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 # PYCHOK used!
18from pygeodesy.datums import Datum, Datums, _earth_ellipsoid, _ellipsoidal_datum, \
19 _WGS84, _EWGS84, _xinstanceof # _spherical_datum
20# from pygeodesy.ellipsoids import _EWGS84 # from .datums
21from pygeodesy.errors import _incompatible, _IsnotError, RangeError, TRFError, \
22 _ValueError, _xattr, _xellipsoidal, _xError, \
23 _xkwds, _xkwds_get, _xkwds_not
24# from pygeodesy.fmath import favg # _MODS
25from pygeodesy.interns import MISSING, NN, _COMMA_, _conversion_, _DOT_, \
26 _ellipsoidal_, _no_, _reframe_, _SPACE_
27from pygeodesy.latlonBase import LatLonBase, _trilaterate5, fabs, _Wrap
28from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
29# from pygeodesy.lcc import toLcc # _MODS
30# from pygeodesy.named import notOverloaded # _MODS
31# from pygeodesy.namedTuples import Vector3Tuple # _MODS
32from pygeodesy.props import deprecated_method, deprecated_property_RO, \
33 Property_RO, property_doc_, property_RO, _update_all
34from pygeodesy.units import Epoch, _1mm as _TOL_M, Radius_
35# from pygeodesy.utily import _Wrap # from .latlonBase
37# from math import fabs # from .latlonBase
39__all__ = _ALL_LAZY.ellipsoidalBase
40__version__ = '23.12.12'
43class CartesianEllipsoidalBase(CartesianBase):
44 '''(INTERNAL) Base class for ellipsoidal C{Cartesian}s.
45 '''
46 _datum = _WGS84 # L{Datum}
47 _reframe = None
49# def __matmul__(self, other): # PYCHOK Python 3.5+
50# '''Return C{NotImplemented} for C{c_ = c @ datum}, C{c_ = c @ reframe} and C{c_ = c @ Transform}.
51# '''
52# RefFrame = _MODS.trf.RefFrame
53# return NotImplemented if isinstance(other, (Datum, RefFrame, Transform)) else \
54# _NotImplemented(self, other)
56 @deprecated_method
57 def convertRefFrame(self, reframe2, reframe, epoch=None):
58 '''DEPRECATED, use method L{toRefFrame}.'''
59 return self.toRefFrame(reframe2, reframe, epoch=epoch)
61 @property_RO
62 def ellipsoidalCartesian(self):
63 '''Get this C{Cartesian}'s ellipsoidal class.
64 '''
65 return type(self)
67 def intersections2(self, radius, center2, radius2, sphere=True,
68 Vector=None, **Vector_kwds):
69 '''Compute the intersection of two spheres or circles, each defined by a
70 cartesian center point and a radius.
72 @arg radius: Radius of this sphere or circle (same units as this point's
73 coordinates).
74 @arg center2: Center of the second sphere or circle (C{Cartesian}, L{Vector3d},
75 C{Vector3Tuple} or C{Vector4Tuple}).
76 @arg radius2: Radius of the second sphere or circle (same units as this and
77 the B{C{other}} point's coordinates).
78 @kwarg sphere: If C{True} compute the center and radius of the intersection
79 of two I{spheres}. If C{False}, ignore the C{z}-component and
80 compute the intersection of two I{circles} (C{bool}).
81 @kwarg Vector: Class to return intersections (C{Cartesian}, L{Vector3d} or
82 C{Vector3Tuple}) or C{None} for an instance of this (sub-)class.
83 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments,
84 ignored if C{B{Vector} is None}.
86 @return: If B{C{sphere}} is C{True}, a 2-tuple of the C{center} and C{radius}
87 of the intersection of the I{spheres}. The C{radius} is C{0.0} for
88 abutting spheres (and the C{center} is aka the I{radical center}).
90 If B{C{sphere}} is C{False}, a 2-tuple with the two intersection
91 points of the I{circles}. For abutting circles, both points are
92 the same instance, aka the I{radical center}.
94 @raise IntersectionError: Concentric, invalid or non-intersecting spheres or circles.
96 @raise TypeError: Invalid B{C{center2}}.
98 @raise UnitError: Invalid B{C{radius}} or B{C{radius2}}.
100 @see: U{Sphere-Sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>},
101 U{Circle-Circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>}
102 Intersection and function L{pygeodesy.radical2}.
103 '''
104 try:
105 return _MODS.vector3d._intersects2(self, Radius_(radius=radius),
106 center2, Radius_(radius2=radius2),
107 sphere=sphere, clas=self.classof,
108 Vector=Vector, **Vector_kwds)
109 except (TypeError, ValueError) as x:
110 raise _xError(x, center=self, radius=radius, center2=center2, radius2=radius2)
112 @property_doc_(''' this cartesian's reference frame (L{RefFrame}).''')
113 def reframe(self):
114 '''Get this cartesian's reference frame (L{RefFrame}) or C{None}.
115 '''
116 return self._reframe
118 @reframe.setter # PYCHOK setter!
119 def reframe(self, reframe):
120 '''Set or clear this cartesian's reference frame (L{RefFrame}) or C{None}.
122 @raise TypeError: The B{C{reframe}} is not a L{RefFrame}.
123 '''
124 _set_reframe(self, reframe)
126 def toRefFrame(self, reframe2, reframe=None, epoch=None):
127 '''Convert this cartesian point from one to an other reference frame.
129 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
130 @arg reframe: Reference frame to convert I{from} (L{RefFrame}),
131 overriding this cartesian's C{reframe}.
132 @kwarg epoch: Optional epoch to observe (C{scalar}, fractional
133 calendar year), overriding B{C{reframe}}'s epoch.
135 @return: The converted point (C{Cartesian}) or this point if
136 conversion is C{nil}.
138 @raise TRFError: No conversion available from B{C{reframe}}
139 to B{C{reframe2}} or invalid B{C{epoch}}.
141 @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a
142 L{RefFrame}.
143 '''
144 r = self.reframe if reframe is None else reframe
145 if r in (None, reframe2):
146 xs = None # XXX _set_reframe(self, reframe2)?
147 else:
148 trf = _MODS.trf
149 _xinstanceof(trf.RefFrame, reframe2=reframe2, reframe=r)
150 _, xs = trf._reframeTransforms2(reframe2, r, epoch)
151 return self.toTransforms_(*xs) if xs else self
153 def toTransforms_(self, *transforms, **datum):
154 '''Apply none, one or several Helmert transforms.
156 @arg transforms: Transforms to apply, in order (L{Transform}s).
157 @kwarg datum: Datum for the transformed point (L{Datum}),
158 overriding this point's datum.
160 @return: The transformed point (C{Cartesian}) or this point
161 if the B{C{transforms}} produce the same point.
162 '''
163 r = self
164 if transforms:
165 xyz = r.xyz
166 for t in transforms:
167 xyz = t.transform(*xyz)
168 d = _xkwds_get(datum, datum=r.datum)
169 if d != r.datum or xyz != r.xyz:
170 r = r.classof(xyz, datum=d)
171 return r
174class LatLonEllipsoidalBase(LatLonBase):
175 '''(INTERNAL) Base class for ellipsoidal C{LatLon}s.
176 '''
177 _datum = _WGS84 # L{Datum}
178 _elevation2to = None # _elevation2 timeout (C{secs})
179 _epoch = None # overriding .reframe.epoch (C{float})
180 _gamma = None # UTM/UPS meridian convergence (C{degrees})
181 _geoidHeight2to = None # _geoidHeight2 timeout (C{secs})
182 _reframe = None # reference frame (L{RefFrame})
183 _scale = None # UTM/UPS scale factor (C{float})
184 _toLLEB_args = () # Etm/Utm/Ups._toLLEB arguments
186 def __init__(self, latlonh, lon=None, height=0, datum=None, reframe=None,
187 epoch=None, wrap=False, name=NN):
188 '''Create an ellipsoidal C{LatLon} point frome the given
189 lat-, longitude and height on the given datum and with
190 the given reference frame and epoch.
192 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or
193 a previous C{LatLon} instance provided C{B{lon}=None}.
194 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or
195 C(None), indicating B{C{latlonh}} is a C{LatLon}.
196 @kwarg height: Optional height above (or below) the earth surface
197 (C{meter}, same units as the datum's ellipsoid axes).
198 @kwarg datum: Optional, ellipsoidal datum to use (L{Datum}, L{Ellipsoid},
199 L{Ellipsoid2} or L{a_f2Tuple}).
200 @kwarg reframe: Optional reference frame (L{RefFrame}).
201 @kwarg epoch: Optional epoch to observe for B{C{reframe}} (C{scalar}),
202 a non-zero, fractional calendar year; silently ignored
203 if C{B{reframe}=None}.
204 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}}
205 (C{bool}).
206 @kwarg name: Optional name (string).
208 @raise RangeError: Value of C{lat} or B{C{lon}} outside the valid
209 range and L{rangerrors} set to C{True}.
211 @raise TypeError: If B{C{latlonh}} is not a C{LatLon}, B{C{datum}} is
212 not a L{Datum}, B{C{reframe}} is not a L{RefFrame}
213 or B{C{epoch}} is not C{scalar} non-zero.
215 @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}.
216 '''
217 LatLonBase.__init__(self, latlonh, lon=lon, height=height, wrap=wrap, name=name)
218 if datum not in (None, self._datum, _EWGS84):
219 self.datum = _ellipsoidal_datum(datum, name=name)
220 if reframe:
221 self.reframe = reframe
222 self.epoch = epoch
224# def __matmul__(self, other): # PYCHOK Python 3.5+
225# '''Return C{NotImplemented} for C{ll_ = ll @ datum} and C{ll_ = ll @ reframe}.
226# '''
227# RefFrame = _MODS.trf.RefFrame
228# return NotImplemented if isinstance(other, (Datum, RefFrame)) else \
229# _NotImplemented(self, other)
231 def antipode(self, height=None):
232 '''Return the antipode, the point diametrically opposite
233 to this point.
235 @kwarg height: Optional height of the antipode, height
236 of this point otherwise (C{meter}).
238 @return: The antipodal point (C{LatLon}).
239 '''
240 lla = LatLonBase.antipode(self, height=height)
241 if lla.datum != self.datum:
242 lla.datum = self.datum
243 return lla
245 @deprecated_property_RO
246 def convergence(self):
247 '''DEPRECATED, use property C{gamma}.'''
248 return self.gamma
250 @deprecated_method
251 def convertDatum(self, datum2):
252 '''DEPRECATED, use method L{toDatum}.'''
253 return self.toDatum(datum2)
255 @deprecated_method
256 def convertRefFrame(self, reframe2):
257 '''DEPRECATED, use method L{toRefFrame}.'''
258 return self.toRefFrame(reframe2)
260 @Property_RO
261 def _css(self):
262 '''(INTERNAL) Get this C{LatLon} point as a Cassini-Soldner location (L{Css}).
263 '''
264 css = _MODS.css
265 return css.toCss(self, height=self.height, Css=css.Css, name=self.name)
267 @property_doc_(''' this points's datum (L{Datum}).''')
268 def datum(self):
269 '''Get this point's datum (L{Datum}).
270 '''
271 return self._datum
273 @datum.setter # PYCHOK setter!
274 def datum(self, datum):
275 '''Set this point's datum I{without conversion} (L{Datum}).
277 @raise TypeError: The B{C{datum}} is not a L{Datum}
278 or not ellipsoidal.
279 '''
280 _xinstanceof(Datum, datum=datum)
281 if not datum.isEllipsoidal:
282 raise _IsnotError(_ellipsoidal_, datum=datum)
283 if self._datum != datum:
284 _update_all(self)
285 self._datum = datum
287 def distanceTo2(self, other, wrap=False):
288 '''I{Approximate} the distance and (initial) bearing between this
289 and an other (ellipsoidal) point based on the radii of curvature.
291 I{Suitable only for short distances up to a few hundred Km
292 or Miles and only between points not near-polar}.
294 @arg other: The other point (C{LatLon}).
295 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{other}}
296 point (C{bool}).
298 @return: An L{Distance2Tuple}C{(distance, initial)}.
300 @raise TypeError: The B{C{other}} point is not C{LatLon}.
302 @raise ValueError: Incompatible datum ellipsoids.
304 @see: Method L{Ellipsoid.distance2} and U{Local, flat earth
305 approximation<https://www.EdWilliams.org/avform.htm#flat>}
306 aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>}
307 formula.
308 '''
309 p = self.others(other)
310 if wrap:
311 p = _Wrap.point(p)
312 E = self.ellipsoids(other)
313 return E.distance2(*(self.latlon + p.latlon))
315 @Property_RO
316 def _elevation2(self):
317 '''(INTERNAL) Get elevation and data source.
318 '''
319 return _MODS.elevations.elevation2(self.lat, self.lon,
320 timeout=self._elevation2to)
322 def elevation2(self, adjust=True, datum=None, timeout=2):
323 '''Return elevation of this point for its or the given datum, ellipsoid
324 or sphere.
326 @kwarg adjust: Adjust the elevation for a B{C{datum}} other than
327 C{NAD83} (C{bool}).
328 @kwarg datum: Optional datum overriding this point's datum (L{Datum},
329 L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar}
330 radius).
331 @kwarg timeout: Optional query timeout (C{seconds}).
333 @return: An L{Elevation2Tuple}C{(elevation, data_source)} or
334 C{(None, error)} in case of errors.
336 @note: The adjustment applied is the difference in geocentric earth
337 radius between the B{C{datum}} and C{NAV83} upon which the
338 L{elevations.elevation2} is based.
340 @note: NED elevation is only available for locations within the
341 U{Conterminous US (CONUS)
342 <https://WikiPedia.org/wiki/Contiguous_United_States>}.
344 @see: Function L{elevations.elevation2} and method C{Ellipsoid.Rgeocentric}
345 for further details and possible C{error}s.
346 '''
347 if self._elevation2to != timeout:
348 self._elevation2to = timeout
349 LatLonEllipsoidalBase._elevation2._update(self)
350 return self._Radjust2(adjust, datum, self._elevation2)
352 def ellipsoid(self, datum=_WGS84):
353 '''Return the ellipsoid of this point's datum or the given datum.
355 @kwarg datum: Default datum (L{Datum}).
357 @return: The ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
358 '''
359 return _xattr(self, datum=datum).ellipsoid
361 @property_RO
362 def ellipsoidalLatLon(self):
363 '''Get this C{LatLon}'s ellipsoidal class.
364 '''
365 return type(self)
367 def ellipsoids(self, other):
368 '''Check the type and ellipsoid of this and an other point's datum.
370 @arg other: The other point (C{LatLon}).
372 @return: This point's datum ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
374 @raise TypeError: The B{C{other}} point is not C{LatLon}.
376 @raise ValueError: Incompatible datum ellipsoids.
377 '''
378 self.others(other, up=2) # ellipsoids' caller
380 E = self.ellipsoid()
381 try: # other may be Sphere, etc.
382 e = other.ellipsoid()
383 except AttributeError:
384 try: # no ellipsoid method, try datum
385 e = other.datum.ellipsoid
386 except AttributeError:
387 e = E # no datum, XXX assume equivalent?
388 if e != E:
389 raise _ValueError(e.named2, txt=_incompatible(E.named2))
390 return E
392 @property_doc_(''' this point's observed or C{reframe} epoch (C{float}).''')
393 def epoch(self):
394 '''Get this point's observed or C{reframe} epoch (C{float}) or C{None}.
395 '''
396 return self._epoch or (self.reframe.epoch if self.reframe else None)
398 @epoch.setter # PYCHOK setter!
399 def epoch(self, epoch):
400 '''Set or clear this point's observed epoch, a fractional
401 calendar year (L{Epoch}, C{scalar}) or C{None}.
403 @raise TRFError: Invalid B{C{epoch}}.
404 '''
405 self._epoch = None if epoch is None else Epoch(epoch)
407 @Property_RO
408 def Equidistant(self):
409 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantKarney} or L{EquidistantExact}).
410 '''
411 try:
412 _ = self.datum.ellipsoid.geodesic
413 return _MODS.azimuthal.EquidistantKarney
414 except ImportError: # no geographiclib
415 return _MODS.azimuthal.EquidistantExact # XXX no longer L{azimuthal.Equidistant}
417 @Property_RO
418 def _etm(self):
419 '''(INTERNAL) Get this C{LatLon} point as an ETM coordinate (L{pygeodesy.toEtm8}).
420 '''
421 etm = _MODS.etm
422 return etm.toEtm8(self, datum=self.datum, Etm=etm.Etm)
424 @property_RO
425 def gamma(self):
426 '''Get this point's UTM or UPS meridian convergence (C{degrees}) or
427 C{None} if not available or not converted from L{Utm} or L{Ups}.
428 '''
429 return self._gamma
431 @Property_RO
432 def _geoidHeight2(self):
433 '''(INTERNAL) Get geoid height and model.
434 '''
435 return _MODS.elevations.geoidHeight2(self.lat, self.lon, model=0,
436 timeout=self._geoidHeight2to)
438 def geoidHeight2(self, adjust=False, datum=None, timeout=2):
439 '''Return geoid height of this point for its or the given datum, ellipsoid
440 or sphere.
442 @kwarg adjust: Adjust the geoid height for a B{C{datum}} other than
443 C{NAD83/NADV88} (C{bool}).
444 @kwarg datum: Optional datum overriding this point's datum (L{Datum},
445 L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar}
446 radius).
447 @kwarg timeout: Optional query timeout (C{seconds}).
449 @return: A L{GeoidHeight2Tuple}C{(height, model_name)} or
450 C{(None, error)} in case of errors.
452 @note: The adjustment applied is the difference in geocentric earth
453 radius between the B{C{datum}} and C{NAV83/NADV88} upon which
454 the L{elevations.geoidHeight2} is based.
456 @note: The geoid height is only available for locations within the
457 U{Conterminous US (CONUS)
458 <https://WikiPedia.org/wiki/Contiguous_United_States>}.
460 @see: Function L{elevations.geoidHeight2} and method C{Ellipsoid.Rgeocentric}
461 for further details and possible C{error}s.
462 '''
463 if self._geoidHeight2to != timeout:
464 self._geoidHeight2to = timeout
465 LatLonEllipsoidalBase._geoidHeight2._update(self)
466 return self._Radjust2(adjust, datum, self._geoidHeight2)
468 def intermediateTo(self, other, fraction, height=None, wrap=False): # PYCHOK no cover
469 '''I{Must be overloaded}.'''
470 _MODS.named.notOverloaded(self, other, fraction, height=height, wrap=wrap)
472 def intersection3(self, end1, other, end2, height=None, wrap=False, # was=True
473 equidistant=None, tol=_TOL_M):
474 '''I{Iteratively} compute the intersection point of two lines, each
475 defined by two points or a start point and bearing from North.
477 @arg end1: End point of this line (C{LatLon}) or the initial
478 bearing at this point (compass C{degrees360}).
479 @arg other: Start point of the other line (C{LatLon}).
480 @arg end2: End point of the other line (C{LatLon}) or the initial
481 bearing at the other point (compass C{degrees360}).
482 @kwarg height: Optional height at the intersection (C{meter},
483 conventionally) or C{None} for the mean height.
484 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
485 B{C{other}} and B{C{end*}} points (C{bool}).
486 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
487 function L{pygeodesy.equidistant}), or C{None}
488 for this point's preferred C{.Equidistant}.
489 @kwarg tol: Tolerance for skew line distance and length and for
490 convergence (C{meter}, conventionally).
492 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)}
493 with C{point} a C{LatLon} instance.
495 @raise ImportError: Package U{geographiclib
496 <https://PyPI.org/project/geographiclib>}
497 not installed or not found, but only if
498 C{B{equidistant}=}L{EquidistantKarney}.
500 @raise IntersectionError: Skew, colinear, parallel or otherwise
501 non-intersecting lines or no convergence
502 for the given B{C{tol}}.
504 @raise TypeError: If B{C{end1}}, B{C{other}} or B{C{end2}} point
505 is not C{LatLon}.
507 @note: For each line specified with an initial bearing, a pseudo-end
508 point is computed as the C{destination} along that bearing at
509 about 1.5 times the distance from the start point to an initial
510 gu-/estimate of the intersection point (and between 1/8 and 3/8
511 of the authalic earth perimeter).
513 @see: I{Karney's} U{intersect.cpp<https://SourceForge.net/p/geographiclib/
514 discussion/1026621/thread/21aaff9f/>}, U{The B{ellipsoidal} case<https://
515 GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>}
516 and U{Karney's paper<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section
517 B{14. MARITIME BOUNDARIES} for more details about the iteration algorithm.
518 '''
519 try:
520 s2 = self.others(other)
521 return _MODS.ellipsoidalBaseDI._intersect3(self, end1,
522 s2, end2,
523 height=height, wrap=wrap,
524 equidistant=equidistant, tol=tol,
525 LatLon=self.classof, datum=self.datum)
526 except (TypeError, ValueError) as x:
527 raise _xError(x, start1=self, end1=end1, other=other, end2=end2,
528 height=height, wrap=wrap, tol=tol)
530 def intersections2(self, radius1, other, radius2, height=None, wrap=False, # was=True
531 equidistant=None, tol=_TOL_M):
532 '''I{Iteratively} compute the intersection points of two circles,
533 each defined by a center point and a radius.
535 @arg radius1: Radius of this circle (C{meter}, conventionally).
536 @arg other: Center of the other circle (C{LatLon}).
537 @arg radius2: Radius of the other circle (C{meter}, same units as
538 B{C{radius1}}).
539 @kwarg height: Optional height for the intersection points (C{meter},
540 conventionally) or C{None} for the I{"radical height"}
541 at the I{radical line} between both centers.
542 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}
543 center (C{bool}).
544 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
545 function L{pygeodesy.equidistant}) or C{None}
546 for this point's preferred C{.Equidistant}.
547 @kwarg tol: Convergence tolerance (C{meter}, same units as
548 B{C{radius1}} and B{C{radius2}}).
550 @return: 2-Tuple of the intersection points, each a C{LatLon}
551 instance. For abutting circles, both intersection
552 points are the same instance, aka the I{radical center}.
554 @raise ImportError: Package U{geographiclib
555 <https://PyPI.org/project/geographiclib>}
556 not installed or not found, but only if
557 C{B{equidistant}=}L{EquidistantKarney}.
559 @raise IntersectionError: Concentric, antipodal, invalid or
560 non-intersecting circles or no
561 convergence for the given B{C{tol}}.
563 @raise TypeError: Invalid B{C{other}} or B{C{equidistant}}.
565 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
567 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
568 calculating-intersection-of-two-circles>}, U{Karney's paper
569 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
570 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
571 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
572 intersections.
573 '''
574 try:
575 c2 = self.others(other)
576 return _MODS.ellipsoidalBaseDI._intersections2(self, radius1,
577 c2, radius2,
578 height=height, wrap=wrap,
579 equidistant=equidistant, tol=tol,
580 LatLon=self.classof, datum=self.datum)
581 except (AssertionError, TypeError, ValueError) as x:
582 raise _xError(x, center=self, radius1=radius1, other=other, radius2=radius2,
583 height=height, wrap=wrap, tol=tol)
585 def isenclosedBy(self, points, wrap=False):
586 '''Check whether a polygon or composite encloses this point.
588 @arg points: The polygon points or clips (C{LatLon}[],
589 L{BooleanFHP} or L{BooleanGH}).
590 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
591 B{C{points}} (C{bool}).
593 @return: C{True} if this point is inside the polygon or composite,
594 C{False} otherwise.
596 @raise PointsError: Insufficient number of B{C{points}}.
598 @raise TypeError: Some B{C{points}} are not C{LatLon}.
600 @raise ValueError: Invalid B{C{point}}, lat- or longitude.
602 @see: Functions L{pygeodesy.isconvex}, L{pygeodesy.isenclosedBy}
603 and L{pygeodesy.ispolar} especially if the B{C{points}} may
604 enclose a pole or wrap around the earth I{longitudinally}.
605 '''
606 return _MODS.points.isenclosedBy(self, points, wrap=wrap)
608 @property_RO
609 def iteration(self):
610 '''Get the most recent C{intersections2} or C{nearestOn} iteration
611 number (C{int}) or C{None} if not available/applicable.
612 '''
613 return self._iteration
615 @Property_RO
616 def _lcc(self):
617 '''(INTERNAL) Get this C{LatLon} point as a Lambert location (L{Lcc}).
618 '''
619 lcc = _MODS.lcc
620 return lcc.toLcc(self, height=self.height, Lcc=lcc.Lcc, name=self.name)
622 def midpointTo(self, other, height=None, fraction=_0_5, wrap=False):
623 '''Find the midpoint on a geodesic between this and an other point.
625 @arg other: The other point (C{LatLon}).
626 @kwarg height: Optional height for midpoint, overriding the
627 mean height (C{meter}).
628 @kwarg fraction: Midpoint location from this point (C{scalar}),
629 may be negative or greater than 1.0.
630 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
631 B{C{other}} point (C{bool}).
633 @return: Midpoint (C{LatLon}).
635 @raise TypeError: The B{C{other}} point is not C{LatLon}.
637 @raise ValueError: Invalid B{C{height}}.
639 @see: Methods C{intermediateTo} and C{rhumbMidpointTo}.
640 '''
641 return self.intermediateTo(other, fraction, height=height, wrap=wrap)
643 def nearestOn(self, point1, point2, within=True, height=None, wrap=False, # was=True
644 equidistant=None, tol=_TOL_M):
645 '''I{Iteratively} locate the closest point on the geodesic between
646 two other (ellipsoidal) points.
648 @arg point1: Start point (C{LatLon}).
649 @arg point2: End point (C{LatLon}).
650 @kwarg within: If C{True} return the closest point I{between}
651 B{C{point1}} and B{C{point2}}, otherwise the
652 closest point elsewhere on the geodesic (C{bool}).
653 @kwarg height: Optional height for the closest point (C{meter},
654 conventionally) or C{None} or C{False} for the
655 interpolated height. If C{False}, the closest
656 takes the heights of the points into account.
657 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both
658 B{C{point1}} and B{C{point2}} (C{bool}).
659 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
660 function L{pygeodesy.equidistant}) or C{None}
661 for this point's preferred C{.Equidistant}.
662 @kwarg tol: Convergence tolerance (C{meter}, conventionally).
664 @return: Closest point (C{LatLon}).
666 @raise ImportError: Package U{geographiclib
667 <https://PyPI.org/project/geographiclib>}
668 not installed or not found, but only if
669 C{B{equidistant}=}L{EquidistantKarney}.
671 @raise TypeError: Invalid B{C{point1}}, B{C{point2}} or
672 B{C{equidistant}}.
674 @raise ValueError: Datum or ellipsoid of B{C{point1}} or B{C{point2}} is
675 incompatible or no convergence for the given B{C{tol}}.
677 @see: I{Karney}'s U{intercept.cpp<https://SourceForge.net/p/geographiclib/
678 discussion/1026621/thread/21aaff9f/>}, U{The B{ellipsoidal} case<https://
679 GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>}
680 and U{Karney's paper<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section
681 B{14. MARITIME BOUNDARIES} for details about the iteration algorithm.
682 '''
683 try:
684 t = _MODS.ellipsoidalBaseDI._nearestOn2(self, point1, point2, within=within,
685 height=height, wrap=wrap,
686 equidistant=equidistant,
687 tol=tol, LatLon=self.classof)
688 except (TypeError, ValueError) as x:
689 raise _xError(x, point=self, point1=point1, point2=point2, within=within,
690 height=height, wrap=wrap, tol=tol)
691 return t.closest
693 @Property_RO
694 def _osgr(self):
695 '''(INTERNAL) Get this C{LatLon} point as an OSGR coordinate (L{Osgr}),
696 based on the OS recommendation.
697 '''
698 return _MODS.osgr.toOsgr(self, kTM=False, name=self.name) # datum=self.datum
700 @Property_RO
701 def _osgrTM(self):
702 '''(INTERNAL) Get this C{LatLon} point as an OSGR coordinate (L{Osgr})
703 based on I{Karney}'s Krüger implementation.
704 '''
705 return _MODS.osgr.toOsgr(self, kTM=True, name=self.name) # datum=self.datum
707 def parse(self, strllh, height=0, datum=None, epoch=None, reframe=None,
708 sep=_COMMA_, wrap=False, name=NN):
709 '''Parse a string consisting of C{"lat, lon[, height]"},
710 representing a similar, ellipsoidal C{LatLon} point.
712 @arg strllh: Lat, lon and optional height (C{str}),
713 see function L{pygeodesy.parse3llh}.
714 @kwarg height: Optional, default height (C{meter} or
715 C{None}).
716 @kwarg datum: Optional datum (L{Datum}), overriding this
717 datum I{without conversion}.
718 @kwarg epoch: Optional datum (L{Epoch}), overriding this
719 epoch I{without conversion}.
720 @kwarg reframe: Optional datum (L{RefFrame}), overriding
721 this reframe I{without conversion}.
722 @kwarg sep: Optional separator (C{str}).
723 @kwarg wrap: If C{True}, wrap or I{normalize} the lat-
724 and longitude (C{bool}).
725 @kwarg name: Optional instance name (C{str}), overriding
726 this name.
728 @return: The similar point (ellipsoidal C{LatLon}).
730 @raise ParseError: Invalid B{C{strllh}}.
731 '''
732 a, b, h = _MODS.dms.parse3llh(strllh, height=height, sep=sep, wrap=wrap)
733 r = self.classof(a, b, height=h, datum=self.datum)
734 if datum not in (None, self.datum):
735 r.datum = datum
736 if epoch not in (None, self.epoch):
737 r.epoch = epoch
738 if reframe not in (None, self.reframe):
739 r.reframe = reframe
740 return self._xnamed(r, name=name, force=True) if name else r
742 def _Radjust2(self, adjust, datum, meter_text2):
743 '''(INTERNAL) Adjust an C{elevation} or C{geoidHeight} with
744 difference in Gaussian radii of curvature of the given
745 datum and NAD83 ellipsoids at this point's latitude.
747 @note: This is an arbitrary, possibly incorrect adjustment.
748 '''
749 if adjust: # Elevation2Tuple or GeoidHeight2Tuple
750 m, t = meter_text2
751 if isinstance(m, float) and fabs(m) > EPS:
752 n = Datums.NAD83.ellipsoid.rocGauss(self.lat)
753 if n > EPS0:
754 # use ratio, datum and NAD83 units may differ
755 E = self.ellipsoid() if datum in (None, self.datum) else \
756 _earth_ellipsoid(datum)
757 r = E.rocGauss(self.lat)
758 if r > EPS0 and fabs(r - n) > EPS: # EPS1
759 m *= r / n
760 meter_text2 = meter_text2.classof(m, t)
761 return self._xnamed(meter_text2)
763 @property_doc_(''' this point's reference frame (L{RefFrame}).''')
764 def reframe(self):
765 '''Get this point's reference frame (L{RefFrame}) or C{None}.
766 '''
767 return self._reframe
769 @reframe.setter # PYCHOK setter!
770 def reframe(self, reframe):
771 '''Set or clear this point's reference frame (L{RefFrame}) or C{None}.
773 @raise TypeError: The B{C{reframe}} is not a L{RefFrame}.
774 '''
775 _set_reframe(self, reframe)
777 @Property_RO
778 def scale(self):
779 '''Get this point's UTM grid or UPS point scale factor (C{float})
780 or C{None} if not converted from L{Utm} or L{Ups}.
781 '''
782 return self._scale
784 def toCss(self, **toCss_kwds):
785 '''Convert this C{LatLon} point to a Cassini-Soldner location.
787 @kwarg toCss_kwds: Optional L{pygeodesy.toCss} keyword arguments.
789 @return: The Cassini-Soldner location (L{Css}).
791 @see: Function L{pygeodesy.toCss}.
792 '''
793 return self._css if not toCss_kwds else _MODS.css.toCss(
794 self, **_xkwds(toCss_kwds, name=self.name))
796 def toDatum(self, datum2, height=None, name=NN):
797 '''Convert this point to an other datum.
799 @arg datum2: Datum to convert I{to} (L{Datum}).
800 @kwarg height: Optional height, overriding the
801 converted height (C{meter}).
802 @kwarg name: Optional name (C{str}), iff converted.
804 @return: The converted point (ellipsoidal C{LatLon})
805 or a copy of this point if B{C{datum2}}
806 matches this point's C{datum}.
808 @raise TypeError: Invalid B{C{datum2}}.
809 '''
810 n = name or self.name
811 d2 = _ellipsoidal_datum(datum2, name=n)
812 if self.datum == d2:
813 r = self.copy(name=name)
814 else:
815 kwds = _xkwds_not(None, LatLon=self.classof, name=n,
816 epoch=self.epoch, reframe=self.reframe)
817 c = self.toCartesian().toDatum(d2)
818 r = c.toLatLon(datum=d2, height=height, **kwds)
819 return r
821 def toEtm(self, **toEtm8_kwds):
822 '''Convert this C{LatLon} point to an ETM coordinate.
824 @kwarg toEtm8_kwds: Optional L{pygeodesy.toEtm8} keyword arguments.
826 @return: The ETM coordinate (L{Etm}).
828 @see: Function L{pygeodesy.toEtm8}.
829 '''
830 return self._etm if not toEtm8_kwds else _MODS.etm.toEtm8(
831 self, **_xkwds(toEtm8_kwds, name=self.name))
833 def toLcc(self, **toLcc_kwds):
834 '''Convert this C{LatLon} point to a Lambert location.
836 @kwarg toLcc_kwds: Optional L{pygeodesy.toLcc} keyword arguments.
838 @return: The Lambert location (L{Lcc}).
840 @see: Function L{pygeodesy.toLcc}.
841 '''
842 return self._lcc if not toLcc_kwds else _MODS.lcc.toLcc(
843 self, **_xkwds(toLcc_kwds, name=self.name))
845 def toMgrs(self, center=False, pole=NN):
846 '''Convert this C{LatLon} point to an MGRS coordinate.
848 @kwarg center: If C{True}, try to I{un}-center MGRS
849 to its C{lowerleft} (C{bool}) or by
850 C{B{center} meter} (C{scalar}).
851 @kwarg pole: Optional top/center for the MGRS UPS
852 projection (C{str}, 'N[orth]' or 'S[outh]').
854 @return: The MGRS coordinate (L{Mgrs}).
856 @see: Method L{toUtmUps} and L{Mgrs.toLatLon}.
857 '''
858 return self.toUtmUps(center=center, pole=pole).toMgrs(center=False)
860 def toOsgr(self, kTM=False, **toOsgr_kwds):
861 '''Convert this C{LatLon} point to an OSGR coordinate.
863 @kwarg kTM: If C{True} use I{Karney}'s Krüger method from module
864 L{ktm}, otherwise I{Ordinance Survery}'s recommended
865 formulation (C{bool}).
866 @kwarg toOsgr_kwds: Optional L{pygeodesy.toOsgr} keyword arguments.
868 @return: The OSGR coordinate (L{Osgr}).
870 @see: Function L{pygeodesy.toOsgr}.
871 '''
872 if toOsgr_kwds:
873 r = _MODS.osgr.toOsgr(self, kTM=kTM, **_xkwds(toOsgr_kwds, name=self.name))
874 else:
875 r = self._osgrTM if kTM else self._osgr
876 return r
878 def toRefFrame(self, reframe2, height=None, name=NN):
879 '''Convert this point to an other reference frame.
881 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
882 @kwarg height: Optional height, overriding the converted
883 height (C{meter}).
884 @kwarg name: Optional name (C{str}), iff converted.
886 @return: The converted point (ellipsoidal C{LatLon}) or this
887 point if conversion is C{nil}, or a copy of this
888 point if the B{C{name}} is non-empty.
890 @raise TRFError: This point's C{reframe} is not defined or
891 conversion from this point's C{reframe} to
892 B{C{reframe2}} is not available.
894 @raise TypeError: Invalid B{C{reframe2}}, not a L{RefFrame}.
895 '''
896 if not self.reframe:
897 t = _SPACE_(_DOT_(repr(self), _reframe_), MISSING)
898 raise TRFError(_no_(_conversion_), txt=t)
900 trf = _MODS.trf
901 trf._xinstanceof(trf.RefFrame, reframe2=reframe2)
903 e, xs = trf._reframeTransforms2(reframe2, self.reframe, self.epoch)
904 if xs:
905 c = self.toCartesian().toTransforms_(*xs)
906 n = name or self.name
907 ll = c.toLatLon(datum=self.datum, epoch=e, height=height,
908 LatLon=self.classof, name=n, reframe=reframe2)
909 else:
910 ll = self.copy(name=name) if name else self
911 return ll
913 def toUps(self, pole=NN, falsed=True, center=False):
914 '''Convert this C{LatLon} point to a UPS coordinate.
916 @kwarg pole: Optional top/center of (stereographic)
917 projection (C{str}, 'N[orth]' or 'S[outh]').
918 @kwarg falsed: False easting and northing (C{bool}).
919 @kwarg center: If C{True}, I{un}-center the UPS
920 to its C{lowerleft} (C{bool}) or
921 by C{B{center} meter} (C{scalar}).
923 @return: The UPS coordinate (L{Ups}).
925 @see: Function L{pygeodesy.toUps8}.
926 '''
927 if self._upsOK(pole, falsed):
928 u = self._ups
929 else:
930 ups = _MODS.ups
931 u = ups.toUps8(self, datum=self.datum, Ups=ups.Ups,
932 pole=pole, falsed=falsed)
933 return _lowerleft(u, center)
935 def toUtm(self, center=False):
936 '''Convert this C{LatLon} point to a UTM coordinate.
938 @kwarg center: If C{True}, I{un}-center the UTM
939 to its C{lowerleft} (C{bool}) or
940 by C{B{center} meter} (C{scalar}).
942 @return: The UTM coordinate (L{Utm}).
944 @see: Method L{Mgrs.toUtm} and function L{pygeodesy.toUtm8}.
945 '''
946 return _lowerleft(self._utm, center)
948 def toUtmUps(self, pole=NN, center=False):
949 '''Convert this C{LatLon} point to a UTM or UPS coordinate.
951 @kwarg pole: Optional top/center of UPS (stereographic)
952 projection (C{str}, 'N[orth]' or 'S[outh]').
953 @kwarg center: If C{True}, I{un}-center the UTM or UPS to
954 its C{lowerleft} (C{bool}) or by C{B{center}
955 meter} (C{scalar}).
957 @return: The UTM or UPS coordinate (L{Utm} or L{Ups}).
959 @see: Function L{pygeodesy.toUtmUps8}.
960 '''
961 if self._utmOK():
962 u = self._utm
963 elif self._upsOK(pole):
964 u = self._ups
965 else: # no cover
966 utmups = _MODS.utmups
967 u = utmups.toUtmUps8(self, datum=self.datum, pole=pole, name=self.name,
968 Utm=utmups.Utm, Ups=utmups.Ups)
969 if isinstance(u, utmups.Utm):
970 self._update(False, _utm=u) # PYCHOK kwds
971 elif isinstance(u, utmups.Ups):
972 self._update(False, _ups=u) # PYCHOK kwds
973 else:
974 _xinstanceof(utmups.Utm, utmups.Ups, toUtmUps8=u)
975 return _lowerleft(u, center)
977 @deprecated_method
978 def to3xyz(self): # PYCHOK no cover
979 '''DEPRECATED, use method C{toEcef}.
981 @return: A L{Vector3Tuple}C{(x, y, z)}.
983 @note: Overloads C{LatLonBase.to3xyz}
984 '''
985 r = self.toEcef()
986 return _MODS.namedTuples.Vector3Tuple(r.x, r.y, r.z, name=self.name)
988 def trilaterate5(self, distance1, point2, distance2, point3, distance3,
989 area=True, eps=EPS1, wrap=False):
990 '''Trilaterate three points by I{area overlap} or I{perimeter
991 intersection} of three intersecting circles.
993 @arg distance1: Distance to this point (C{meter}), same units
994 as B{C{eps}}).
995 @arg point2: Second center point (C{LatLon}).
996 @arg distance2: Distance to point2 (C{meter}, same units as
997 B{C{eps}}).
998 @arg point3: Third center point (C{LatLon}).
999 @arg distance3: Distance to point3 (C{meter}, same units as
1000 B{C{eps}}).
1001 @kwarg area: If C{True} compute the area overlap, otherwise the
1002 perimeter intersection of the circles (C{bool}).
1003 @kwarg eps: The required I{minimal overlap} for C{B{area}=True}
1004 or the I{intersection margin} for C{B{area}=False}
1005 (C{meter}, conventionally).
1006 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
1007 B{C{point2}} and B{C{point3}} (C{bool}).
1009 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)}
1010 with C{min} and C{max} in C{meter}, same units as B{C{eps}},
1011 the corresponding trilaterated points C{minPoint} and
1012 C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number
1013 of trilatered points found for the given B{C{eps}}.
1015 If only a single trilaterated point is found, C{min I{is}
1016 max}, C{minPoint I{is} maxPoint} and C{n = 1}.
1018 For C{B{area}=True}, C{min} and C{max} are the smallest
1019 respectively largest I{radial} overlap found.
1021 For C{B{area}=False}, C{min} and C{max} represent the
1022 nearest respectively farthest intersection margin.
1024 If C{B{area}=True} and all 3 circles are concentric, C{n=0}
1025 and C{minPoint} and C{maxPoint} are the B{C{point#}} with
1026 the smallest B{C{distance#}} C{min} respectively C{max} the
1027 largest B{C{distance#}}.
1029 @raise IntersectionError: Trilateration failed for the given B{C{eps}},
1030 insufficient overlap for C{B{area}=True}, no
1031 circle intersections for C{B{area}=False} or
1032 all circles are (near-)concentric.
1034 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
1036 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}},
1037 B{C{distance2}} or B{C{distance3}}.
1039 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2}
1040 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib
1041 <https://PyPI.org/project/geographiclib>} if installed, otherwise
1042 the accurate (but slower) C{ellipsoidalExact.LatLon} methods.
1043 '''
1044 return _trilaterate5(self, distance1,
1045 self.others(point2=point2), distance2,
1046 self.others(point3=point3), distance3,
1047 area=area, eps=eps, wrap=wrap)
1049 @Property_RO
1050 def _ups(self): # __dict__ value overwritten by method C{toUtmUps}
1051 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}),
1052 see L{pygeodesy.toUps8}.
1053 '''
1054 ups = _MODS.ups
1055 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups,
1056 pole=NN, falsed=True, name=self.name)
1058 def _upsOK(self, pole=NN, falsed=True):
1059 '''(INTERNAL) Check matching C{Ups}.
1060 '''
1061 try:
1062 u = self._ups
1063 except RangeError:
1064 return False
1065 return falsed and (u.pole == pole[:1].upper() or not pole)
1067 @Property_RO
1068 def _utm(self): # __dict__ value overwritten by method C{toUtmUps}
1069 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}),
1070 see L{pygeodesy.toUtm8}.
1071 '''
1072 utm = _MODS.utm
1073 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name)
1075 def _utmOK(self):
1076 '''(INTERNAL) Check C{Utm}.
1077 '''
1078 try:
1079 _ = self._utm
1080 except RangeError:
1081 return False
1082 return True
1085def _lowerleft(utmups, center):
1086 '''(INTERNAL) Optionally I{un}-center C{utmups}.
1087 '''
1088 if center in (False, 0, _0_0):
1089 u = utmups
1090 elif center in (True,):
1091 u = utmups._lowerleft
1092 else:
1093 u = _MODS.utmupsBase._lowerleft(utmups, center)
1094 return u
1097def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True
1098 equidistant=None, tol=_TOL_M, **LatLon_and_kwds):
1099 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact,
1100 -GeodSolve, -Karney and -Vincenty to embellish exceptions.
1101 '''
1102 try:
1103 p = _xellipsoidal(point=point)
1104 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within,
1105 height=height, wrap=wrap,
1106 equidistant=equidistant,
1107 tol=tol, **LatLon_and_kwds)
1108 except (TypeError, ValueError) as x:
1109 raise _xError(x, point=point, point1=point1, point2=point2)
1110 return t.closest
1113def _set_reframe(inst, reframe):
1114 '''(INTERNAL) Set or clear an instance's reference frame.
1115 '''
1116 if reframe is not None:
1117 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe)
1118 inst._reframe = reframe
1119 elif inst.reframe is not None:
1120 inst._reframe = None
1123__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase)
1125# **) MIT License
1126#
1127# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1128#
1129# Permission is hereby granted, free of charge, to any person obtaining a
1130# copy of this software and associated documentation files (the "Software"),
1131# to deal in the Software without restriction, including without limitation
1132# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1133# and/or sell copies of the Software, and to permit persons to whom the
1134# Software is furnished to do so, subject to the following conditions:
1135#
1136# The above copyright notice and this permission notice shall be included
1137# in all copies or substantial portions of the Software.
1138#
1139# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1140# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1141# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1142# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1143# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1144# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1145# OTHER DEALINGS IN THE SOFTWARE.