Coverage for pygeodesy/ellipsoidalBase.py: 95%
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2# -*- coding: utf-8 -*-
4u'''(INTERNAL) Private ellipsoidal base classes C{CartesianEllipsoidalBase}
5and C{LatLonEllipsoidalBase}.
7A pure Python implementation of geodesy tools for ellipsoidal earth models,
8transcoded in part from JavaScript originals by I{(C) Chris Veness 2005-2016}
9and published under the same MIT Licence**, see for example U{latlon-ellipsoidal
10<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
11'''
12# make sure int/int division yields float quotient, see .basics
13from __future__ import division as _; del _ # PYCHOK semicolon
15# from pygeodesy.basics import _xinstanceof # from .datums
16from pygeodesy.constants import EPS, EPS0, EPS1, _0_0, _0_5
17from pygeodesy.cartesianBase import CartesianBase, _ellipsoidal_ # PYCHOK used!
18from pygeodesy.datums import Datum, Datums, _ellipsoidal_datum, \
19 _spherical_datum, _WGS84, _xinstanceof
20from pygeodesy.errors import _incompatible, _IsnotError, RangeError, TRFError, \
21 _ValueError, _xellipsoidal, _xError, _xkwds, \
22 _xkwds_get, _xkwds_not
23# from pygeodesy.interns import _ellipsoidal_ # from .cartesianBase
24from pygeodesy.interns import MISSING, NN, _COMMA_, _conversion_, _datum_, \
25 _DOT_, _no_, _reframe_, _SPACE_
26from pygeodesy.latlonBase import fabs, LatLonBase, _trilaterate5, Vector3Tuple
27from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
28# from pygeodesy.lcc import toLcc # from ._MODS
29# from pygeodesy.named import notOverloaded # from ._MODS
30# from pygeodesy.namedTuples import Vector3Tuple # from .latlonBase
31from pygeodesy.props import deprecated_method, deprecated_property_RO, \
32 Property_RO, property_doc_, property_RO, _update_all
33from pygeodesy.units import Epoch, _1mm as _TOL_M, Radius_
35# from math import fabs # from .karney
37__all__ = _ALL_LAZY.ellipsoidalBase
38__version__ = '23.04.02'
41class CartesianEllipsoidalBase(CartesianBase):
42 '''(INTERNAL) Base class for ellipsoidal C{Cartesian}s.
43 '''
44 _datum = _WGS84 # L{Datum}
45 _reframe = None
47# def __matmul__(self, other): # PYCHOK Python 3.5+
48# '''Return C{NotImplemented} for C{c_ = c @ datum}, C{c_ = c @ reframe} and C{c_ = c @ Transform}.
49# '''
50# RefFrame = _MODS.trf.RefFrame
51# return NotImplemented if isinstance(other, (Datum, RefFrame, Transform)) else \
52# _NotImplemented(self, other)
54 @deprecated_method
55 def convertRefFrame(self, reframe2, reframe, epoch=None):
56 '''DEPRECATED, use method L{toRefFrame}.'''
57 return self.toRefFrame(reframe2, reframe, epoch=epoch)
59 def intersections2(self, radius, center2, radius2, sphere=True,
60 Vector=None, **Vector_kwds):
61 '''Compute the intersection of two spheres or circles, each defined by a
62 cartesian center point and a radius.
64 @arg radius: Radius of this sphere or circle (same units as this point's
65 coordinates).
66 @arg center2: Center of the second sphere or circle (C{Cartesian}, L{Vector3d},
67 C{Vector3Tuple} or C{Vector4Tuple}).
68 @arg radius2: Radius of the second sphere or circle (same units as this and
69 the B{C{other}} point's coordinates).
70 @kwarg sphere: If C{True} compute the center and radius of the intersection
71 of two I{spheres}. If C{False}, ignore the C{z}-component and
72 compute the intersection of two I{circles} (C{bool}).
73 @kwarg Vector: Class to return intersections (C{Cartesian}, L{Vector3d} or
74 C{Vector3Tuple}) or C{None} for an instance of this (sub-)class.
75 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments,
76 ignored if C{B{Vector} is None}.
78 @return: If B{C{sphere}} is C{True}, a 2-tuple of the C{center} and C{radius}
79 of the intersection of the I{spheres}. The C{radius} is C{0.0} for
80 abutting spheres (and the C{center} is aka I{radical center}).
82 If B{C{sphere}} is C{False}, a 2-tuple with the two intersection
83 points of the I{circles}. For abutting circles, both points are
84 the same instance, aka I{radical center}.
86 @raise IntersectionError: Concentric, invalid or non-intersecting spheres or circles.
88 @raise TypeError: Invalid B{C{center2}}.
90 @raise UnitError: Invalid B{C{radius}} or B{C{radius2}}.
92 @see: U{Sphere-Sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>},
93 U{Circle-Circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>}
94 Intersection and function L{pygeodesy.radical2}.
95 '''
96 try:
97 return _MODS.vector3d._intersects2(self, Radius_(radius=radius),
98 center2, Radius_(radius2=radius2),
99 sphere=sphere, clas=self.classof,
100 Vector=Vector, **Vector_kwds)
101 except (TypeError, ValueError) as x:
102 raise _xError(x, center=self, radius=radius, center2=center2, radius2=radius2)
104 @property_doc_(''' this cartesian's reference frame (L{RefFrame}).''')
105 def reframe(self):
106 '''Get this cartesian's reference frame (L{RefFrame}) or C{None}.
107 '''
108 return self._reframe
110 @reframe.setter # PYCHOK setter!
111 def reframe(self, reframe):
112 '''Set or clear this cartesian's reference frame (L{RefFrame}) or C{None}.
114 @raise TypeError: The B{C{reframe}} is not a L{RefFrame}.
115 '''
116 _set_reframe(self, reframe)
118 def toRefFrame(self, reframe2, reframe=None, epoch=None):
119 '''Convert this cartesian point from one to an other reference frame.
121 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
122 @arg reframe: Reference frame to convert I{from} (L{RefFrame}),
123 overriding this cartesian's C{reframe}.
124 @kwarg epoch: Optional epoch to observe (C{scalar}, fractional
125 calendar year), overriding B{C{reframe}}'s epoch.
127 @return: The converted point (C{Cartesian}) or this point if
128 conversion is C{nil}.
130 @raise TRFError: No conversion available from B{C{reframe}}
131 to B{C{reframe2}} or invalid B{C{epoch}}.
133 @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a
134 L{RefFrame}.
135 '''
136 r = self.reframe if reframe is None else reframe
137 if r in (None, reframe2):
138 xs = None # XXX _set_reframe(self, reframe2)?
139 else:
140 trf = _MODS.trf
141 _xinstanceof(trf.RefFrame, reframe2=reframe2, reframe=r)
142 _, xs = trf._reframeTransforms2(reframe2, r, epoch)
143 return self.toTransforms_(*xs) if xs else self
145 def toTransforms_(self, *transforms, **datum):
146 '''Apply none, one or several Helmert transforms.
148 @arg transforms: Transforms to apply, in order (L{Transform}s).
149 @kwarg datum: Datum for the transformed point (L{Datum}),
150 overriding this point's datum.
152 @return: The transformed point (C{Cartesian}) or this point
153 if the B{C{transforms}} produce the same point.
154 '''
155 r = self
156 if transforms:
157 xyz = r.xyz
158 for t in transforms:
159 xyz = t.transform(*xyz)
160 d = _xkwds_get(datum, datum=r.datum)
161 if d != r.datum or xyz != r.xyz:
162 r = r.classof(xyz, datum=d)
163 return r
166class LatLonEllipsoidalBase(LatLonBase):
167 '''(INTERNAL) Base class for ellipsoidal C{LatLon}s.
168 '''
169 _datum = _WGS84 # L{Datum}
170 _elevation2to = None # _elevation2 timeout (C{secs})
171 _epoch = None # overriding .reframe.epoch (C{float})
172 _gamma = None # UTM/UPS meridian convergence (C{degrees})
173 _geoidHeight2to = None # _geoidHeight2 timeout (C{secs})
174 _reframe = None # reference frame (L{RefFrame})
175 _scale = None # UTM/UPS scale factor (C{float})
176 _toLLEB_args = () # Etm/Utm/Ups._toLLEB arguments
178 def __init__(self, lat, lon, height=0, datum=None, reframe=None,
179 epoch=None, name=NN):
180 '''Create an ellipsoidal C{LatLon} point frome the given
181 lat-, longitude and height on the given datum and with
182 the given reference frame and epoch.
184 @arg lat: Latitude (C{degrees} or DMS C{[N|S]}).
185 @arg lon: Longitude (C{degrees} or DMS C{str[E|W]}).
186 @kwarg height: Optional elevation (C{meter}, the same units
187 as the datum's half-axes).
188 @kwarg datum: Optional, ellipsoidal datum to use (L{Datum},
189 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
190 @kwarg reframe: Optional reference frame (L{RefFrame}).
191 @kwarg epoch: Optional epoch to observe for B{C{reframe}}
192 (C{scalar}), a non-zero, fractional calendar
193 year; silently ignored if C{B{reframe} is None}.
194 @kwarg name: Optional name (string).
196 @raise RangeError: Value of B{C{lat}} or B{C{lon}} outside the valid
197 range and C{rangerrors} set to C{True}.
199 @raise TypeError: B{C{datum}} is not a L{Datum}, B{C{reframe}}
200 is not a L{RefFrame} or B{C{epoch}} is not
201 C{scalar} non-zero.
203 @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}.
205 @example:
207 >>> p = LatLon(51.4778, -0.0016) # height=0, datum=Datums.WGS84
208 '''
209 LatLonBase.__init__(self, lat, lon, height=height, name=name)
210 if datum not in (None, self._datum):
211 self.datum = _ellipsoidal_datum(datum, name=name)
212 if reframe:
213 self.reframe = reframe
214 self.epoch = epoch
216# def __matmul__(self, other): # PYCHOK Python 3.5+
217# '''Return C{NotImplemented} for C{ll_ = ll @ datum} and C{ll_ = ll @ reframe}.
218# '''
219# RefFrame = _MODS.trf.RefFrame
220# return NotImplemented if isinstance(other, (Datum, RefFrame)) else \
221# _NotImplemented(self, other)
223 def antipode(self, height=None):
224 '''Return the antipode, the point diametrically opposite
225 to this point.
227 @kwarg height: Optional height of the antipode, height
228 of this point otherwise (C{meter}).
230 @return: The antipodal point (C{LatLon}).
231 '''
232 lla = LatLonBase.antipode(self, height=height)
233 if lla.datum != self.datum:
234 lla.datum = self.datum
235 return lla
237 @deprecated_property_RO
238 def convergence(self):
239 '''DEPRECATED, use property C{gamma}.'''
240 return self.gamma
242 @deprecated_method
243 def convertDatum(self, datum2):
244 '''DEPRECATED, use method L{toDatum}.'''
245 return self.toDatum(datum2)
247 @deprecated_method
248 def convertRefFrame(self, reframe2):
249 '''DEPRECATED, use method L{toRefFrame}.'''
250 return self.toRefFrame(reframe2)
252 @Property_RO
253 def _css(self):
254 '''(INTERNAL) Get this C{LatLon} point as a Cassini-Soldner location (L{Css}).
255 '''
256 css = _MODS.css
257 return css.toCss(self, height=self.height, Css=css.Css, name=self.name)
259 @property_doc_(''' this points's datum (L{Datum}).''')
260 def datum(self):
261 '''Get this point's datum (L{Datum}).
262 '''
263 return self._datum
265 @datum.setter # PYCHOK setter!
266 def datum(self, datum):
267 '''Set this point's datum I{without conversion} (L{Datum}).
269 @raise TypeError: The B{C{datum}} is not a L{Datum}
270 or not ellipsoidal.
271 '''
272 _xinstanceof(Datum, datum=datum)
273 if not datum.isEllipsoidal:
274 raise _IsnotError(_ellipsoidal_, datum=datum)
275 if self._datum != datum:
276 _update_all(self)
277 self._datum = datum
279 def distanceTo2(self, other):
280 '''I{Approximate} the distance and (initial) bearing between this
281 and an other (ellipsoidal) point based on the radii of curvature.
283 I{Suitable only for short distances up to a few hundred Km
284 or Miles and only between points not near-polar}.
286 @arg other: The other point (C{LatLon}).
288 @return: An L{Distance2Tuple}C{(distance, initial)}.
290 @raise TypeError: The B{C{other}} point is not C{LatLon}.
292 @raise ValueError: Incompatible datum ellipsoids.
294 @see: Method L{Ellipsoid.distance2} and U{Local, flat earth
295 approximation<https://www.EdWilliams.org/avform.htm#flat>}
296 aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>}
297 formula.
298 '''
299 return self.ellipsoids(other).distance2(self.lat, self.lon,
300 other.lat, other.lon)
302 @Property_RO
303 def _elevation2(self):
304 '''(INTERNAL) Get elevation and data source.
305 '''
306 return _MODS.elevations.elevation2(self.lat, self.lon,
307 timeout=self._elevation2to)
309 def elevation2(self, adjust=True, datum=None, timeout=2):
310 '''Return elevation of this point for its or the given datum, ellipsoid
311 or sphere.
313 @kwarg adjust: Adjust the elevation for a B{C{datum}} other than
314 C{NAD83} (C{bool}).
315 @kwarg datum: Optional datum overriding this point's datum (L{Datum},
316 L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar}
317 radius).
318 @kwarg timeout: Optional query timeout (C{seconds}).
320 @return: An L{Elevation2Tuple}C{(elevation, data_source)} or
321 C{(None, error)} in case of errors.
323 @note: The adjustment applied is the difference in geocentric earth
324 radius between the B{C{datum}} and C{NAV83} upon which the
325 L{elevations.elevation2} is based.
327 @note: NED elevation is only available for locations within the
328 U{Conterminous US (CONUS)
329 <https://WikiPedia.org/wiki/Contiguous_United_States>}.
331 @see: Function L{elevations.elevation2} and method C{Ellipsoid.Rgeocentric}
332 for further details and possible C{error}s.
333 '''
334 if self._elevation2to != timeout:
335 self._elevation2to = timeout
336 LatLonEllipsoidalBase._elevation2._update(self)
337 return self._Radjust2(adjust, datum, self._elevation2)
339 def ellipsoid(self, datum=_WGS84):
340 '''Return the ellipsoid of this point's datum or the given datum.
342 @kwarg datum: Default datum (L{Datum}).
344 @return: The ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
345 '''
346 return getattr(self, _datum_, datum).ellipsoid
348 def ellipsoids(self, other):
349 '''Check the type and ellipsoid of this and an other point's datum.
351 @arg other: The other point (C{LatLon}).
353 @return: This point's datum ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
355 @raise TypeError: The B{C{other}} point is not C{LatLon}.
357 @raise ValueError: Incompatible datum ellipsoids.
358 '''
359 self.others(other, up=2) # ellipsoids' caller
361 E = self.ellipsoid()
362 try: # other may be Sphere, etc.
363 e = other.ellipsoid()
364 except AttributeError:
365 try: # no ellipsoid method, try datum
366 e = other.datum.ellipsoid
367 except AttributeError:
368 e = E # no datum, XXX assume equivalent?
369 if e != E:
370 raise _ValueError(e.named2, txt=_incompatible(E.named2))
371 return E
373 @property_doc_(''' this point's observed or C{reframe} epoch (C{float}).''')
374 def epoch(self):
375 '''Get this point's observed or C{reframe} epoch (C{float}) or C{None}.
376 '''
377 return self._epoch or (self.reframe.epoch if self.reframe else None)
379 @epoch.setter # PYCHOK setter!
380 def epoch(self, epoch):
381 '''Set or clear this point's observed epoch, a fractional
382 calendar year (L{Epoch}, C{scalar}) or C{None}.
384 @raise TRFError: Invalid B{C{epoch}}.
385 '''
386 self._epoch = None if epoch is None else Epoch(epoch)
388 @Property_RO
389 def Equidistant(self):
390 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantKarney} or L{EquidistantExact}).
391 '''
392 try:
393 _ = self.datum.ellipsoid.geodesic
394 return _MODS.azimuthal.EquidistantKarney
395 except ImportError: # no geographiclib
396 return _MODS.azimuthal.EquidistantExact # XXX no longer L{azimuthal.Equidistant}
398 @Property_RO
399 def _etm(self):
400 '''(INTERNAL) Get this C{LatLon} point as an ETM coordinate (L{pygeodesy.toEtm8}).
401 '''
402 etm = _MODS.etm
403 return etm.toEtm8(self, datum=self.datum, Etm=etm.Etm)
405 @property_RO
406 def gamma(self):
407 '''Get this point's UTM or UPS meridian convergence (C{degrees}) or
408 C{None} if not available or not converted from L{Utm} or L{Ups}.
409 '''
410 return self._gamma
412 @Property_RO
413 def _geoidHeight2(self):
414 '''(INTERNAL) Get geoid height and model.
415 '''
416 return _MODS.elevations.geoidHeight2(self.lat, self.lon, model=0,
417 timeout=self._geoidHeight2to)
419 def geoidHeight2(self, adjust=False, datum=None, timeout=2):
420 '''Return geoid height of this point for its or the given datum, ellipsoid
421 or sphere.
423 @kwarg adjust: Adjust the geoid height for a B{C{datum}} other than
424 C{NAD83/NADV88} (C{bool}).
425 @kwarg datum: Optional datum overriding this point's datum (L{Datum},
426 L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar}
427 radius).
428 @kwarg timeout: Optional query timeout (C{seconds}).
430 @return: A L{GeoidHeight2Tuple}C{(height, model_name)} or
431 C{(None, error)} in case of errors.
433 @note: The adjustment applied is the difference in geocentric earth
434 radius between the B{C{datum}} and C{NAV83/NADV88} upon which
435 the L{elevations.geoidHeight2} is based.
437 @note: The geoid height is only available for locations within the
438 U{Conterminous US (CONUS)
439 <https://WikiPedia.org/wiki/Contiguous_United_States>}.
441 @see: Function L{elevations.geoidHeight2} and method C{Ellipsoid.Rgeocentric}
442 for further details and possible C{error}s.
443 '''
444 if self._geoidHeight2to != timeout:
445 self._geoidHeight2to = timeout
446 LatLonEllipsoidalBase._geoidHeight2._update(self)
447 return self._Radjust2(adjust, datum, self._geoidHeight2)
449 def intermediateTo(self, other, fraction, height=None, wrap=False): # PYCHOK no cover
450 '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}.
451 '''
452 _MODS.named.notOverloaded(self, other, fraction, height=height, wrap=wrap)
454 def intersection3(self, end1, other, end2, height=None, wrap=True,
455 equidistant=None, tol=_TOL_M):
456 '''Iteratively compute the intersection point of two paths, each
457 defined by two points or a start point and bearing from North.
459 @arg end1: End point of this path (C{LatLon}) or the initial
460 bearing at this point (compass C{degrees360}).
461 @arg other: Start point of the other path (C{LatLon}).
462 @arg end2: End point of the other path (C{LatLon}) or the
463 initial bearing at the other point (compass
464 C{degrees360}).
465 @kwarg height: Optional height at the intersection (C{meter},
466 conventionally) or C{None} for the mean height.
467 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
468 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
469 function L{pygeodesy.equidistant}), or C{None}
470 for this point's preferred C{.Equidistant}.
471 @kwarg tol: Tolerance for skew line distance and length and for
472 convergence (C{meter}, conventionally).
474 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)}
475 with C{point} a C{LatLon} instance.
477 @raise ImportError: Package U{geographiclib
478 <https://PyPI.org/project/geographiclib>}
479 not installed or not found, but only if
480 C{B{equidistant}=}L{EquidistantKarney}.
482 @raise IntersectionError: Skew, colinear, parallel or otherwise
483 non-intersecting paths or no convergence
484 for the given B{C{tol}}.
486 @raise TypeError: If B{C{end1}}, B{C{other}} or B{C{end2}} point
487 is not C{LatLon}.
489 @note: For each path specified with an initial bearing, a pseudo-end
490 point is computed as the C{destination} along that bearing at
491 about 1.5 times the distance from the start point to an initial
492 gu-/estimate of the intersection point (and between 1/8 and 3/8
493 of the authalic earth perimeter).
495 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
496 calculating-intersection-of-two-circles>} and U{Karney's paper
497 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
498 BOUNDARIES} for more details about the iteration algorithm.
499 '''
500 try:
501 s2 = self.others(other)
502 return _MODS.ellipsoidalBaseDI._intersect3(self, end1,
503 s2, end2,
504 height=height, wrap=wrap,
505 equidistant=equidistant, tol=tol,
506 LatLon=self.classof, datum=self.datum)
507 except (TypeError, ValueError) as x:
508 raise _xError(x, start1=self, end1=end1, other=other, end2=end2,
509 height=height, wrap=wrap, tol=tol)
511 def intersections2(self, radius1, other, radius2, height=None, wrap=True,
512 equidistant=None, tol=_TOL_M):
513 '''Iteratively compute the intersection points of two circles,
514 each defined by a center point and a radius.
516 @arg radius1: Radius of this circle (C{meter}, conventionally).
517 @arg other: Center of the other circle (C{LatLon}).
518 @arg radius2: Radius of the other circle (C{meter}, same units as
519 B{C{radius1}}).
520 @kwarg height: Optional height for the intersection points (C{meter},
521 conventionally) or C{None} for the I{"radical height"}
522 at the I{radical line} between both centers.
523 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
524 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
525 function L{pygeodesy.equidistant}), or C{None}
526 for this point's preferred C{.Equidistant}.
527 @kwarg tol: Convergence tolerance (C{meter}, same units as
528 B{C{radius1}} and B{C{radius2}}).
530 @return: 2-Tuple of the intersection points, each a C{LatLon}
531 instance. For abutting circles, both intersection
532 points are the same instance, aka I{radical center}.
534 @raise ImportError: Package U{geographiclib
535 <https://PyPI.org/project/geographiclib>}
536 not installed or not found, but only if
537 C{B{equidistant}=}L{EquidistantKarney}.
539 @raise IntersectionError: Concentric, antipodal, invalid or
540 non-intersecting circles or no
541 convergence for the given B{C{tol}}.
543 @raise TypeError: Invalid B{C{other}} or B{C{equidistant}}.
545 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
547 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
548 calculating-intersection-of-two-circles>}, U{Karney's paper
549 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
550 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
551 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
552 intersections.
553 '''
554 try:
555 c2 = self.others(other)
556 return _MODS.ellipsoidalBaseDI._intersections2(self, radius1,
557 c2, radius2,
558 height=height, wrap=wrap,
559 equidistant=equidistant, tol=tol,
560 LatLon=self.classof, datum=self.datum)
561 except (AssertionError, TypeError, ValueError) as x:
562 raise _xError(x, center=self, radius1=radius1, other=other, radius2=radius2,
563 height=height, wrap=wrap, tol=tol)
565 @Property_RO
566 def isEllipsoidalLatLon(self):
567 '''Get C{LatLon} base.
568 '''
569 return True
571 def isenclosedBy(self, points, wrap=False):
572 '''Check whether a polygon or composite encloses this point.
574 @arg points: The polygon points or clips (C{LatLon}[],
575 L{BooleanFHP} or L{BooleanGH}).
576 @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}).
578 @return: C{True} if this point is inside the polygon or composite,
579 C{False} otherwise.
581 @raise PointsError: Insufficient number of B{C{points}}.
583 @raise TypeError: Some B{C{points}} are not C{LatLon}.
585 @raise ValueError: Invalid B{C{point}}, lat- or longitude.
587 @see: Functions L{pygeodesy.isconvex}, L{pygeodesy.isenclosedBy}
588 and L{pygeodesy.ispolar} especially if the B{C{points}} may
589 enclose a pole or wrap around the earth I{longitudinally}.
590 '''
591 return _MODS.points.isenclosedBy(self, points, wrap=wrap)
593 @property_RO
594 def iteration(self):
595 '''Get the most recent C{intersections2} or C{nearestOn} iteration
596 number (C{int}) or C{None} if not available/applicable.
597 '''
598 return self._iteration
600 @Property_RO
601 def _lcc(self):
602 '''(INTERNAL) Get this C{LatLon} point as a Lambert location (L{Lcc}).
603 '''
604 lcc = _MODS.lcc
605 return lcc.toLcc(self, height=self.height, Lcc=lcc.Lcc, name=self.name)
607 def midpointTo(self, other, height=None, fraction=_0_5, wrap=False):
608 '''Find the midpoint on a geodesic between this and an other point.
610 @arg other: The other point (C{LatLon}).
611 @kwarg height: Optional height for midpoint, overriding the
612 mean height (C{meter}).
613 @kwarg fraction: Midpoint location from this point (C{scalar}),
614 may be negative or greater than 1.0.
615 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
617 @return: Midpoint (C{LatLon}).
619 @raise TypeError: The B{C{other}} point is not C{LatLon}.
621 @raise ValueError: Invalid B{C{height}}.
623 @see: Methods C{intermediateTo} and C{rhumbMidpointTo}.
624 '''
625 return self.intermediateTo(other, fraction, height=height, wrap=wrap)
627 def nearestOn(self, point1, point2, within=True, height=None, wrap=True,
628 equidistant=None, tol=_TOL_M):
629 '''Iteratively locate the closest point on the geodesic between
630 two other (ellipsoidal) points.
632 @arg point1: Start point (C{LatLon}).
633 @arg point2: End point (C{LatLon}).
634 @kwarg within: If C{True} return the closest point I{between}
635 B{C{point1}} and B{C{point2}}, otherwise the
636 closest point elsewhere on the geodesic (C{bool}).
637 @kwarg height: Optional height for the closest point (C{meter},
638 conventionally) or C{None} or C{False} for the
639 interpolated height. If C{False}, the closest
640 takes the heights of the points into account.
641 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
642 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
643 function L{pygeodesy.equidistant}), or C{None}
644 for this point's preferred C{.Equidistant}.
645 @kwarg tol: Convergence tolerance (C{meter}, conventionally).
647 @return: Closest point (C{LatLon}).
649 @raise ImportError: Package U{geographiclib
650 <https://PyPI.org/project/geographiclib>}
651 not installed or not found, but only if
652 C{B{equidistant}=}L{EquidistantKarney}.
654 @raise TypeError: Invalid B{C{point1}}, B{C{point2}} or
655 B{C{equidistant}}.
657 @raise ValueError: Datum or ellipsoid of B{C{point1}} or B{C{point2}} is
658 incompatible or no convergence for the given B{C{tol}}.
660 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
661 calculating-intersection-of-two-circles>} and U{Karney's paper
662 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
663 BOUNDARIES} for details about the iteration algorithm.
664 '''
665 try:
666 t = _MODS.ellipsoidalBaseDI._nearestOn2(self, point1, point2, within=within,
667 height=height, wrap=wrap,
668 equidistant=equidistant,
669 tol=tol, LatLon=self.classof)
670 except (TypeError, ValueError) as x:
671 raise _xError(x, point=self, point1=point1, point2=point2, within=within,
672 height=height, wrap=wrap, tol=tol)
673 return t.closest
675 @Property_RO
676 def _osgr(self):
677 '''(INTERNAL) Get this C{LatLon} point as an OSGR coordinate (L{Osgr}),
678 based on the OS recommendation.
679 '''
680 return _MODS.osgr.toOsgr(self, kTM=False, name=self.name) # datum=self.datum
682 @Property_RO
683 def _osgrTM(self):
684 '''(INTERNAL) Get this C{LatLon} point as an OSGR coordinate (L{Osgr})
685 based on I{Karney}'s Krüger implementation.
686 '''
687 return _MODS.osgr.toOsgr(self, kTM=True, name=self.name) # datum=self.datum
689 def parse(self, strllh, height=0, datum=None, epoch=None, reframe=None,
690 sep=_COMMA_, name=NN):
691 '''Parse a string representing a similar, ellipsoidal C{LatLon}
692 point, consisting of C{"lat, lon[, height]"}.
694 @arg strllh: Lat, lon and optional height (C{str}),
695 see function L{pygeodesy.parse3llh}.
696 @kwarg height: Optional, default height (C{meter} or
697 C{None}).
698 @kwarg datum: Optional datum (L{Datum}), overriding this
699 datum I{without conversion}.
700 @kwarg epoch: Optional datum (L{Epoch}), overriding this
701 epoch I{without conversion}.
702 @kwarg reframe: Optional datum (L{RefFrame}), overriding
703 this reframe I{without conversion}.
704 @kwarg sep: Optional separator (C{str}).
705 @kwarg name: Optional instance name (C{str}), overriding
706 this name.
708 @return: The similar point (ellipsoidal C{LatLon}).
710 @raise ParseError: Invalid B{C{strllh}}.
711 '''
712 a, b, h = _MODS.dms.parse3llh(strllh, height=height, sep=sep)
713 r = self.classof(a, b, height=h, datum=self.datum)
714 if datum not in (None, self.datum):
715 r.datum = datum
716 if epoch not in (None, self.epoch):
717 r.epoch = epoch
718 if reframe not in (None, self.reframe):
719 r.reframe = reframe
720 return self._xnamed(r, name=name, force=True) if name else r
722 def _Radjust2(self, adjust, datum, meter_text2):
723 '''(INTERNAL) Adjust an C{elevation} or C{geoidHeight} with
724 difference in Gaussian radii of curvature of the given
725 datum and NAD83 ellipsoids at this point's latitude.
727 @note: This is an arbitrary, possibly incorrect adjustment.
728 '''
729 if adjust: # Elevation2Tuple or GeoidHeight2Tuple
730 m, t = meter_text2
731 if isinstance(m, float) and fabs(m) > EPS:
732 n = Datums.NAD83.ellipsoid.rocGauss(self.lat)
733 if n > EPS0:
734 # use ratio, datum and NAD83 units may differ
735 E = self.ellipsoid() if datum in (None, self.datum) else \
736 _spherical_datum(datum).ellipsoid
737 r = E.rocGauss(self.lat)
738 if r > EPS0 and fabs(r - n) > EPS: # EPS1
739 m *= r / n
740 meter_text2 = meter_text2.classof(m, t)
741 return self._xnamed(meter_text2)
743 @property_doc_(''' this point's reference frame (L{RefFrame}).''')
744 def reframe(self):
745 '''Get this point's reference frame (L{RefFrame}) or C{None}.
746 '''
747 return self._reframe
749 @reframe.setter # PYCHOK setter!
750 def reframe(self, reframe):
751 '''Set or clear this point's reference frame (L{RefFrame}) or C{None}.
753 @raise TypeError: The B{C{reframe}} is not a L{RefFrame}.
754 '''
755 _set_reframe(self, reframe)
757 @Property_RO
758 def scale(self):
759 '''Get this point's UTM grid or UPS point scale factor (C{float})
760 or C{None} if not converted from L{Utm} or L{Ups}.
761 '''
762 return self._scale
764 def toCss(self, **toCss_kwds):
765 '''Convert this C{LatLon} point to a Cassini-Soldner location.
767 @kwarg toCss_kwds: Optional L{pygeodesy.toCss} keyword arguments.
769 @return: The Cassini-Soldner location (L{Css}).
771 @see: Function L{pygeodesy.toCss}.
772 '''
773 return self._css if not toCss_kwds else _MODS.css.toCss(
774 self, **_xkwds(toCss_kwds, name=self.name))
776 def toDatum(self, datum2, height=None, name=NN):
777 '''Convert this point to an other datum.
779 @arg datum2: Datum to convert I{to} (L{Datum}).
780 @kwarg height: Optional height, overriding the
781 converted height (C{meter}).
782 @kwarg name: Optional name (C{str}), iff converted.
784 @return: The converted point (ellipsoidal C{LatLon})
785 or a copy of this point if B{C{datum2}}
786 matches this point's C{datum}.
788 @raise TypeError: Invalid B{C{datum2}}.
790 @example:
792 >>> p = LatLon(51.4778, -0.0016) # default Datums.WGS84
793 >>> p.toDatum(Datums.OSGB36) # 51.477284°N, 000.00002°E
794 '''
795 n = name or self.name
796 d2 = _ellipsoidal_datum(datum2, name=n)
797 if self.datum == d2:
798 r = self.copy(name=name)
799 else:
800 kwds = _xkwds_not(None, LatLon=self.classof, name=n,
801 epoch=self.epoch, reframe=self.reframe)
802 c = self.toCartesian().toDatum(d2)
803 r = c.toLatLon(datum=d2, height=height, **kwds)
804 return r
806 def toEtm(self, **toEtm8_kwds):
807 '''Convert this C{LatLon} point to an ETM coordinate.
809 @kwarg toEtm8_kwds: Optional L{pygeodesy.toEtm8} keyword arguments.
811 @return: The ETM coordinate (L{Etm}).
813 @see: Function L{pygeodesy.toEtm8}.
814 '''
815 return self._etm if not toEtm8_kwds else _MODS.etm.toEtm8(
816 self, **_xkwds(toEtm8_kwds, name=self.name))
818 def toLcc(self, **toLcc_kwds):
819 '''Convert this C{LatLon} point to a Lambert location.
821 @kwarg toLcc_kwds: Optional L{pygeodesy.toLcc} keyword arguments.
823 @return: The Lambert location (L{Lcc}).
825 @see: Function L{pygeodesy.toLcc}.
826 '''
827 return self._lcc if not toLcc_kwds else _MODS.lcc.toLcc(
828 self, **_xkwds(toLcc_kwds, name=self.name))
830 def toMgrs(self, center=False, pole=NN):
831 '''Convert this C{LatLon} point to an MGRS coordinate.
833 @kwarg center: If C{True}, try to I{un}-center MGRS
834 to its C{lowerleft} (C{bool}) or by
835 C{B{center} meter} (C{scalar}).
836 @kwarg pole: Optional top/center for the MGRS UPS
837 projection (C{str}, 'N[orth]' or 'S[outh]').
839 @return: The MGRS coordinate (L{Mgrs}).
841 @see: Method L{toUtmUps} and L{Mgrs.toLatLon}.
842 '''
843 return self.toUtmUps(center=center, pole=pole).toMgrs(center=False)
845 def toOsgr(self, kTM=False, **toOsgr_kwds):
846 '''Convert this C{LatLon} point to an OSGR coordinate.
848 @kwarg kTM: If C{True} use I{Karney}'s Krüger method from module
849 L{ktm}, otherwise I{Ordinance Survery}'s recommended
850 formulation (C{bool}).
851 @kwarg toOsgr_kwds: Optional L{pygeodesy.toOsgr} keyword arguments.
853 @return: The OSGR coordinate (L{Osgr}).
855 @see: Function L{pygeodesy.toOsgr}.
856 '''
857 if toOsgr_kwds:
858 r = _MODS.osgr.toOsgr(self, kTM=kTM, **_xkwds(toOsgr_kwds, name=self.name))
859 else:
860 r = self._osgrTM if kTM else self._osgr
861 return r
863 def toRefFrame(self, reframe2, height=None, name=NN):
864 '''Convert this point to an other reference frame.
866 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
867 @kwarg height: Optional height, overriding the converted
868 height (C{meter}).
869 @kwarg name: Optional name (C{str}), iff converted.
871 @return: The converted point (ellipsoidal C{LatLon}) or this
872 point if conversion is C{nil}, or a copy of this
873 point if the B{C{name}} is non-empty.
875 @raise TRFError: This point's C{reframe} is not defined or
876 conversion from this point's C{reframe} to
877 B{C{reframe2}} is not available.
879 @raise TypeError: Invalid B{C{reframe2}}, not a L{RefFrame}.
881 @example:
883 >>> p = LatLon(51.4778, -0.0016, reframe=RefFrames.ETRF2000) # default Datums.WGS84
884 >>> p.toRefFrame(RefFrames.ITRF2014) # 51.477803°N, 000.001597°W, +0.01m
885 >>> p.toRefFrame(RefFrames.ITRF2014, height=0) # 51.477803°N, 000.001597°W
886 '''
887 if not self.reframe:
888 t = _SPACE_(_DOT_(repr(self), _reframe_), MISSING)
889 raise TRFError(_no_(_conversion_), txt=t)
891 trf = _MODS.trf
892 trf._xinstanceof(trf.RefFrame, reframe2=reframe2)
894 e, xs = trf._reframeTransforms2(reframe2, self.reframe, self.epoch)
895 if xs:
896 c = self.toCartesian().toTransforms_(*xs)
897 n = name or self.name
898 ll = c.toLatLon(datum=self.datum, epoch=e, height=height,
899 LatLon=self.classof, name=n, reframe=reframe2)
900 else:
901 ll = self.copy(name=name) if name else self
902 return ll
904 def toUps(self, pole=NN, falsed=True, center=False):
905 '''Convert this C{LatLon} point to a UPS coordinate.
907 @kwarg pole: Optional top/center of (stereographic)
908 projection (C{str}, 'N[orth]' or 'S[outh]').
909 @kwarg falsed: False easting and northing (C{bool}).
910 @kwarg center: If C{True}, I{un}-center the UPS
911 to its C{lowerleft} (C{bool}) or
912 by C{B{center} meter} (C{scalar}).
914 @return: The UPS coordinate (L{Ups}).
916 @see: Function L{pygeodesy.toUps8}.
917 '''
918 if self._upsOK(pole, falsed):
919 u = self._ups
920 else:
921 ups = _MODS.ups
922 u = ups.toUps8(self, datum=self.datum, Ups=ups.Ups,
923 pole=pole, falsed=falsed)
924 return _lowerleft(u, center)
926 def toUtm(self, center=False):
927 '''Convert this C{LatLon} point to a UTM coordinate.
929 @kwarg center: If C{True}, I{un}-center the UTM
930 to its C{lowerleft} (C{bool}) or
931 by C{B{center} meter} (C{scalar}).
933 @return: The UTM coordinate (L{Utm}).
935 @see: Method L{Mgrs.toUtm} and function L{pygeodesy.toUtm8}.
936 '''
937 return _lowerleft(self._utm, center)
939 def toUtmUps(self, pole=NN, center=False):
940 '''Convert this C{LatLon} point to a UTM or UPS coordinate.
942 @kwarg pole: Optional top/center of UPS (stereographic)
943 projection (C{str}, 'N[orth]' or 'S[outh]').
944 @kwarg center: If C{True}, I{un}-center the UTM or UPS to
945 its C{lowerleft} (C{bool}) or by C{B{center}
946 meter} (C{scalar}).
948 @return: The UTM or UPS coordinate (L{Utm} or L{Ups}).
950 @see: Function L{pygeodesy.toUtmUps8}.
951 '''
952 if self._utmOK():
953 u = self._utm
954 elif self._upsOK(pole):
955 u = self._ups
956 else: # no cover
957 utmups = _MODS.utmups
958 u = utmups.toUtmUps8(self, datum=self.datum, pole=pole, name=self.name,
959 Utm=utmups.Utm, Ups=utmups.Ups)
960 if isinstance(u, utmups.Utm):
961 self._update(False, _utm=u) # PYCHOK kwds
962 elif isinstance(u, utmups.Ups):
963 self._update(False, _ups=u) # PYCHOK kwds
964 else:
965 _xinstanceof(utmups.Utm, utmups.Ups, toUtmUps8=u)
966 return _lowerleft(u, center)
968 def toWm(self, **toWm_kwds):
969 '''Convert this C{LatLon} point to a WM coordinate.
971 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments.
973 @return: The WM coordinate (L{Wm}).
975 @see: Function L{pygeodesy.toWm}.
976 '''
977 return self._wm if not toWm_kwds else _MODS.webmercator.toWm(
978 self, **_xkwds(toWm_kwds, name=self.name))
980 @deprecated_method
981 def to3xyz(self): # PYCHOK no cover
982 '''DEPRECATED, use method C{toEcef}.
984 @return: A L{Vector3Tuple}C{(x, y, z)}.
986 @note: Overloads C{LatLonBase.to3xyz}
987 '''
988 r = self.toEcef()
989 return Vector3Tuple(r.x, r.y, r.z, name=self.name)
991 def trilaterate5(self, distance1, point2, distance2, point3, distance3,
992 area=True, eps=EPS1, wrap=False):
993 '''Trilaterate three points by area overlap or perimeter intersection
994 of three intersecting circles.
996 @arg distance1: Distance to this point (C{meter}), same units
997 as B{C{eps}}).
998 @arg point2: Second center point (C{LatLon}).
999 @arg distance2: Distance to point2 (C{meter}, same units as
1000 B{C{eps}}).
1001 @arg point3: Third center point (C{LatLon}).
1002 @arg distance3: Distance to point3 (C{meter}, same units as
1003 B{C{eps}}).
1004 @kwarg area: If C{True} compute the area overlap, otherwise the
1005 perimeter intersection of the circles (C{bool}).
1006 @kwarg eps: The required I{minimal overlap} for C{B{area}=True}
1007 or the I{intersection margin} for C{B{area}=False}
1008 (C{meter}, conventionally).
1009 @kwarg wrap: Wrap/unroll angular distances (C{bool}).
1011 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)}
1012 with C{min} and C{max} in C{meter}, same units as B{C{eps}},
1013 the corresponding trilaterated points C{minPoint} and
1014 C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number
1015 of trilatered points found for the given B{C{eps}}.
1017 If only a single trilaterated point is found, C{min I{is}
1018 max}, C{minPoint I{is} maxPoint} and C{n = 1}.
1020 For C{B{area}=True}, C{min} and C{max} are the smallest
1021 respectively largest I{radial} overlap found.
1023 For C{B{area}=False}, C{min} and C{max} represent the
1024 nearest respectively farthest intersection margin.
1026 If C{B{area}=True} and all 3 circles are concentric, C{n=0}
1027 and C{minPoint} and C{maxPoint} are the B{C{point#}} with
1028 the smallest B{C{distance#}} C{min} respectively C{max} the
1029 largest B{C{distance#}}.
1031 @raise IntersectionError: Trilateration failed for the given B{C{eps}},
1032 insufficient overlap for C{B{area}=True} or
1033 no intersection or all (near-)concentric for
1034 C{B{area}=False}.
1036 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
1038 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}},
1039 B{C{distance2}} or B{C{distance3}}.
1041 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2}
1042 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib
1043 <https://PyPI.org/project/geographiclib>} if installed, otherwise
1044 uses the accurate (but slower) C{ellipsoidalExact.LatLon} methods.
1045 '''
1046 return _trilaterate5(self, distance1,
1047 self.others(point2=point2), distance2,
1048 self.others(point3=point3), distance3,
1049 area=area, eps=eps, wrap=wrap)
1051 @Property_RO
1052 def _ups(self): # __dict__ value overwritten by method C{toUtmUps}
1053 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}),
1054 see L{pygeodesy.toUps8}.
1055 '''
1056 ups = _MODS.ups
1057 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups,
1058 pole=NN, falsed=True, name=self.name)
1060 def _upsOK(self, pole=NN, falsed=True):
1061 '''(INTERNAL) Check matching C{Ups}.
1062 '''
1063 try:
1064 u = self._ups
1065 except RangeError:
1066 return False
1067 return falsed and (u.pole == pole[:1].upper() or not pole)
1069 @Property_RO
1070 def _utm(self): # __dict__ value overwritten by method C{toUtmUps}
1071 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}),
1072 see L{pygeodesy.toUtm8}.
1073 '''
1074 utm = _MODS.utm
1075 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name)
1077 def _utmOK(self):
1078 '''(INTERNAL) Check C{Utm}.
1079 '''
1080 try:
1081 _ = self._utm
1082 except RangeError:
1083 return False
1084 return True
1086 @Property_RO
1087 def _wm(self):
1088 '''(INTERNAL) Get this C{LatLon} point as webmercator (L{Wm}).
1089 '''
1090 return _MODS.webmercator.toWm(self)
1093def _lowerleft(utmups, center):
1094 '''(INTERNAL) Optionally I{un}-center C{utmups}.
1095 '''
1096 if center in (False, 0, _0_0):
1097 u = utmups
1098 elif center in (True,):
1099 u = utmups._lowerleft
1100 else:
1101 u = _MODS.utmupsBase._lowerleft(utmups, center)
1102 return u
1105def _nearestOn(point, point1, point2, within=True, height=None, wrap=True,
1106 equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds):
1107 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact,
1108 -GeodSolve, -Karney and -Vincenty to embellish exceptions.
1109 '''
1110 try:
1111 p = _xellipsoidal(point=point)
1112 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within,
1113 height=height, wrap=wrap,
1114 equidistant=equidistant, tol=tol,
1115 LatLon=LatLon, **LatLon_kwds)
1116 except (TypeError, ValueError) as x:
1117 raise _xError(x, point=point, point1=point1, point2=point2)
1118 return t.closest
1121def _set_reframe(inst, reframe):
1122 '''(INTERNAL) Set or clear an instance's reference frame.
1123 '''
1124 if reframe is not None:
1125 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe)
1126 inst._reframe = reframe
1127 elif inst.reframe is not None:
1128 inst._reframe = None
1131__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase)
1133# **) MIT License
1134#
1135# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1136#
1137# Permission is hereby granted, free of charge, to any person obtaining a
1138# copy of this software and associated documentation files (the "Software"),
1139# to deal in the Software without restriction, including without limitation
1140# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1141# and/or sell copies of the Software, and to permit persons to whom the
1142# Software is furnished to do so, subject to the following conditions:
1143#
1144# The above copyright notice and this permission notice shall be included
1145# in all copies or substantial portions of the Software.
1146#
1147# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1148# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1149# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1150# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1151# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1152# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1153# OTHER DEALINGS IN THE SOFTWARE.