the SW and NE lat-/longitude of a great circle
144 bounding box centered at this location.
146 @arg wide: Longitudinal box width (C{meter}, same units as
147 B{C{radius}} or C{degrees} if B{C{radius}} is C{None}).
148 @arg tall: Latitudinal box size (C{meter}, same units as
149 B{C{radius}} or C{degrees} if B{C{radius}} is C{None}).
150 @kwarg radius: Mean earth radius (C{meter}) or C{None} if I{both}
151 B{C{wide}} and B{C{tall}} are in C{degrees}.
152 @kwarg height: Height for C{latlonSW} and C{latlonNE} (C{meter}),
153 overriding the point's height.
155 @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)}, the
156 lower-left and upper-right corner (C{LatLon}).
158 @see: U{https://www.Movable-Type.co.UK/scripts/latlong-db.html}
159 '''
160 w = Scalar_(wide=wide) * _0_5
161 t = Scalar_(tall=tall) * _0_5
162 if radius is not None:
163 r = Radius_(radius)
164 c = cos(self.phi)
165 w = degrees(asin(w / r) / c) if fabs(c) > EPS0 else _0_0 # XXX
166 t = degrees(t / r)
167 y, t = self.lat, fabs(t)
168 x, w = self.lon, fabs(w)
170 h = self._heigHt(height)
171 sw = self.classof(y - t, x - w, height=h)
172 ne = self.classof(y + t, x + w, height=h)
173 return Bounds2Tuple(sw, ne, name=self.name)
175 def chordTo(self, other, height=None, wrap=False):
176 '''Compute the length of the chord through the earth between
177 this and an other point.
179 @arg other: The other point (C{LatLon}).
180 @kwarg height: Overriding height for both points (C{meter})
181 or C{None} for each point's height.
182 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{other}}
183 point (C{bool}).
185 @return: The chord length (conventionally C{meter}).
187 @raise TypeError: The B{C{other}} point is not C{LatLon}.
188 '''
189 def _v3d(ll):
190 t = ll.toEcef(height=height) # .toVector(Vector=Vector3d)
191 return Vector3d(t.x, t.y, t.z)
193 p = self.others(other)
194 if wrap:
195 p = _Wrap.point(p)
196 return _v3d(self).minus(_v3d(p)).length
198 def circin6(self, point2, point3, eps=EPS4, wrap=False):
199 '''Return the radius and center of the I{inscribed} aka I{In-}circle
200 of the (planar) triangle formed by this and two other points.
202 @arg point2: Second point (C{LatLon}).
203 @arg point3: Third point (C{LatLon}).
204 @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}.
205 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and
206 B{C{point3}} (C{bool}).
208 @return: L{Circin6Tuple}C{(radius, center, deltas, cA, cB, cC)}. The
209 C{center} and contact points C{cA}, C{cB} and C{cC}, each an
210 instance of this (sub-)class, are co-planar with this and the
211 two given points, see the B{Note} below.
213 @raise ImportError: Package C{numpy} not found, not installed or older
214 than version 1.10.
216 @raise IntersectionError: Near-coincident or -colinear points or
217 a trilateration or C{numpy} issue.
219 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
221 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted
222 back to geodetic lat-, longitude and height. The latter, conventionally
223 in C{meter} indicates whether the C{center} is above, below or on the
224 surface of the earth model. If C{deltas} is C{None}, the C{center} is
225 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon,
226 height)} representing the differences between both results from
227 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
229 @see: Function L{pygeodesy.circin6}, method L{circum3}, U{Incircle
230 <https://MathWorld.Wolfram.com/Incircle.html>} and U{Contact Triangle
231 <https://MathWorld.Wolfram.com/ContactTriangle.html>}.
232 '''
233 with _toCartesian3(self, point2, point3, wrap) as cs:
234 r, c, d, cA, cB, cC = _circin6(*cs, eps=eps, useZ=True, dLL3=True,
235 datum=self.datum) # PYCHOK unpack
236 return Circin6Tuple(r, c.toLatLon(), d, cA.toLatLon(), cB.toLatLon(), cC.toLatLon())
238 def circum3(self, point2, point3, circum=True, eps=EPS4, wrap=False):
239 '''Return the radius and center of the smallest circle I{through} or I{containing}
240 this and two other points.
242 @arg point2: Second point (C{LatLon}).
243 @arg point3: Third point (C{LatLon}).
244 @kwarg circum: If C{True} return the C{circumradius} and C{circumcenter},
245 always, ignoring the I{Meeus}' Type I case (C{bool}).
246 @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}.
247 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and
248 B{C{point3}} (C{bool}).
250 @return: A L{Circum3Tuple}C{(radius, center, deltas)}. The C{center}, an
251 instance of this (sub-)class, is co-planar with this and the two
252 given points. If C{deltas} is C{None}, the C{center} is
253 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat,
254 lon, height)} representing the difference between both results
255 from L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
257 @raise ImportError: Package C{numpy} not found, not installed or older than
258 version 1.10.
260 @raise IntersectionError: Near-concentric, -coincident or -colinear points,
261 incompatible C{Ecef} classes or a trilateration
262 or C{numpy} issue.
264 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
266 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted
267 back to geodetic lat-, longitude and height. The latter, conventionally
268 in C{meter} indicates whether the C{center} is above, below or on the
269 surface of the earth model. If C{deltas} is C{None}, the C{center} is
270 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon,
271 height)} representing the difference between both results from
272 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.
274 @see: Function L{pygeodesy.circum3} and methods L{circin6} and L{circum4_}.
275 '''
276 with _toCartesian3(self, point2, point3, wrap, circum=circum) as cs:
277 r, c, d = _circum3(*cs, circum=circum, eps=eps, useZ=True, dLL3=True, # XXX -3d2
278 clas=cs[0].classof, datum=self.datum) # PYCHOK unpack
279 return Circum3Tuple(r, c.toLatLon(), d)
281 def circum4_(self, *points, **wrap):
282 '''Best-fit a sphere through this and two or more other points.
284 @arg points: The other points (each a C{LatLon}).
285 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{points}}
286 (C{bool}), default C{False}.
288 @return: L{Circum4Tuple}C{(radius, center, rank, residuals)} with C{center}
289 an instance of this (sub-)class.
291 @raise ImportError: Package C{numpy} not found, not installed or older than
292 version 1.10.
294 @raise NumPyError: Some C{numpy} issue.
296 @raise TypeError: One of the B{C{points}} invalid.
298 @raise ValueError: Too few B{C{points}}.
300 @see: Function L{pygeodesy.circum4_} and L{circum3}.
301 '''
302 def _cs(ps, C, wrap=False):
303 _wp = _Wrap.point if wrap else (lambda p: p)
304 for i, p in enumerate(ps):
305 yield C(i=i, points=_wp(p))
307 C = self._toCartesianEcef
308 c = C(point=self)
309 t = circum4_(c, Vector=c.classof, *_cs(points, C, **wrap))
310 c = t.center.toLatLon(LatLon=self.classof)
311 return t.dup(center=c)
313 @property
314 def clipid(self):
315 '''Get the (polygonal) clip (C{int}).
316 '''
317 return self._clipid
319 @clipid.setter # PYCHOK setter!
320 def clipid(self, clipid):
321 '''Get the (polygonal) clip (C{int}).
322 '''
323 self._clipid = int(clipid)
325 @deprecated_method
326 def compassAngle(self, other, **adjust_wrap): # PYCHOK no cover
327 '''DEPRECATED, use method L{compassAngleTo}.'''
328 return self.compassAngleTo(other, **adjust_wrap)
330 def compassAngleTo(self, other, **adjust_wrap):
331 '''Return the angle from North for the direction vector between
332 this and an other point.
334 Suitable only for short, non-near-polar vectors up to a few
335 hundred Km or Miles. Use method C{initialBearingTo} for
336 larger distances.
338 @arg other: The other point (C{LatLon}).
339 @kwarg adjust_wrap: Optional keyword arguments for function
340 L{pygeodesy.compassAngle}.
342 @return: Compass angle from North (C{degrees360}).
344 @raise TypeError: The B{C{other}} point is not C{LatLon}.
346 @note: Courtesy of Martin Schultz.
348 @see: U{Local, flat earth approximation
349 <https://www.EdWilliams.org/avform.htm#flat>}.
350 '''
351 p = self.others(other)
352 return compassAngle(self.lat, self.lon, p.lat, p.lon, **adjust_wrap)
354 def cosineAndoyerLambertTo(self, other, wrap=False):
355 '''Compute the distance between this and an other point using the U{Andoyer-Lambert correction<https://
356 navlib.net/wp-content/uploads/2013/10/admiralty-manual-of-navigation-vol-1-1964-english501c.pdf>}
357 of the U{Law of Cosines<https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>} formula.
359 @arg other: The other point (C{LatLon}).
360 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
361 the B{C{other}} point (C{bool}).
363 @return: Distance (C{meter}, same units as the axes of this
364 point's datum ellipsoid).
366 @raise TypeError: The B{C{other}} point is not C{LatLon}.
368 @see: Function L{pygeodesy.cosineAndoyerLambert} and methods
369 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo},
370 C{distanceTo*}, L{equirectangularTo}, L{euclideanTo},
371 L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo},
372 L{thomasTo} and L{vincentysTo}.
373 '''
374 return self._distanceTo_(cosineAndoyerLambert_, other, wrap=wrap)
376 def cosineForsytheAndoyerLambertTo(self, other, wrap=False):
377 '''Compute the distance between this and an other point using
378 the U{Forsythe-Andoyer-Lambert correction
379 <https://www2.UNB.Ca/gge/Pubs/TR77.pdf>} of the U{Law of Cosines
380 <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>}
381 formula.
383 @arg other: The other point (C{LatLon}).
384 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
385 the B{C{other}} point (C{bool}).
387 @return: Distance (C{meter}, same units as the axes of
388 this point's datum ellipsoid).
390 @raise TypeError: The B{C{other}} point is not C{LatLon}.
392 @see: Function L{pygeodesy.cosineForsytheAndoyerLambert} and methods
393 L{cosineAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
394 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
395 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}.
396 '''
397 return self._distanceTo_(cosineForsytheAndoyerLambert_, other, wrap=wrap)
399 def cosineLawTo(self, other, radius=None, wrap=False):
400 '''Compute the distance between this and an other point using the
401 U{spherical Law of Cosines
402 <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>}
403 formula.
405 @arg other: The other point (C{LatLon}).
406 @kwarg radius: Mean earth radius (C{meter}) or C{None}
407 for the mean radius of this point's datum
408 ellipsoid.
409 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
410 the B{C{other}} point (C{bool}).
412 @return: Distance (C{meter}, same units as B{C{radius}}).
414 @raise TypeError: The B{C{other}} point is not C{LatLon}.
416 @see: Function L{pygeodesy.cosineLaw} and methods L{cosineAndoyerLambertTo},
417 L{cosineForsytheAndoyerLambertTo}, C{distanceTo*}, L{equirectangularTo},
418 L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},
419 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
420 '''
421 return self._distanceTo(cosineLaw, other, radius, wrap=wrap)
423 @property_RO
424 def datum(self): # PYCHOK no cover
425 '''I{Must be overloaded}.'''
426 notOverloaded(self)
428 def destinationXyz(self, delta, LatLon=None, **LatLon_kwds):
429 '''Calculate the destination using a I{local} delta from this point.
431 @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu},
432 L{Ned} or L{Local9Tuple}).
433 @kwarg LatLon: Optional (geodetic) class to return the destination
434 or C{None}.
435 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
436 arguments, ignored if C{B{LatLon} is None}.
438 @return: Destination as a C{B{LatLon}(lat, lon, **B{LatLon_kwds})}
439 instance or if C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat,
440 lon, height)} respectively L{LatLon4Tuple}C{(lat, lon,
441 height, datum)} depending on whether a C{datum} keyword
442 is un-/specified.
444 @raise TypeError: Invalid B{C{delta}}, B{C{LatLon}} or B{C{LatLon_kwds}}.
445 '''
446 t = self._ltp._local2ecef(delta, nine=True)
447 return t.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, name=self.name))
449 def _distanceTo(self, func, other, radius=None, **kwds):
450 '''(INTERNAL) Helper for distance methods C{<func>To}.
451 '''
452 p, r = self.others(other, up=2), radius
453 if r is None:
454 r = self._datum.ellipsoid.R1 if self._datum else R_M
455 return func(self.lat, self.lon, p.lat, p.lon, radius=r, **kwds)
457 def _distanceTo_(self, func_, other, wrap=False, radius=None):
458 '''(INTERNAL) Helper for (ellipsoidal) methods C{<func>To}.
459 '''
460 p = self.others(other, up=2)
461 D = self.datum
462 lam21, phi2, _ = _Wrap.philam3(self.lam, p.phi, p.lam, wrap)
463 r = func_(phi2, self.phi, lam21, datum=D)
464 return r * (D.ellipsoid.a if radius is None else radius)
466 @Property_RO
467 def Ecef(self):
468 '''Get the ECEF I{class} (L{EcefKarney}), I{lazily}.
469 '''
470 return _MODS.ecef.EcefKarney # default
472 @Property_RO
473 def _Ecef_forward(self):
474 '''(INTERNAL) Helper for L{_ecef9} and L{toEcef} (C{callable}).
475 '''
476 return self.Ecef(self.datum, name=self.name).forward
478 @Property_RO
479 def _ecef9(self):
480 '''(INTERNAL) Helper for L{toCartesian}, L{toEcef} and L{toCartesian} (L{Ecef9Tuple}).
481 '''
482 return self._Ecef_forward(self, M=True)
484 @deprecated_method
485 def equals(self, other, eps=None): # PYCHOK no cover
486 '''DEPRECATED, use method L{isequalTo}.'''
487 return self.isequalTo(other, eps=eps)
489 @deprecated_method
490 def equals3(self, other, eps=None): # PYCHOK no cover
491 '''DEPRECATED, use method L{isequalTo3}.'''
492 return self.isequalTo3(other, eps=eps)
494 def equirectangularTo(self, other, **radius_adjust_limit_wrap):
495 '''Compute the distance between this and an other point
496 using the U{Equirectangular Approximation / Projection
497 <https://www.Movable-Type.co.UK/scripts/latlong.html#equirectangular>}.
499 Suitable only for short, non-near-polar distances up to a
500 few hundred Km or Miles. Use method L{haversineTo} or
501 C{distanceTo*} for more accurate and/or larger distances.
503 @arg other: The other point (C{LatLon}).
504 @kwarg radius_adjust_limit_wrap: Optional keyword arguments
505 for function L{pygeodesy.equirectangular},
506 overriding the default mean C{radius} of this
507 point's datum ellipsoid.
509 @return: Distance (C{meter}, same units as B{C{radius}}).
511 @raise TypeError: The B{C{other}} point is not C{LatLon}.
513 @see: Function L{pygeodesy.equirectangular} and methods L{cosineAndoyerLambertTo},
514 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
515 C{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},
516 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
517 '''
518 return self._distanceTo(equirectangular, other, **radius_adjust_limit_wrap)
520 def euclideanTo(self, other, **radius_adjust_wrap):
521 '''Approximate the C{Euclidian} distance between this and
522 an other point.
524 See function L{pygeodesy.euclidean} for the available B{C{options}}.
526 @arg other: The other point (C{LatLon}).
527 @kwarg radius_adjust_wrap: Optional keyword arguments for function
528 L{pygeodesy.euclidean}, overriding the default mean
529 C{radius} of this point's datum ellipsoid.
531 @return: Distance (C{meter}, same units as B{C{radius}}).
533 @raise TypeError: The B{C{other}} point is not C{LatLon}.
535 @see: Function L{pygeodesy.euclidean} and methods L{cosineAndoyerLambertTo},
536 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
537 L{equirectangularTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},
538 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
539 '''
540 return self._distanceTo(euclidean, other, **radius_adjust_wrap)
542 def flatLocalTo(self, other, radius=None, wrap=False):
543 '''Compute the distance between this and an other point using the
544 U{ellipsoidal Earth to plane projection
545 <https://WikiPedia.org/wiki/Geographical_distance#Ellipsoidal_Earth_projected_to_a_plane>}
546 aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>} formula.
548 @arg other: The other point (C{LatLon}).
549 @kwarg radius: Mean earth radius (C{meter}) or C{None} for
550 the I{equatorial radius} of this point's
551 datum ellipsoid.
552 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
553 the B{C{other}} point (C{bool}).
555 @return: Distance (C{meter}, same units as B{C{radius}}).
557 @raise TypeError: The B{C{other}} point is not C{LatLon}.
559 @raise ValueError: Invalid B{C{radius}}.
561 @see: Function L{pygeodesy.flatLocal}/L{pygeodesy.hubeny}, methods
562 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo},
563 L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo},
564 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo} and
565 U{local, flat Earth approximation<https://www.edwilliams.org/avform.htm#flat>}.
566 '''
567 return self._distanceTo_(flatLocal_, other, wrap=wrap, radius=
568 radius if radius in (None, R_M, _1_0, 1) else Radius(radius)) # PYCHOK kwargs
570 hubenyTo = flatLocalTo # for Karl Hubeny
572 def flatPolarTo(self, other, **radius_wrap):
573 '''Compute the distance between this and an other point using
574 the U{polar coordinate flat-Earth<https://WikiPedia.org/wiki/
575 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula.
577 @arg other: The other point (C{LatLon}).
578 @kwarg radius_wrap: Optional keyword arguments for function
579 L{pygeodesy.flatPolar}, overriding the
580 default mean C{radius} of this point's
581 datum ellipsoid.
583 @return: Distance (C{meter}, same units as B{C{radius}}).
585 @raise TypeError: The B{C{other}} point is not C{LatLon}.
587 @see: Function L{pygeodesy.flatPolar} and methods L{cosineAndoyerLambertTo},
588 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
589 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
590 L{haversineTo}, L{thomasTo} and L{vincentysTo}.
591 '''
592 return self._distanceTo(flatPolar, other, **radius_wrap)
594 def hartzell(self, los=None, earth=None):
595 '''Compute the intersection of a Line-Of-Sight (los) from this Point-Of-View
596 (pov) with this point's ellipsoid surface.
598 @kwarg los: Line-Of-Sight, I{direction} to earth (L{Los}, L{Vector3d})
599 or C{None} to point to the ellipsoid's center.
600 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},
601 L{a_f2Tuple} or C{scalar} radius in C{meter}) overriding
602 this point's C{datum} ellipsoid.
604 @return: The ellipsoid intersection (C{LatLon}) with C{.height} set
605 to the distance to this C{pov}.
607 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov}
608 is inside the ellipsoid or B{C{los}} points
609 outside or away from the ellipsoid.
611 @raise TypeError: Invalid B{C{los}}.
613 @see: Function C{hartzell} for further details.
614 '''
615 return _hartzell(self, los, earth, LatLon=self.classof)
617 def haversineTo(self, other, **radius_wrap):
618 '''Compute the distance between this and an other point using the
619 U{Haversine<https://www.Movable-Type.co.UK/scripts/latlong.html>}
620 formula.
622 @arg other: The other point (C{LatLon}).
623 @kwarg radius_wrap: Optional keyword arguments for function
624 L{pygeodesy.haversine}, overriding the
625 default mean C{radius} of this point's
626 datum ellipsoid.
628 @return: Distance (C{meter}, same units as B{C{radius}}).
630 @raise TypeError: The B{C{other}} point is not C{LatLon}.
632 @see: Function L{pygeodesy.haversine} and methods L{cosineAndoyerLambertTo},
633 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
634 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
635 L{flatPolarTo}, L{thomasTo} and L{vincentysTo}.
636 '''
637 return self._distanceTo(haversine, other, **radius_wrap)
639 def _havg(self, other, f=_0_5, h=None):
640 '''(INTERNAL) Weighted, average height.
642 @arg other: An other point (C{LatLon}).
643 @kwarg f: Optional fraction (C{float}).
644 @kwarg h: Overriding height (C{meter}).
646 @return: Average, fractional height (C{float}) or
647 the overriding B{C{height}} (C{Height}).
648 '''
649 return Height(h) if h is not None else \
650 _MODS.fmath.favg(self.height, other.height, f=f)
652 @Property
653 def height(self):
654 '''Get the height (C{meter}).
655 '''
656 return self._height
658 @height.setter # PYCHOK setter!
659 def height(self, height):
660 '''Set the height (C{meter}).
662 @raise TypeError: Invalid B{C{height}} C{type}.
664 @raise ValueError: Invalid B{C{height}}.
665 '''
666 h = Height(height)
667 if self._height != h:
668 _update_all(self)
669 self._height = h
671 def _heigHt(self, height):
672 '''(INTERNAL) Overriding this C{height}.
673 '''
674 return self.height if height is None else Height(height)
676 def height4(self, earth=None, normal=True, LatLon=None, **LatLon_kwds):
677 '''Compute the height above or below and the projection of this point
678 on this datum's or on an other earth's ellipsoid surface.
680 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius
681 I{overriding} this datum (L{Datum}, L{Ellipsoid},
682 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
683 L{JacobiConformal} or C{meter}, conventionally).
684 @kwarg normal: If C{True} the projection is the nearest point on the
685 ellipsoid's surface, otherwise the intersection of the
686 radial line to the center and the ellipsoid's surface.
687 @kwarg LatLon: Optional class to return the height and projection
688 (C{LatLon}) or C{None}.
689 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
690 ignored if C{B{LatLon} is None}.
692 @note: Use keyword argument C{height=0} to override C{B{LatLon}.height}
693 to {0} or any other C{scalar}, conventionally in C{meter}.
695 @return: An instance of B{C{LatLon}} or if C{B{LatLon} is None}, a
696 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
697 and C{z} coordinates and height C{h} in C{meter}, conventionally.
699 @raise TriaxialError: No convergence in triaxial root finding.
701 @raise TypeError: Invalid B{C{earth}}.
703 @see: L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
704 '''
705 c = self.toCartesian()
706 if LatLon is None:
707 r = c.height4(earth=earth, normal=normal)
708 else:
709 r = c.height4(earth=earth, normal=normal, Cartesian=c.classof, height=0)
710 r = r.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, height=r.height))
711 return r
713 def heightStr(self, prec=-2, m=_m_):
714 '''Return this point's B{C{height}} as C{str}ing.
716 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
717 @kwarg m: Optional unit of the height (C{str}).
719 @see: Function L{pygeodesy.hstr}.
720 '''
721 return _MODS.streprs.hstr(self.height, prec=prec, m=m)
723 @deprecated_method
724 def isantipode(self, other, eps=EPS): # PYCHOK no cover
725 '''DEPRECATED, use method L{isantipodeTo}.'''
726 return self.isantipodeTo(other, eps=eps)
728 def isantipodeTo(self, other, eps=EPS):
729 '''Check whether this and an other point are antipodal,
730 on diametrically opposite sides of the earth.
732 @arg other: The other point (C{LatLon}).
733 @kwarg eps: Tolerance for near-equality (C{degrees}).
735 @return: C{True} if points are antipodal within the given
736 tolerance, C{False} otherwise.
737 '''
738 p = self.others(other)
739 return isantipode(*(self.latlon + p.latlon), eps=eps)
741 @Property_RO
742 def isEllipsoidal(self):
743 '''Check whether this point is ellipsoidal (C{bool} or C{None} if unknown).
744 '''
745 return self.datum.isEllipsoidal if self._datum else None
747 @Property_RO
748 def isEllipsoidalLatLon(self):
749 '''Get C{LatLon} base.
750 '''
751 return False
753 def isequalTo(self, other, eps=None):
754 '''Compare this point with an other point, I{ignoring} height.
756 @arg other: The other point (C{LatLon}).
757 @kwarg eps: Tolerance for equality (C{degrees}).
759 @return: C{True} if both points are identical,
760 I{ignoring} height, C{False} otherwise.
762 @raise TypeError: The B{C{other}} point is not C{LatLon}
763 or mismatch of the B{C{other}} and
764 this C{class} or C{type}.
766 @raise UnitError: Invalid B{C{eps}}.
768 @see: Method L{isequalTo3}.
769 '''
770 return _isequalTo(self, self.others(other), eps=eps)
772 def isequalTo3(self, other, eps=None):
773 '''Compare this point with an other point, I{including} height.
775 @arg other: The other point (C{LatLon}).
776 @kwarg eps: Tolerance for equality (C{degrees}).
778 @return: C{True} if both points are identical
779 I{including} height, C{False} otherwise.
781 @raise TypeError: The B{C{other}} point is not C{LatLon}
782 or mismatch of the B{C{other}} and
783 this C{class} or C{type}.
785 @see: Method L{isequalTo}.
786 '''
787 return self.height == self.others(other).height and \
788 _isequalTo(self, other, eps=eps)
790 @Property_RO
791 def isnormal(self):
792 '''Return C{True} if this point is normal (C{bool}),
793 meaning C{abs(lat) <= 90} and C{abs(lon) <= 180}.
795 @see: Methods L{normal}, L{toNormal} and functions
796 L{pygeodesy.isnormal} and L{pygeodesy.normal}.
797 '''
798 return isnormal(self.lat, self.lon, eps=0)
800 @Property_RO
801 def isSpherical(self):
802 '''Check whether this point is spherical (C{bool} or C{None} if unknown).
803 '''
804 return self.datum.isSpherical if self._datum else None
806 @Property_RO
807 def lam(self):
808 '''Get the longitude (B{C{radians}}).
809 '''
810 return radians(self.lon)
812 @Property
813 def lat(self):
814 '''Get the latitude (C{degrees90}).
815 '''
816 return self._lat
818 @lat.setter # PYCHOK setter!
819 def lat(self, lat):
820 '''Set the latitude (C{str[N|S]} or C{degrees}).
822 @raise ValueError: Invalid B{C{lat}}.
823 '''
824 lat = Lat(lat) # parseDMS(lat, suffix=_NS_, clip=90)
825 if self._lat != lat:
826 _update_all(self)
827 self._lat = lat
829 @Property
830 def latlon(self):
831 '''Get the lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).
832 '''
833 return LatLon2Tuple(self._lat, self._lon, name=self.name)
835 @latlon.setter # PYCHOK setter!
836 def latlon(self, latlonh):
837 '''Set the lat- and longitude and optionally the height
838 (2- or 3-tuple or comma- or space-separated C{str}
839 of C{degrees90}, C{degrees180} and C{meter}).
841 @raise TypeError: Height of B{C{latlonh}} not C{scalar} or
842 B{C{latlonh}} not C{list} or C{tuple}.
844 @raise ValueError: Invalid B{C{latlonh}} or M{len(latlonh)}.
846 @see: Function L{pygeodesy.parse3llh} to parse a B{C{latlonh}}
847 string into a 3-tuple C{(lat, lon, h)}.
848 '''
849 if isstr(latlonh):
850 latlonh = parse3llh(latlonh, height=self.height)
851 else:
852 _xinstanceof(list, tuple, latlonh=latlonh)
853 if len(latlonh) == 3:
854 h = Height(latlonh[2], name=Fmt.SQUARE(latlonh=2))
855 elif len(latlonh) != 2:
856 raise _ValueError(latlonh=latlonh)
857 else:
858 h = self.height
860 llh = Lat(latlonh[0]), Lon(latlonh[1]), h # parseDMS2(latlonh[0], latlonh[1])
861 if (self._lat, self._lon, self._height) != llh:
862 _update_all(self)
863 self._lat, self._lon, self._height = llh
865 def latlon2(self, ndigits=0):
866 '''Return this point's lat- and longitude in C{degrees}, rounded.
868 @kwarg ndigits: Number of (decimal) digits (C{int}).
870 @return: A L{LatLon2Tuple}C{(lat, lon)}, both C{float}
871 and rounded away from zero.
873 @note: The C{round}ed values are always C{float}, also
874 if B{C{ndigits}} is omitted.
875 '''
876 return LatLon2Tuple(round(self.lat, ndigits),
877 round(self.lon, ndigits), name=self.name)
879 @deprecated_method
880 def latlon_(self, ndigits=0): # PYCHOK no cover
881 '''DEPRECATED, use method L{latlon2}.'''
882 return self.latlon2(ndigits=ndigits)
884 latlon2round = latlon_ # PYCHOK no cover
886 @Property
887 def latlonheight(self):
888 '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).
889 '''
890 return self.latlon.to3Tuple(self.height)
892 @latlonheight.setter # PYCHOK setter!
893 def latlonheight(self, latlonh):
894 '''Set the lat- and longitude and optionally the height
895 (2- or 3-tuple or comma- or space-separated C{str}
896 of C{degrees90}, C{degrees180} and C{meter}).
898 @see: Property L{latlon} for more details.
899 '''
900 self.latlon = latlonh
902 @Property
903 def lon(self):
904 '''Get the longitude (C{degrees180}).
905 '''
906 return self._lon
908 @lon.setter # PYCHOK setter!
909 def lon(self, lon):
910 '''Set the longitude (C{str[E|W]} or C{degrees}).
912 @raise ValueError: Invalid B{C{lon}}.
913 '''
914 lon = Lon(lon) # parseDMS(lon, suffix=_EW_, clip=180)
915 if self._lon != lon:
916 _update_all(self)
917 self._lon = lon
919 @Property_RO
920 def _ltp(self):
921 '''(INTERNAL) Cache for L{toLtp}.
922 '''
923 return _MODS.ltp.Ltp(self, ecef=self.Ecef(self.datum), name=self.name)
925 def nearestOn6(self, points, closed=False, height=None, wrap=False):
926 '''Locate the point on a path or polygon closest to this point.
928 Points are converted to and distances are computed in
929 I{geocentric}, cartesian space.
931 @arg points: The path or polygon points (C{LatLon}[]).
932 @kwarg closed: Optionally, close the polygon (C{bool}).
933 @kwarg height: Optional height, overriding the height of
934 this and all other points (C{meter}). If
935 C{None}, take the height of points into
936 account for distances.
937 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
938 the B{C{points}} (C{bool}).
940 @return: A L{NearestOn6Tuple}C{(closest, distance, fi, j,
941 start, end)} with the C{closest}, the C{start}
942 and the C{end} point each an instance of this
943 C{LatLon} and C{distance} in C{meter}, same
944 units as the cartesian axes.
946 @raise PointsError: Insufficient number of B{C{points}}.
948 @raise TypeError: Some B{C{points}} or some B{C{points}}'
949 C{Ecef} invalid.
951 @raise ValueError: Some B{C{points}}' C{Ecef} is incompatible.
953 @see: Function L{pygeodesy.nearestOn6}.
954 '''
955 def _cs(Ps, h, w, C):
956 p = None # not used
957 for i, q in Ps.enumerate():
958 if w and i:
959 q = _unrollon(p, q)
960 yield C(height=h, i=i, up=3, points=q)
961 p = q
963 C = self._toCartesianEcef # to verify datum and Ecef
964 Ps = self.PointsIter(points, wrap=wrap)
966 c = C(height=height, this=self) # this Cartesian
967 t = nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed)
968 c, s, e = t.closest, t.start, t.end
970 kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon
971 height=height)
972 _r = self.Ecef(self.datum).reverse
973 p = _r(c).toLatLon(**kwds)
974 s = _r(s).toLatLon(**kwds) if s is not c else p
975 e = _r(e).toLatLon(**kwds) if e is not c else p
976 return t.dup(closest=p, start=s, end=e)
978 def normal(self):
979 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and
980 C{abs(lon) <= 180}.
982 @return: C{True} if this point was I{normal}, C{False} if it
983 wasn't (but is now).
985 @see: Property L{isnormal} and method L{toNormal}.
986 '''
987 n = self.isnormal
988 if not n:
989 self.latlon = normal(*self.latlon)
990 return n
992 @Property_RO
993 def _N_vector(self):
994 '''(INTERNAL) Get the (C{nvectorBase._N_vector_})
995 '''
996 return _MODS.nvectorBase._N_vector_(*self.xyzh)
998 @Property_RO
999 def phi(self):
1000 '''Get the latitude (B{C{radians}}).
1001 '''
1002 return radians(self.lat)
1004 @Property_RO
1005 def philam(self):
1006 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).
1007 '''
1008 return PhiLam2Tuple(self.phi, self.lam, name=self.name)
1010 def philam2(self, ndigits=0):
1011 '''Return this point's lat- and longitude in C{radians}, rounded.
1013 @kwarg ndigits: Number of (decimal) digits (C{int}).
1015 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float}
1016 and rounded away from zero.
1018 @note: The C{round}ed values are always C{float}, also
1019 if B{C{ndigits}} is omitted.
1020 '''
1021 return PhiLam2Tuple(round(self.phi, ndigits),
1022 round(self.lam, ndigits), name=self.name)
1024 @Property_RO
1025 def philamheight(self):
1026 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
1027 '''
1028 return self.philam.to3Tuple(self.height)
1030 @deprecated_method
1031 def points(self, points, closed=True): # PYCHOK no cover
1032 '''DEPRECATED, use method L{points2}.'''
1033 return self.points2(points, closed=closed)
1035 def points2(self, points, closed=True):
1036 '''Check a path or polygon represented by points.
1038 @arg points: The path or polygon points (C{LatLon}[])
1039 @kwarg closed: Optionally, consider the polygon closed,
1040 ignoring any duplicate or closing final
1041 B{C{points}} (C{bool}).
1043 @return: A L{Points2Tuple}C{(number, points)}, an C{int}
1044 and C{list} or C{tuple}.
1046 @raise PointsError: Insufficient number of B{C{points}}.
1048 @raise TypeError: Some B{C{points}} are not C{LatLon}.
1049 '''
1050 return _MODS.iters.points2(points, closed=closed, base=self)
1052 def PointsIter(self, points, loop=0, dedup=False, wrap=False):
1053 '''Return a C{PointsIter} iterator.
1055 @arg points: The path or polygon points (C{LatLon}[])
1056 @kwarg loop: Number of loop-back points (non-negative C{int}).
1057 @kwarg dedup: Skip duplicate points (C{bool}).
1058 @kwarg wrap: If C{True}, wrap or I{normalize} the
1059 enum-/iterated B{C{points}} (C{bool}).
1061 @return: A new C{PointsIter} iterator.
1063 @raise PointsError: Insufficient number of B{C{points}}.
1064 '''
1065 return PointsIter(points, base=self, loop=loop, dedup=dedup, wrap=wrap)
1067 def radii11(self, point2, point3, wrap=False):
1068 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent}
1069 circles of a (planar) triangle formed by this and two other points.
1071 @arg point2: Second point (C{LatLon}).
1072 @arg point3: Third point (C{LatLon}).
1073 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and
1074 B{C{point3}} (C{bool}).
1076 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.
1078 @raise IntersectionError: Near-coincident or -colinear points.
1080 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
1082 @see: Function L{pygeodesy.radii11}, U{Incircle
1083 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles
1084 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent
1085 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}.
1086 '''
1087 with _toCartesian3(self, point2, point3, wrap) as cs:
1088 return _radii11ABC(*cs, useZ=True)[0]
1090 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3
1091 '''(INTERNAL) Get the C{rhumb} for this point's datum or for
1092 the B{C{radius}}' earth model iff non-C{None}.
1093 '''
1094 try:
1095 d = self._rhumb3dict
1096 t = d[(exact, radius)]
1097 except KeyError:
1098 D = self.datum if radius is None else _spherical_datum(radius) # ellipsoidal OK
1099 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical)
1100 t = r, D, _MODS.karney.Caps
1101 while d:
1102 d.popitem()
1103 d[(exact, radius)] = t # cache 3-tuple
1104 return t
1106 @Property_RO
1107 def _rhumb3dict(self):
1108 return {} # single-item cache
1110 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False):
1111 '''Return the azimuth (bearing) of a rhumb line (loxodrome)
1112 between this and an other (ellipsoidal) point.
1114 @arg other: The other point (C{LatLon}).
1115 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1116 see method L{Ellipsoid.rhumb_}.
1117 @kwarg radius: Optional earth radius (C{meter}) or earth model
1118 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1119 L{a_f2Tuple}), overriding this point's datum.
1120 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1121 B{C{other}} point (C{bool}).
1123 @return: Rhumb azimuth (compass C{degrees360}).
1125 @raise TypeError: The B{C{other}} point is incompatible or
1126 B{C{radius}} is invalid.
1127 '''
1128 r, _, Cs = self._rhumb3(exact, radius)
1129 return r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12
1131 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None):
1132 '''Return the destination point having travelled the given distance
1133 from this point along a rhumb line (loxodrome) at the given azimuth.
1135 @arg distance: Distance travelled (C{meter}, same units as this
1136 point's datum (ellipsoid) axes or B{C{radius}},
1137 may be negative.
1138 @arg azimuth: Azimuth (bearing) at this point (compass C{degrees}).
1139 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1140 see method L{Ellipsoid.rhumb_}.
1141 @kwarg radius: Optional earth radius (C{meter}) or earth model
1142 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1143 L{a_f2Tuple}), overriding this point's datum.
1144 @kwarg height: Optional height, overriding the default height
1145 (C{meter}).
1147 @return: The destination point (ellipsoidal C{LatLon}).
1149 @raise TypeError: Invalid B{C{radius}}.
1151 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}},
1152 B{C{radius}} or B{C{height}}.
1153 '''
1154 r, D, _ = self._rhumb3(exact, radius)
1155 d = r._Direct(self, azimuth, distance)
1156 h = self._heigHt(height)
1157 return self.classof(d.lat2, d.lon2, datum=D, height=h)
1159 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False):
1160 '''Return the distance from this to an other point along
1161 a rhumb line (loxodrome).
1163 @arg other: The other point (C{LatLon}).
1164 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1165 see method L{Ellipsoid.rhumb_}.
1166 @kwarg radius: Optional earth radius (C{meter}) or earth model
1167 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1168 L{a_f2Tuple}), overriding this point's datum.
1169 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1170 B{C{other}} point (C{bool}).
1172 @return: Distance (C{meter}, the same units as this point's
1173 datum (ellipsoid) axes or B{C{radius}}.
1175 @raise TypeError: The B{C{other}} point is incompatible or
1176 B{C{radius}} is invalid.
1178 @raise ValueError: Invalid B{C{radius}}.
1179 '''
1180 r, _, Cs = self._rhumb3(exact, radius)
1181 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12
1183 def rhumbLine(self, azimuth_other, exact=False, radius=None, wrap=False,
1184 **name_caps):
1185 '''Get a rhumb line through this point at a given azimuth or
1186 through this and an other point.
1188 @arg azimuth_other: The azimuth of the rhumb line (compass
1189 C{degrees}) or the other point (C{LatLon}).
1190 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1191 see method L{Ellipsoid.rhumb_}.
1192 @kwarg radius: Optional earth radius (C{meter}) or earth model
1193 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1194 L{a_f2Tuple}), overriding this point's datum.
1195 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1196 C{azimuth_B{other}} point (C{bool}).
1197 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see
1198 L{RhumbLine} C{B{caps}}.
1200 @return: A C{RhumbLine} instance.
1202 @raise TypeError: Invalid B{C{radius}} or BC{C{azimuth_other}}
1203 not a C{scalar} nor a C{LatLon}.
1205 @see: Modules L{rhumbaux} and L{rhumbx}.
1206 '''
1207 r, _, _ = self._rhumb3(exact, radius)
1208 a, kwds = azimuth_other, _xkwds(name_caps, name=self.name)
1209 if isscalar(a):
1210 r = r._DirectLine(self, a, **kwds)
1211 elif isinstance(a, LatLonBase):
1212 r = r._InverseLine(self, a, wrap, **kwds)
1213 else:
1214 raise _TypeError(azimuth_other=a)
1215 return r
1217 def rhumbMidpointTo(self, other, exact=False, radius=None,
1218 height=None, fraction=_0_5, wrap=False):
1219 '''Return the (loxodromic) midpoint on the rhumb line between
1220 this and an other point.
1222 @arg other: The other point (C{LatLon}).
1223 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),
1224 see method L{Ellipsoid.rhumb_}.
1225 @kwarg radius: Optional earth radius (C{meter}) or earth model
1226 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or
1227 L{a_f2Tuple}), overriding this point's datum.
1228 @kwarg height: Optional height, overriding the mean height
1229 (C{meter}).
1230 @kwarg fraction: Midpoint location from this point (C{scalar}), 0
1231 for this, 1 for the B{C{other}}, 0.5 for halfway
1232 between this and the B{C{other}} point, may be
1233 negative or greater than 1.
1234 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
1235 B{C{other}} point (C{bool}).
1237 @return: The midpoint at the given B{C{fraction}} along the
1238 rhumb line (C{LatLon}).
1240 @raise TypeError: The B{C{other}} point is incompatible or
1241 B{C{radius}} is invalid.
1243 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}.
1244 '''
1245 r, D, _ = self._rhumb3(exact, radius)
1246 f = Scalar(fraction=fraction)
1247 d = r._Inverse(self, other, wrap) # C.AZIMUTH_DISTANCE
1248 d = r._Direct( self, d.azi12, d.s12 * f)
1249 h = self._havg(other, f=f, h=height)
1250 return self.classof(d.lat2, d.lon2, datum=D, height=h)
1252 def thomasTo(self, other, wrap=False):
1253 '''Compute the distance between this and an other point using
1254 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>}
1255 formula.
1257 @arg other: The other point (C{LatLon}).
1258 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
1259 the B{C{other}} point (C{bool}).
1261 @return: Distance (C{meter}, same units as the axes of
1262 this point's datum ellipsoid).
1264 @raise TypeError: The B{C{other}} point is not C{LatLon}.
1266 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo},
1267 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
1268 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
1269 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}.
1270 '''
1271 return self._distanceTo_(thomas_, other, wrap=wrap)
1273 @deprecated_method
1274 def to2ab(self): # PYCHOK no cover
1275 '''DEPRECATED, use property L{philam}.'''
1276 return self.philam
1278 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds):
1279 '''Convert this point to cartesian, I{geocentric} coordinates,
1280 also known as I{Earth-Centered, Earth-Fixed} (ECEF).
1282 @kwarg height: Optional height, overriding this point's height
1283 (C{meter}, conventionally).
1284 @kwarg Cartesian: Optional class to return the geocentric
1285 coordinates (C{Cartesian}) or C{None}.
1286 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}}
1287 keyword arguments, ignored if
1288 C{B{Cartesian} is None}.
1290 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None},
1291 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,
1292 datum)} with C{C=0} and C{M} if available.
1294 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.
1295 '''
1296 r = self._ecef9 if height is None else self.toEcef(height=height)
1297 if Cartesian is not None: # class or .classof
1298 r = self._xnamed(Cartesian(r, **Cartesian_kwds))
1299 _xdatum(r.datum, self.datum)
1300 return r
1302 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point):
1303 '''(INTERNAL) Convert to cartesian and check Ecef's before and after.
1304 '''
1305 p = self.others(up=up, **name_point)
1306 c = p.toCartesian(height=height)
1307 E = self.Ecef
1308 if E:
1309 for p in (p, c):
1310 e = getattr(p, LatLonBase.Ecef.name, None)
1311 if e not in (None, E): # PYCHOK no cover
1312 n, _ = name_point.popitem()
1313 if i is not None:
1314 Fmt.SQUARE(n, i)
1315 raise _ValueError(n, e, txt=_incompatible(E.__name__))
1316 return c
1318 def toDatum(self, datum2, height=None, name=NN):
1319 '''I{Must be overloaded}.'''
1320 notOverloaded(self, datum2, height=height, name=name)
1322 def toEcef(self, height=None, M=False):
1323 '''Convert this point to I{geocentric} coordinates, also known as
1324 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).
1326 @kwarg height: Optional height, overriding this point's height
1327 (C{meter}, conventionally).
1328 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}).
1330 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
1331 with C{C=0} and C{M} if available.
1333 @raise EcefError: A C{.datum} or an ECEF issue.
1334 '''
1335 return self._ecef9 if height in (None, self.height) else \
1336 self._Ecef_forward(self.lat, self.lon, height=height, M=M)
1338 @deprecated_method
1339 def to3llh(self, height=None): # PYCHOK no cover
1340 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.'''
1341 return self.latlonheight if height in (None, self.height) else \
1342 self.latlon.to3Tuple(height)
1344 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):
1345 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}.
1347 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}
1348 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
1349 @kwarg ltp: The I{local tangent plane} (LTP) to use,
1350 overriding this point's LTP (L{Ltp}).
1351 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
1352 arguments, ignored if C{B{Xyz} is None}.
1354 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
1355 a L{Local9Tuple}C{(x, y, z, lat, lon, height,
1356 ltp, ecef, M)} with C{M=None}, always.
1358 @raise TypeError: Invalid B{C{ltp}}.
1359 '''
1360 p = _MODS.ltp._xLtp(ltp, self._ltp)
1361 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)
1363 def toLtp(self, Ecef=None):
1364 '''Return the I{local tangent plane} (LTP) for this point.
1366 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...
1367 L{EcefYou}), overriding this point's C{Ecef}.
1368 '''
1369 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp(
1370 self, ecef=Ecef(self.datum), name=self.name)
1372 def toNormal(self, deep=False, name=NN):
1373 '''Get this point I{normalized} to C{abs(lat) <= 90}
1374 and C{abs(lon) <= 180}.
1376 @kwarg deep: If C{True} make a deep, otherwise a
1377 shallow copy (C{bool}).
1378 @kwarg name: Optional name of the copy (C{str}).
1380 @return: A copy of this point, I{normalized} and
1381 optionally renamed (C{LatLon}).
1383 @see: Property L{isnormal}, method L{normal} and function
1384 L{pygeodesy.normal}.
1385 '''
1386 ll = self.copy(deep=deep)
1387 _ = ll.normal()
1388 if name:
1389 ll.rename(name)
1390 return ll
1392 def toNvector(self, h=None, Nvector=None, **Nvector_kwds):
1393 '''Convert this point to C{n-vector} (normal to the earth's surface)
1394 components, I{including height}.
1396 @kwarg h: Optional height, overriding this point's
1397 height (C{meter}).
1398 @kwarg Nvector: Optional class to return the C{n-vector}
1399 components (C{Nvector}) or C{None}.
1400 @kwarg Nvector_kwds_wrap: Optional, additional B{C{Nvector}}
1401 keyword arguments, ignored if C{B{Nvector}
1402 is None}.
1404 @return: A B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)}
1405 if B{C{Nvector}} is C{None}.
1407 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}.
1408 '''
1409 return self.toVector(Vector=Nvector, h=self.height if h is None else h,
1410 ll=self, **Nvector_kwds)
1412 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected
1413 '''Convert this point to a "lat, lon[, +/-height]" string, formatted
1414 in the given C{B{form}at}.
1416 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see
1417 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.
1418 @kwarg joined: Separator to join the lat-, longitude and heigth
1419 strings (C{str} or C{None} or C{NN} for non-joined).
1420 @kwarg m: Optional unit of the height (C{str}), use C{None} to
1421 exclude height from the returned string.
1422 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator},
1423 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword
1424 arguments, see function L{pygeodesy.latDMS} or
1425 L{pygeodesy.lonDMS}.
1427 @return: This point in the specified C{B{form}at}, etc. (C{str} or
1428 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if
1429 C{B{joined}=NN} or C{B{joined}=None}).
1431 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more
1432 details about keyword arguments C{B{form}at}, C{B{prec}ision},
1433 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.
1435 @example:
1437 >>> LatLon(51.4778, -0.0016).toStr() # 51°28′40″N, 000°00′06″W
1438 >>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W
1439 >>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m
1440 '''
1441 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),
1442 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))
1443 if self.height and m is not None:
1444 t += (self.heightStr(m=m),)
1445 return joined.join(t) if joined else t
1447 def toVector(self, Vector=None, **Vector_kwds):
1448 '''Convert this point to C{n-vector} (normal to the earth's
1449 surface) components, I{ignoring height}.
1451 @kwarg Vector: Optional class to return the C{n-vector}
1452 components (L{Vector3d}) or C{None}.
1453 @kwarg Vector_kwds: Optional, additional B{C{Vector}}
1454 keyword arguments, ignored if
1455 C{B{Vector} is None}.
1457 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)}
1458 if B{C{Vector}} is C{None}.
1460 @raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}.
1462 @note: These are C{n-vector} x, y and z components,
1463 I{NOT} geocentric (ECEF) x, y and z coordinates!
1464 '''
1465 r = self._vector3tuple
1466 if Vector is not None:
1467 r = Vector(*r, **_xkwds(Vector_kwds, name=self.name))
1468 return r
1470 def toVector3d(self):
1471 '''Convert this point to C{n-vector} (normal to the earth's
1472 surface) components, I{ignoring height}.
1474 @return: Unit vector (L{Vector3d}).
1476 @note: These are C{n-vector} x, y and z components,
1477 I{NOT} geocentric (ECEF) x, y and z coordinates!
1478 '''
1479 return self._vector3d # XXX .unit()
1481 def toWm(self, **toWm_kwds):
1482 '''Convert this point to a WM coordinate.
1484 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments.
1486 @return: The WM coordinate (L{Wm}).
1488 @see: Function L{pygeodesy.toWm}.
1489 '''
1490 return self._wm if not toWm_kwds else _MODS.webmercator.toWm(
1491 self, **_xkwds(toWm_kwds, name=self.name))
1493 @deprecated_method
1494 def to3xyz(self): # PYCHOK no cover
1495 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector},
1496 L{toVector3d} or perhaps (geocentric) L{toEcef}.'''
1497 return self.xyz # self.toVector()
1499 @Property_RO
1500 def _vector3d(self):
1501 '''(INTERNAL) Cache for L{toVector3d}.
1502 '''
1503 return self.toVector(Vector=Vector3d) # XXX .unit()
1505 @Property_RO
1506 def _vector3tuple(self):
1507 '''(INTERNAL) Cache for L{toVector}.
1508 '''
1509 return philam2n_xyz(self.phi, self.lam, name=self.name)
1511 def vincentysTo(self, other, **radius_wrap):
1512 '''Compute the distance between this and an other point using
1513 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>}
1514 spherical formula.
1516 @arg other: The other point (C{LatLon}).
1517 @kwarg radius_wrap: Optional keyword arguments for function
1518 L{pygeodesy.vincentys}, overriding the
1519 default mean C{radius} of this point's
1520 datum ellipsoid.
1522 @return: Distance (C{meter}, same units as B{C{radius}}).
1524 @raise TypeError: The B{C{other}} point is not C{LatLon}.
1526 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo},
1527 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},
1528 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},
1529 L{flatPolarTo}, L{haversineTo} and L{thomasTo}.
1530 '''
1531 return self._distanceTo(vincentys, other, **_xkwds(radius_wrap, radius=None))
1533 @Property_RO
1534 def _wm(self):
1535 '''(INTERNAL) Get this point as webmercator (L{Wm}).
1536 '''
1537 return _MODS.webmercator.toWm(self)
1539 @Property_RO
1540 def xyz(self):
1541 '''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)})
1543 @note: These are C{n-vector} x, y and z components, I{NOT}
1544 geocentric (ECEF) x, y and z coordinates!
1545 '''
1546 return self.toVector(Vector=Vector3Tuple)
1548 @Property_RO
1549 def xyzh(self):
1550 '''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)})
1552 @note: These are C{n-vector} x, y and z components, I{NOT}
1553 geocentric (ECEF) x, y and z coordinates!
1554 '''
1555 return self.xyz.to4Tuple(self.height)
1558class _toCartesian3(object): # see also .geodesicw._wargs, .vector2d._numpy
1559 '''(INTERNAL) Wrapper to convert 2 other points.
1560 '''
1561 @contextmanager # <https://www.python.org/dev/peps/pep-0343/> Examples
1562 def __call__(self, p, p2, p3, wrap, **kwds):
1563 try:
1564 if wrap:
1565 p2, p3 = map1(_Wrap.point, p2, p3)
1566 kwds = _xkwds(kwds, wrap=wrap)
1567 yield (p. toCartesian().copy(name=_point_), # copy to rename
1568 p._toCartesianEcef(up=4, point2=p2),
1569 p._toCartesianEcef(up=4, point3=p3))
1570 except (AssertionError, TypeError, ValueError) as x:
1571 raise _xError(x, point=p, point2=p2, point3=p3, **kwds)
1573_toCartesian3 = _toCartesian3() # PYCHOK singleton
1576def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13
1577 radius=R_M, wrap=False):
1578 '''(INTERNAL) Trilaterate three points by I{area overlap} or by
1579 I{perimeter intersection} of three circles.
1581 @note: The B{C{radius}} is only needed for both the n-vectorial
1582 and C{sphericalTrigonometry.LatLon.distanceTo} methods and
1583 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve},
1584 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods.
1585 '''
1586 p2, p3, w = _unrollon3(p1, p2, p3, wrap)
1588 r1 = Distance_(distance1=d1)
1589 r2 = Distance_(distance2=d2)
1590 r3 = Distance_(distance3=d3)
1591 m = 0 if area else (r1 + r2 + r3)
1592 pc = 0
1593 t = []
1594 for _ in range(3):
1595 try: # intersection of circle (p1, r1) and (p2, r2)
1596 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w)
1598 if area: # check overlap
1599 if c1 is c2: # abutting
1600 c = c1
1601 else: # nearest point on radical
1602 c = p3.nearestOn(c1, c2, within=True, wrap=w)
1603 d = r3 - p3.distanceTo(c, radius=radius, wrap=w)
1604 if d > eps: # sufficient overlap
1605 t.append((d, c))
1606 m = max(m, d)
1608 else: # check intersection
1609 for c in ((c1,) if c1 is c2 else (c1, c2)):
1610 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w))
1611 if d < eps: # below margin
1612 t.append((d, c))
1613 m = min(m, d)
1615 except IntersectionError as x:
1616 if _concentric_ in str(x): # XXX ConcentricError?
1617 pc += 1
1619 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate
1621 if t: # get min, max, points and count ...
1622 t = tuple(sorted(t))
1623 n = len(t), # as 1-tuple
1624 # ... or for a single trilaterated result,
1625 # min *is* max, min- *is* maxPoint and n=1, 2 or 3
1626 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...)
1628 elif area and pc == 3: # all pairwise concentric ...
1629 r, p = min((r1, p1), (r2, p2), (r3, p3))
1630 m = max(r1, r2, r3)
1631 # ... return "smallest" point twice, the smallest
1632 # and largest distance and n=0 for concentric
1633 return Trilaterate5Tuple(float(r), p, float(m), p, 0)
1635 n, f = (_overlap_, max) if area else (_intersection_, min)
1636 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m))
1637 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t)
1640__all__ += _ALL_DOCS(LatLonBase)
1642# **) MIT License
1643#
1644# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1645#
1646# Permission is hereby granted, free of charge, to any person obtaining a
1647# copy of this software and associated documentation files (the "Software"),
1648# to deal in the Software without restriction, including without limitation
1649# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1650# and/or sell copies of the Software, and to permit persons to whom the
1651# Software is furnished to do so, subject to the following conditions:
1652#
1653# The above copyright notice and this permission notice shall be included
1654# in all copies or substantial portions of the Software.
1655#
1656# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1657# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1658# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1659# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1660# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1661# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1662# OTHER DEALINGS IN THE SOFTWARE.