Coverage for pygeodesy/ellipsoidalBase.py: 94%
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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 2005-2024}
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.azimuthal import EquidistantExact, EquidistantKarney # _MODS
16from pygeodesy.basics import _isin, _xinstanceof
17from pygeodesy.constants import EPS, EPS0, EPS1, _0_0, _0_5
18from pygeodesy.cartesianBase import CartesianBase # PYCHOK used!
19# from pygeodesy.css import toCss # _MODS
20from pygeodesy.datums import Datum, Datums, _earth_ellipsoid, _ellipsoidal_datum, \
21 Transform, _WGS84, _EWGS84 # _spherical_datum
22# from pygeodesy.dms import parse3llh # _MODS
23# from pygeodesy.elevations import elevation2, geoidHeight2 # _MODS
24# from pygeodesy.ellipsoidalBaseDI import _intersect3, _intersections2, _nearestOn2 # _MODS
25# from pygeodesy.ellipsoids import _EWGS84 # from .datums
26from pygeodesy.errors import _IsnotError, RangeError, _TypeError, _xattr, _xellipsoidal, \
27 _xellipsoids, _xError, _xkwds, _xkwds_not
28# from pygeodesy.etm import etm, toEtm8 # _MODS
29# from pygeodesy.fmath import favg # _MODS
30from pygeodesy.interns import NN, _COMMA_, _ellipsoidal_
31from pygeodesy.latlonBase import LatLonBase, _trilaterate5, fabs, _Wrap
32from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
33# from pygeodesy.lcc import toLcc # _MODS
34# from pygeodesy.namedTuples import Vector3Tuple # _MODS
35# from pygeodesy.osgr import toOsgr # _MODS
36# from pygeodesy.points import isenclosedBy # _MODS
37from pygeodesy.props import deprecated_method, deprecated_property_RO, \
38 Property_RO, property_doc_, property_RO, _update_all
39# from pygeodesy.trf import RefFrame, _toRefFrame # _MODS
40from pygeodesy.units import Epoch, _isDegrees, Radius_, _1mm as _TOL_M
41# from pygeodesy import ups, utm, utmups # MODS
42# from pygeodesy.utmupsBase import _lowerleft # MODS
43# from pygeodesy.utily import _Wrap # from .latlonBase
44# from pygeodesy.vector3d import _intersects2 # _MODS
46# from math import fabs # from .latlonBase
48__all__ = _ALL_LAZY.ellipsoidalBase
49__version__ = '25.04.14'
52class CartesianEllipsoidalBase(CartesianBase):
53 '''(INTERNAL) Base class for ellipsoidal C{Cartesian}s.
54 '''
55 _datum = _WGS84 # L{Datum}
56 _epoch = None # overriding .reframe.epoch (C{float})
57 _reframe = None # reference frame (L{RefFrame})
59 def __init__(self, x_xyz, y=None, z=None, reframe=None, epoch=None,
60 **datum_ll_name):
61 '''New ellispoidal C{Cartesian...}.
63 @kwarg reframe: Optional reference frame (L{RefFrame}).
64 @kwarg epoch: Optional epoch to observe for B{C{reframe}} (C{scalar}),
65 a non-zero, fractional calendar year; silently ignored
66 if C{B{reframe}=None}.
68 @raise TypeError: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}} coordinate
69 or B{C{x_xyz}} not a C{Cartesian} L{Ecef9Tuple},
70 L{Vector3Tuple} or L{Vector4Tuple} or B{C{datum}} is
71 not a L{Datum}, B{C{reframe}} is not a L{RefFrame} or
72 B{C{epoch}} is not C{scalar} non-zero.
74 @see: Class L{CartesianBase<CartesianBase.__init__>} for more details.
75 '''
76 CartesianBase.__init__(self, x_xyz, y=y, z=z, **datum_ll_name)
77 if reframe:
78 self.reframe = reframe
79 self.epoch = epoch
81# def __matmul__(self, other): # PYCHOK Python 3.5+
82# '''Return C{NotImplemented} for C{c_ = c @ datum}, C{c_ = c @ reframe} and C{c_ = c @ Transform}.
83# '''
84# RefFrame = _MODS.trf.RefFrame
85# return NotImplemented if isinstance(other, (Datum, RefFrame, Transform)) else \
86# _NotImplemented(self, other)
88 @deprecated_method
89 def convertRefFrame(self, reframe2, reframe, epoch=None):
90 '''DEPRECATED, use method L{toRefFrame}.'''
91 return self.toRefFrame(reframe2, reframe=reframe, epoch=epoch) # PYCHOK no cover
93 @property_RO
94 def ellipsoidalCartesian(self):
95 '''Get this C{Cartesian}'s ellipsoidal class.
96 '''
97 return type(self)
99 @property_doc_(''' this cartesian's observed or C{reframe} epoch (C{float}).''')
100 def epoch(self):
101 '''Get this cartesian's observed or C{reframe} epoch (C{Epoch}) or C{None}.
102 '''
103 return self._epoch or (self.reframe.epoch if self.reframe else None)
105 @epoch.setter # PYCHOK setter!
106 def epoch(self, epoch):
107 '''Set or clear this cartesian's observed epoch, a fractional
108 calendar year (L{Epoch}, C{scalar} or C{str}) or C{None}.
110 @raise TRFError: Invalid B{C{epoch}}.
111 '''
112 self._epoch = None if epoch is None else Epoch(epoch)
114 def intersections2(self, radius, center2, radius2, sphere=True,
115 Vector=None, **Vector_kwds):
116 '''Compute the intersection of two spheres or circles, each defined by a
117 cartesian center point and a radius.
119 @arg radius: Radius of this sphere or circle (same units as this point's
120 coordinates).
121 @arg center2: Center of the second sphere or circle (C{Cartesian}, L{Vector3d},
122 C{Vector3Tuple} or C{Vector4Tuple}).
123 @arg radius2: Radius of the second sphere or circle (same units as this and
124 the B{C{other}} point's coordinates).
125 @kwarg sphere: If C{True}, compute the center and radius of the intersection
126 of two I{spheres}. If C{False}, ignore the C{z}-component and
127 compute the intersection of two I{circles} (C{bool}).
128 @kwarg Vector: Class to return intersections (C{Cartesian}, L{Vector3d} or
129 C{Vector3Tuple}) or C{None} for an instance of this (sub-)class.
130 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments,
131 ignored if C{B{Vector} is None}.
133 @return: If C{B{sphere} is True}, a 2-tuple of the C{center} and C{radius} of
134 the intersection of the I{spheres}. The C{radius} is C{0.0} for
135 abutting spheres (and the C{center} is aka the I{radical center}).
137 If C{B{sphere} is False}, a 2-tuple with the two intersection points
138 of the I{circles}. For abutting circles, both points are the same
139 instance, aka the I{radical center}.
141 @raise IntersectionError: Concentric, invalid or non-intersecting spheres or circles.
143 @raise TypeError: Invalid B{C{center2}}.
145 @raise UnitError: Invalid B{C{radius}} or B{C{radius2}}.
147 @see: U{Sphere-Sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>},
148 U{Circle-Circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>}
149 Intersection and function L{pygeodesy.radical2}.
150 '''
151 try:
152 return _MODS.vector3d._intersects2(self, Radius_(radius=radius),
153 center2, Radius_(radius2=radius2),
154 sphere=sphere, clas=self.classof,
155 Vector=Vector, **Vector_kwds)
156 except (TypeError, ValueError) as x:
157 raise _xError(x, center=self, radius=radius, center2=center2, radius2=radius2)
159 @property_doc_(''' this cartesian's reference frame (L{RefFrame}).''')
160 def reframe(self):
161 '''Get this cartesian's reference frame (L{RefFrame}) or C{None}.
162 '''
163 return self._reframe
165 @reframe.setter # PYCHOK setter!
166 def reframe(self, reframe):
167 '''Set or clear this cartesian's reference frame (L{RefFrame}) or C{None}.
169 @raise TypeError: The B{C{reframe}} is not a L{RefFrame}.
170 '''
171 _set_reframe(self, reframe)
173 def toLatLon(self, datum=None, height=None, **LatLon_and_kwds): # PYCHOK signature
174 '''Convert this cartesian to a I{geodetic} (lat-/longitude) point.
176 @see: Method L{toLatLon<cartesianBase.CartesianBase.toLatLon>}
177 for further details.
178 '''
179 kwds = LatLon_and_kwds
180 if kwds:
181 kwds = _xkwds(kwds, reframe=self.reframe, epoch=self.epoch)
182 return CartesianBase.toLatLon(self, datum=datum, height=height, **kwds)
184 def toRefFrame(self, reframe2, reframe=None, epoch=None, epoch2=None, **name):
185 '''Convert this point to an other reference frame and epoch.
187 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
188 @kwarg reframe: Optional reference frame to convert I{from} (L{RefFrame}),
189 overriding this point's reference frame.
190 @kwarg epoch: Optional epoch (L{Epoch}, C{scalar} or C{str}), overriding
191 this point's C{epoch or B{reframe}.epoch}.
192 @kwarg epoch2: Optional epoch to observe for the converted point (L{Epoch},
193 C{scalar} or C{str}), otherwise B{C{epoch}}.
194 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding C{B{reframe2}.name}.
196 @return: The converted point (ellipsoidal C{Cartesian}) or if conversion
197 C{isunity}, this point or a copy of this point if the B{C{name}}
198 is non-empty.
200 @raise TRFError: This point's C{reframe} is not defined, invalid B{C{epoch}}
201 or B{C{epoch2}} or conversion from this point's C{reframe}
202 to B{C{reframe2}} is not available.
204 @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a L{RefFrame}.
205 '''
206 return _MODS.trf._toRefFrame(self, reframe2, reframe=reframe, epoch=epoch,
207 epoch2=epoch2, **name)
209 @deprecated_method
210 def toTransforms_(self, *transforms, **datum): # PYCHOK no cover
211 '''DEPRECATED on 2024.02.14, use method C{toTransform}.'''
212 r = self
213 for t in transforms:
214 r = r.toTransform(t)
215 return r.dup(**datum) if datum else r
218class LatLonEllipsoidalBase(LatLonBase):
219 '''(INTERNAL) Base class for ellipsoidal C{LatLon}s.
220 '''
221 _datum = _WGS84 # L{Datum}
222 _elevation2to = None # _elevation2 timeout (C{secs})
223 _epoch = None # overriding .reframe.epoch (C{float})
224 _gamma = None # UTM/UPS meridian convergence (C{degrees})
225 _geoidHeight2to = None # _geoidHeight2 timeout (C{secs})
226 _reframe = None # reference frame (L{RefFrame})
227 _scale = None # UTM/UPS scale factor (C{float})
228 _toLLEB_args = () # Etm/Utm/Ups._toLLEB arguments
230 def __init__(self, latlonh, lon=None, height=0, datum=_WGS84, reframe=None,
231 epoch=None, wrap=False, **name):
232 '''Create an ellipsoidal C{LatLon} point from the given lat-, longitude
233 and height on the given datum, reference frame and epoch.
235 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or
236 a previous C{LatLon} instance provided C{B{lon}=None}.
237 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or C(None),
238 indicating B{C{latlonh}} is a C{LatLon}.
239 @kwarg height: Optional height above (or below) the earth surface (C{meter},
240 same units as the datum's ellipsoid axes).
241 @kwarg datum: Optional, ellipsoidal datum to use (L{Datum}, L{Ellipsoid},
242 L{Ellipsoid2} or L{a_f2Tuple}).
243 @kwarg reframe: Optional reference frame (L{RefFrame}).
244 @kwarg epoch: Optional epoch to observe for B{C{reframe}} (C{scalar}), a
245 non-zero, fractional calendar year, but silently ignored if
246 C{B{reframe}=None}.
247 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}} (C{bool}).
248 @kwarg name: Optional C{B{name}=NN} (C{str}).
250 @raise RangeError: Value of C{lat} or B{C{lon}} outside the valid range and
251 L{rangerrors} set to C{True}.
253 @raise TypeError: If B{C{latlonh}} is not a C{LatLon}, B{C{datum}} is not a
254 L{Datum}, B{C{reframe}} is not a L{RefFrame} or B{C{epoch}}
255 is not C{scalar} non-zero.
257 @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}.
258 '''
259 LatLonBase.__init__(self, latlonh, lon=lon, height=height, wrap=wrap, **name)
260 if not _isin(datum, None, self._datum, _EWGS84):
261 self.datum = _ellipsoidal_datum(datum, name=self.name)
262 if reframe:
263 self.reframe = reframe
264 self.epoch = epoch
266# def __matmul__(self, other): # PYCHOK Python 3.5+
267# '''Return C{NotImplemented} for C{ll_ = ll @ datum} and C{ll_ = ll @ reframe}.
268# '''
269# RefFrame = _MODS.trf.RefFrame
270# return NotImplemented if isinstance(other, (Datum, RefFrame)) else \
271# _NotImplemented(self, other)
273 def antipode(self, height=None):
274 '''Return the antipode, the point diametrically opposite
275 to this point.
277 @kwarg height: Optional height of the antipode, height
278 of this point otherwise (C{meter}).
280 @return: The antipodal point (C{LatLon}).
281 '''
282 lla = LatLonBase.antipode(self, height=height)
283 if lla.datum != self.datum:
284 lla.datum = self.datum
285 return lla
287 @deprecated_property_RO
288 def convergence(self):
289 '''DEPRECATED, use property C{gamma}.'''
290 return self.gamma # PYCHOK no cover
292 @deprecated_method
293 def convertDatum(self, datum2):
294 '''DEPRECATED, use method L{toDatum}.'''
295 return self.toDatum(datum2)
297 @deprecated_method
298 def convertRefFrame(self, reframe2):
299 '''DEPRECATED, use method L{toRefFrame}.'''
300 return self.toRefFrame(reframe2)
302 @property_doc_(''' this points's datum (L{Datum}).''')
303 def datum(self):
304 '''Get this point's datum (L{Datum}).
305 '''
306 return self._datum
308 @datum.setter # PYCHOK setter!
309 def datum(self, datum):
310 '''Set this point's datum I{without conversion} (L{Datum}).
312 @raise TypeError: The B{C{datum}} is not a L{Datum} or not ellipsoidal.
313 '''
314 _xinstanceof(Datum, datum=datum)
315 if not datum.isEllipsoidal:
316 raise _IsnotError(_ellipsoidal_, datum=datum)
317 if self._datum != datum:
318 _update_all(self)
319 self._datum = datum
321 def distanceTo2(self, other, wrap=False):
322 '''I{Approximate} the distance and (initial) bearing between this
323 and an other (ellipsoidal) point based on the radii of curvature.
325 I{Suitable only for short distances up to a few hundred Km
326 or Miles and only between points not near-polar}.
328 @arg other: The other point (C{LatLon}).
329 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{other}}
330 point (C{bool}).
332 @return: An L{Distance2Tuple}C{(distance, initial)}.
334 @raise TypeError: The B{C{other}} point is not C{LatLon}.
336 @raise ValueError: Incompatible datum ellipsoids.
338 @see: Method L{Ellipsoid.distance2} and U{Local, flat earth
339 approximation<https://www.EdWilliams.org/avform.htm#flat>}
340 aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>}
341 formula.
342 '''
343 p = self.others(other)
344 if wrap: # PYCHOK no cover
345 p = _Wrap.point(p)
346 E = self.ellipsoids(other)
347 return E.distance2(*(self.latlon + p.latlon))
349 @Property_RO
350 def _elevation2(self):
351 '''(INTERNAL) Get elevation and data source.
352 '''
353 return _MODS.elevations.elevation2(self.lat, self.lon,
354 timeout=self._elevation2to)
356 def elevation2(self, adjust=True, datum=None, timeout=2):
357 '''Return elevation of this point for its or the given datum, ellipsoid
358 or sphere.
360 @kwarg adjust: Adjust the elevation for a B{C{datum}} other than
361 C{NAD83} (C{bool}).
362 @kwarg datum: Optional datum overriding this point's datum (L{Datum},
363 L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar}
364 radius).
365 @kwarg timeout: Optional query timeout (C{seconds}).
367 @return: An L{Elevation2Tuple}C{(elevation, data_source)} or
368 C{(None, error)} in case of errors.
370 @note: The adjustment applied is the difference in geocentric earth
371 radius between the B{C{datum}} and C{NAV83} upon which the
372 L{elevations.elevation2} is based.
374 @note: NED elevation is only available for locations within the U{Conterminous
375 US (CONUS)<https://WikiPedia.org/wiki/Contiguous_United_States>}.
377 @see: Function L{elevations.elevation2} and method C{Ellipsoid.Rgeocentric}
378 for further details and possible C{error}s.
379 '''
380 if self._elevation2to != timeout:
381 self._elevation2to = timeout
382 LatLonEllipsoidalBase._elevation2._update(self)
383 return self._Radjust2(adjust, datum, self._elevation2)
385 def ellipsoid(self, datum=_WGS84):
386 '''Return the ellipsoid of this point's datum or the given datum.
388 @kwarg datum: Default datum (L{Datum}).
390 @return: The ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
391 '''
392 return _xattr(self, datum=datum).ellipsoid
394 @property_RO
395 def ellipsoidalLatLon(self):
396 '''Get this C{LatLon}'s ellipsoidal class.
397 '''
398 return type(self)
400 def ellipsoids(self, other):
401 '''Check the type and ellipsoid of this and an other point's datum.
403 @arg other: The other point (C{LatLon}).
405 @return: This point's datum ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
407 @raise TypeError: The B{C{other}} point is not C{LatLon}.
409 @raise ValueError: Incompatible datum ellipsoids.
410 '''
411 self.others(other, up=2) # ellipsoids' caller
413 E = self.ellipsoid()
414 try: # other may be Sphere, etc.
415 e = other.ellipsoid()
416 except AttributeError:
417 try: # no ellipsoid method, try datum
418 e = other.datum.ellipsoid
419 except AttributeError:
420 e = E # no datum, XXX assume equivalent?
421 return _xellipsoids(E, e)
423 @property_doc_(''' this point's observed or C{reframe} epoch (C{float}).''')
424 def epoch(self):
425 '''Get this point's observed or C{reframe} epoch (L{Epoch}) or C{None}.
426 '''
427 return self._epoch or (self.reframe.epoch if self.reframe else None)
429 @epoch.setter # PYCHOK setter!
430 def epoch(self, epoch):
431 '''Set or clear this point's observed epoch, a fractional
432 calendar year (L{Epoch}, C{scalar} or C{str}) or C{None}.
434 @raise TRFError: Invalid B{C{epoch}}.
435 '''
436 self._epoch = None if epoch is None else Epoch(epoch)
438 @Property_RO
439 def Equidistant(self):
440 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantKarney} or L{EquidistantExact}).
441 '''
442 try:
443 _ = self.datum.ellipsoid.geodesic
444 return _MODS.azimuthal.EquidistantKarney
445 except ImportError: # no geographiclib
446 return _MODS.azimuthal.EquidistantExact # XXX no longer L{azimuthal.Equidistant}
448 @Property_RO
449 def _etm(self):
450 '''(INTERNAL) Get this C{LatLon} point as an ETM coordinate (L{pygeodesy.toEtm8}).
451 '''
452 etm = _MODS.etm
453 return etm.toEtm8(self, datum=self.datum, Etm=etm.Etm)
455 @property_RO
456 def gamma(self):
457 '''Get this point's UTM or UPS meridian convergence (C{degrees}) or
458 C{None} if not available or not converted from L{Utm} or L{Ups}.
459 '''
460 return self._gamma
462 @Property_RO
463 def _geoidHeight2(self):
464 '''(INTERNAL) Get geoid height and model.
465 '''
466 return _MODS.elevations.geoidHeight2(self.lat, self.lon, model=0,
467 timeout=self._geoidHeight2to)
469 def geoidHeight2(self, adjust=False, datum=None, timeout=2):
470 '''Return geoid height of this point for its or the given datum, ellipsoid
471 or sphere.
473 @kwarg adjust: Adjust the geoid height for a B{C{datum}} other than
474 C{NAD83/NADV88} (C{bool}).
475 @kwarg datum: Optional datum overriding this point's datum (L{Datum},
476 L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar}
477 radius).
478 @kwarg timeout: Optional query timeout (C{seconds}).
480 @return: A L{GeoidHeight2Tuple}C{(height, model_name)} or
481 C{(None, error)} in case of errors.
483 @note: The adjustment applied is the difference in geocentric earth
484 radius between the B{C{datum}} and C{NAV83/NADV88} upon which
485 the L{elevations.geoidHeight2} is based.
487 @note: The geoid height is only available for locations within the U{Conterminous
488 US (CONUS)<https://WikiPedia.org/wiki/Contiguous_United_States>}.
490 @see: Function L{elevations.geoidHeight2} and method C{Ellipsoid.Rgeocentric}
491 for further details and possible C{error}s.
492 '''
493 if self._geoidHeight2to != timeout:
494 self._geoidHeight2to = timeout
495 LatLonEllipsoidalBase._geoidHeight2._update(self)
496 return self._Radjust2(adjust, datum, self._geoidHeight2)
498 def intermediateTo(self, other, fraction, height=None, wrap=False): # PYCHOK no cover
499 '''I{Must be overloaded}.'''
500 self._notOverloaded(other, fraction, height=height, wrap=wrap)
502 def intersection3(self, end1, start2, end2, height=None, wrap=False, # was=True
503 equidistant=None, tol=_TOL_M):
504 '''I{Iteratively} compute the intersection point of two geodesic lines, each
505 given as two points or as a start point and a bearing from North.
507 @arg end1: End point of this line (C{LatLon}) or the initial bearing at
508 this point (compass C{degrees360}).
509 @arg start2: Start point of the second line (this C{LatLon}).
510 @arg end2: End point of the second line (this C{LatLon}) or the initial
511 bearing at B{C{start2}} (compass C{degrees360}).
512 @kwarg height: Optional height at the intersection (C{meter}, conventionally)
513 or C{None} for the mean height.
514 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{start2}} and
515 both B{C{end*}} points (C{bool}).
516 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
517 L{pygeodesy.equidistant}), or C{None} for this point's
518 preferred C{.Equidistant}.
519 @kwarg tol: Tolerance for convergence and skew line distance and length
520 (C{meter}, conventionally).
522 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
523 a C{LatLon} instance.
525 @raise ImportError: Package U{geographiclib
526 <https://PyPI.org/project/geographiclib>} not
527 installed or not found, but only in case
528 C{B{equidistant}=}L{EquidistantKarney}.
530 @raise IntersectionError: Skew, colinear, parallel or otherwise non-intersecting
531 lines or no convergence for the given B{C{tol}}.
533 @raise TypeError: Invalid B{C{end1}}, B{C{start2}} or B{C{end2}}.
535 @note: For each line specified with an initial bearing, a pseudo-end point is
536 computed as the C{destination} along that bearing at about 1.5 times the
537 distance from the start point to an initial gu-/estimate of the intersection
538 point (and between 1/8 and 3/8 of the C{authalic} earth perimeter).
540 @see: I{Karney's} U{intersect.cpp<https://SourceForge.net/p/geographiclib/
541 discussion/1026621/thread/21aaff9f/>}, U{The B{ellipsoidal} case<https://
542 GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>}
543 and U{Karney's paper<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section
544 B{14. MARITIME BOUNDARIES} for more details about the iteration algorithm.
545 '''
546 try:
547 s2 = self.others(start2=start2)
548 return _MODS.ellipsoidalBaseDI._intersect3(self, end1,
549 s2, end2,
550 height=height, wrap=wrap,
551 equidistant=equidistant, tol=tol,
552 LatLon=self.classof, datum=self.datum)
553 except (TypeError, ValueError) as x:
554 raise _xError(x, start1=self, end1=end1, start2=start2, end2=end2,
555 height=height, wrap=wrap, tol=tol)
557 def intersections2(self, radius1, center2, radius2, height=None, wrap=False, # was=True
558 equidistant=None, tol=_TOL_M):
559 '''I{Iteratively} compute the intersection points of two circles, each
560 defined by a center point and a radius.
562 @arg radius1: Radius of this circle (C{meter}, conventionally).
563 @arg center2: Center of the other circle (this C{LatLon}).
564 @arg radius2: Radius of the other circle (C{meter}, same units as
565 B{C{radius1}}).
566 @kwarg height: Optional height for the intersection points (C{meter},
567 conventionally) or C{None} for the I{"radical height"}
568 at the I{radical line} between both centers.
569 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}
570 (C{bool}).
571 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
572 function L{pygeodesy.equidistant}) or C{None}
573 for this point's preferred C{.Equidistant}.
574 @kwarg tol: Convergence tolerance (C{meter}, same units as
575 B{C{radius1}} and B{C{radius2}}).
577 @return: 2-Tuple of the intersection points, each a C{LatLon}
578 instance. For abutting circles, both intersection
579 points are the same instance, aka the I{radical center}.
581 @raise ImportError: Package U{geographiclib
582 <https://PyPI.org/project/geographiclib>}
583 not installed or not found, but only if
584 C{B{equidistant}=}L{EquidistantKarney}.
586 @raise IntersectionError: Concentric, antipodal, invalid or
587 non-intersecting circles or no
588 convergence for the given B{C{tol}}.
590 @raise TypeError: Invalid B{C{center2}} or B{C{equidistant}}.
592 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
594 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
595 calculating-intersection-of-two-circles>}, U{Karney's paper
596 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
597 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
598 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
599 intersections.
600 '''
601 try:
602 c2 = self.others(center2=center2)
603 return _MODS.ellipsoidalBaseDI._intersections2(self, radius1,
604 c2, radius2,
605 height=height, wrap=wrap,
606 equidistant=equidistant, tol=tol,
607 LatLon=self.classof, datum=self.datum)
608 except (AssertionError, TypeError, ValueError) as x:
609 raise _xError(x, center=self, radius1=radius1, center2=center2, radius2=radius2,
610 height=height, wrap=wrap, tol=tol)
612 def isenclosedBy(self, points, wrap=False):
613 '''Check whether a polygon or composite encloses this point.
615 @arg points: The polygon points or clips (C{LatLon}[],
616 L{BooleanFHP} or L{BooleanGH}).
617 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
618 B{C{points}} (C{bool}).
620 @return: C{True} if this point is inside the polygon or composite,
621 C{False} otherwise.
623 @raise PointsError: Insufficient number of B{C{points}}.
625 @raise TypeError: Some B{C{points}} are not C{LatLon}.
627 @raise ValueError: Invalid B{C{point}}, lat- or longitude.
629 @see: Functions L{pygeodesy.isconvex}, L{pygeodesy.isenclosedBy}
630 and L{pygeodesy.ispolar} especially if the B{C{points}} may
631 enclose a pole or wrap around the earth I{longitudinally}.
632 '''
633 return _MODS.points.isenclosedBy(self, points, wrap=wrap)
635 @property_RO
636 def iteration(self):
637 '''Get the most recent C{intersections2} or C{nearestOn} iteration
638 number (C{int}) or C{None} if not available/applicable.
639 '''
640 return self._iteration
642 def midpointTo(self, other, height=None, fraction=_0_5, wrap=False):
643 '''Find the midpoint on a geodesic between this and an other point.
645 @arg other: The other point (C{LatLon}).
646 @kwarg height: Optional height for midpoint, overriding the
647 mean height (C{meter}).
648 @kwarg fraction: Midpoint location from this point (C{scalar}),
649 may be negative or greater than 1.0.
650 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
651 B{C{other}} point (C{bool}).
653 @return: Midpoint (C{LatLon}).
655 @raise TypeError: The B{C{other}} point is not C{LatLon}.
657 @raise ValueError: Invalid B{C{height}}.
659 @see: Methods C{intermediateTo} and C{rhumbMidpointTo}.
660 '''
661 return self.intermediateTo(other, fraction, height=height, wrap=wrap)
663 def nearestOn(self, point1, point2, within=True, height=None, wrap=False, # was=True
664 equidistant=None, tol=_TOL_M):
665 '''I{Iteratively} locate the closest point on the geodesic (line)
666 between two other (ellipsoidal) points.
668 @arg point1: Start point of the geodesic (C{LatLon}).
669 @arg point2: End point of the geodesic (C{LatLon}).
670 @kwarg within: If C{True}, return the closest point I{between} B{C{point1}} and
671 B{C{point2}}, otherwise the closest point elsewhere on the geodesic
672 (C{bool}).
673 @kwarg height: Optional height for the closest point (C{meter}, conventionally)
674 or C{None} or C{False} for the interpolated height. If C{False},
675 the closest takes the heights of the points into account.
676 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both B{C{point1}} and
677 B{C{point2}} (C{bool}).
678 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
679 L{pygeodesy.equidistant}) or C{None} for this point's preferred
680 C{Equidistant}, like L{Equidistant<LatLonEllipsoidalBase.Equidistant>}.
681 @kwarg tol: Convergence tolerance (C{meter}, conventionally).
683 @return: Closest point (C{LatLon}).
685 @raise ImportError: Package U{geographiclib
686 <https://PyPI.org/project/geographiclib>}
687 not installed or not found, but only if
688 C{B{equidistant}=}L{EquidistantKarney}.
690 @raise TypeError: Invalid B{C{point1}}, B{C{point2}} or B{C{equidistant}}.
692 @raise ValueError: Datum or ellipsoid of B{C{point1}} or B{C{point2}} is incompatible
693 or no convergence for the given B{C{tol}}.
695 @see: I{Karney}'s U{intercept.cpp<https://SourceForge.net/p/geographiclib/
696 discussion/1026621/thread/21aaff9f/>}, U{The B{ellipsoidal} case<https://
697 GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>}
698 and U{Karney's paper<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section
699 B{14. MARITIME BOUNDARIES} for details about the iteration algorithm.
700 '''
701 try:
702 t = _MODS.ellipsoidalBaseDI._nearestOn2(self, point1, point2, within=within,
703 height=height, wrap=wrap,
704 equidistant=equidistant,
705 tol=tol, LatLon=self.classof)
706 except (TypeError, ValueError) as x:
707 raise _xError(x, point=self, point1=point1, point2=point2, within=within,
708 height=height, wrap=wrap, tol=tol)
709 return t.closest
711 def parse(self, strllh, height=0, datum=None, epoch=None, reframe=None,
712 sep=_COMMA_, wrap=False, **name):
713 '''Parse a string consisting of C{"lat, lon[, height]"},
714 representing a similar, ellipsoidal C{LatLon} point.
716 @arg strllh: Lat, lon and optional height (C{str}), see function
717 L{pygeodesy.parse3llh}.
718 @kwarg height: Optional, default height (C{meter} or C{None}).
719 @kwarg datum: Optional datum (L{Datum}), overriding this datum
720 I{without conversion}.
721 @kwarg epoch: Optional datum (L{Epoch}), overriding this epoch
722 I{without conversion}.
723 @kwarg reframe: Optional reference frame (L{RefFrame}), overriding
724 this reframe I{without conversion}.
725 @kwarg sep: Optional separator (C{str}).
726 @kwarg wrap: If C{True}, wrap or I{normalize} the lat- and
727 longitude (C{bool}).
728 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
730 @return: The similar point (ellipsoidal C{LatLon}).
732 @raise ParseError: Invalid B{C{strllh}}.
733 '''
734 a, b, h = _MODS.dms.parse3llh(strllh, height=height, sep=sep, wrap=wrap)
735 return self.classof(a, b, height=h, datum=datum or self.datum,
736 epoch=epoch or self.epoch,
737 reframe=reframe or self.reframe, **name)
739 def _Radjust2(self, adjust, datum, meter_text2):
740 '''(INTERNAL) Adjust an C{elevation} or C{geoidHeight} with
741 difference in Gaussian radii of curvature of the given
742 datum and NAD83 ellipsoids at this point's latitude.
744 @note: This is an arbitrary, possibly incorrect adjustment.
745 '''
746 if adjust: # Elevation2Tuple or GeoidHeight2Tuple
747 m, t = meter_text2
748 if isinstance(m, float) and fabs(m) > EPS: # PYCHOK no cover
749 n = Datums.NAD83.ellipsoid.rocGauss(self.lat)
750 if n > EPS0:
751 # use ratio, datum and NAD83 units may differ
752 E = self.ellipsoid() if _isin(datum, None, self.datum) else \
753 _earth_ellipsoid(datum)
754 r = E.rocGauss(self.lat)
755 if r > EPS0 and fabs(r - n) > EPS: # EPS1
756 m *= r / n
757 meter_text2 = meter_text2.classof(m, t)
758 return self._xnamed(meter_text2)
760 @property_doc_(''' this point's reference frame (L{RefFrame}).''')
761 def reframe(self):
762 '''Get this point's reference frame (L{RefFrame}) or C{None}.
763 '''
764 return self._reframe
766 @reframe.setter # PYCHOK setter!
767 def reframe(self, reframe):
768 '''Set or clear this point's reference frame (L{RefFrame}) or C{None}.
770 @raise TypeError: The B{C{reframe}} is not a L{RefFrame}.
771 '''
772 _set_reframe(self, reframe)
774 @Property_RO
775 def scale(self):
776 '''Get this point's UTM grid or UPS point scale factor (C{float})
777 or C{None} if not converted from L{Utm} or L{Ups}.
778 '''
779 return self._scale
781 def toCartesian(self, height=None, **Cartesian_and_kwds): # PYCHOK signature
782 '''Convert this point to cartesian, I{geocentric} coordinates,
783 also known as I{Earth-Centered, Earth-Fixed} (ECEF).
785 @see: Method L{toCartesian<latlonBase.LatLonBase.toCartesian>}
786 for further details.
787 '''
788 kwds = Cartesian_and_kwds
789 if kwds:
790 kwds = _xkwds(kwds, reframe=self.reframe, epoch=self.epoch)
791 return LatLonBase.toCartesian(self, height=height, **kwds)
793 def toCss(self, **toCss_kwds):
794 '''Convert this C{LatLon} point to a Cassini-Soldner location.
796 @kwarg toCss_kwds: Optional L{pygeodesy.toCss} keyword arguments.
798 @return: The Cassini-Soldner location (L{Css}).
800 @see: Function L{pygeodesy.toCss}.
801 '''
802 return _MODS.css.toCss(self, **self._name1__(toCss_kwds))
804 def toDatum(self, datum2, height=None, **name):
805 '''Convert this point to an other datum.
807 @arg datum2: Datum to convert I{to} (L{Datum}).
808 @kwarg height: Optional height, overriding the
809 converted height (C{meter}).
810 @kwarg name: Optional C{B{name}=NN} (C{str}).
812 @return: The converted point (this C{LatLon}) or a copy
813 of this point if B{C{datum2}} matches this
814 point's C{datum}.
816 @raise TypeError: Invalid B{C{datum2}}.
817 '''
818 n = self._name__(name)
819 d2 = _ellipsoidal_datum(datum2, name=n)
820 if self.datum == d2:
821 r = self.copy(name=n)
822 else:
823 kwds = _xkwds_not(None, LatLon=self.classof, name=n,
824 epoch=self.epoch, reframe=self.reframe)
825 c = self.toCartesian().toDatum(d2)
826 r = c.toLatLon(datum=d2, height=height, **kwds)
827 return r
829 def toEtm(self, **toEtm8_kwds):
830 '''Convert this C{LatLon} point to an ETM coordinate.
832 @kwarg toEtm8_kwds: Optional L{pygeodesy.toEtm8} keyword arguments.
834 @return: The ETM coordinate (L{Etm}).
836 @see: Function L{pygeodesy.toEtm8}.
837 '''
838 return _MODS.etm.toEtm8(self, **self._name1__(toEtm8_kwds)) if toEtm8_kwds else self._etm
840 def toLcc(self, **toLcc_kwds):
841 '''Convert this C{LatLon} point to a Lambert location.
843 @kwarg toLcc_kwds: Optional L{pygeodesy.toLcc} keyword arguments.
845 @return: The Lambert location (L{Lcc}).
847 @see: Function L{pygeodesy.toLcc}.
848 '''
849 return _MODS.lcc.toLcc(self, **self._name1__(toLcc_kwds))
851 def toMgrs(self, center=False, pole=NN):
852 '''Convert this C{LatLon} point to an MGRS coordinate.
854 @kwarg center: If C{True}, try to I{un}-center MGRS
855 to its C{lowerleft} (C{bool}) or by
856 C{B{center} meter} (C{scalar}).
857 @kwarg pole: Optional top/center for the MGRS UPS
858 projection (C{str}, 'N[orth]' or 'S[outh]').
860 @return: The MGRS coordinate (L{Mgrs}).
862 @see: Method L{toUtmUps} and L{Mgrs.toLatLon}.
863 '''
864 return self.toUtmUps(center=center, pole=pole).toMgrs(center=False)
866 def toOsgr(self, kTM=False, **toOsgr_kwds):
867 '''Convert this C{LatLon} point to an OSGR coordinate.
869 @kwarg kTM: If C{True}, use I{Karney}'s Krüger method from module
870 L{ktm}, otherwise I{Ordinance Survery}'s recommended
871 formulation (C{bool}).
872 @kwarg toOsgr_kwds: Optional L{pygeodesy.toOsgr} keyword arguments.
874 @return: The OSGR coordinate (L{Osgr}).
876 @see: Function L{pygeodesy.toOsgr}.
877 '''
878 return _MODS.osgr.toOsgr(self, kTM=kTM, **self._name1__(toOsgr_kwds))
880 def toRefFrame(self, reframe2, reframe=None, epoch=None, epoch2=None, height=None, **name):
881 '''Convert this point to an other reference frame and epoch.
883 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
884 @kwarg reframe: Optional reference frame to convert I{from} (L{RefFrame}),
885 overriding this point's reference frame.
886 @kwarg epoch: Optional epoch (L{Epoch}, C{scalar} or C{str}), overriding
887 this point's C{epoch or B{reframe}.epoch}.
888 @kwarg epoch2: Optional epoch to observe for the converted point (L{Epoch},
889 C{scalar} or C{str}), otherwise B{C{epoch}}.
890 @kwarg height: Optional height, overriding the converted height (C{meter}).
891 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding C{B{reframe2}.name}.
893 @return: The converted point (ellipsoidal C{LatLon}) or if conversion
894 C{isunity}, this point or a copy of this point if the B{C{name}}
895 is non-empty.
897 @raise TRFError: This point's C{reframe} is not defined, invalid B{C{epoch}}
898 or B{C{epoch2}} or conversion from this point's C{reframe}
899 to B{C{reframe2}} is not available.
901 @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a L{RefFrame}.
902 '''
903 return _MODS.trf._toRefFrame(self, reframe2, reframe=reframe, epoch=epoch,
904 epoch2=epoch2, height=height, **name)
906 def toTransform(self, transform, inverse=False, datum=None, **LatLon_kwds):
907 '''Apply a Helmert transform to this geodetic point.
909 @arg transform: Transform to apply (L{Transform} or L{TransformXform}).
910 @kwarg inverse: Apply the inverse of the Helmert transform (C{bool}).
911 @kwarg datum: Datum for the transformed point (L{Datum}), overriding
912 this point's datum but I{not} taken it into account.
913 @kwarg LatLon_kwds: Optional keyword arguments for the transformed
914 point, like C{B{height}=...}.
916 @return: A transformed point (C{LatLon}) or a copy of this point if
917 C{B{transform}.isunity}.
919 @raise TypeError: Invalid B{C{transform}}.
920 '''
921 _xinstanceof(Transform, transform=transform)
922 d = datum or self.datum
923 if transform.isunity:
924 r = self.dup(datum=d, **LatLon_kwds)
925 else:
926 c = self.toCartesian()
927 c = c.toTransform(transform, inverse=inverse, datum=d)
928 r = c.toLatLon(LatLon=self.classof, **_xkwds(LatLon_kwds, height=self.height))
929 return r
931 def toUps(self, pole=NN, falsed=True, center=False):
932 '''Convert this C{LatLon} point to a UPS coordinate.
934 @kwarg pole: Optional top/center of (stereographic)
935 projection (C{str}, 'N[orth]' or 'S[outh]').
936 @kwarg falsed: False easting and northing (C{bool}).
937 @kwarg center: If C{True}, I{un}-center the UPS to its
938 C{lowerleft} (C{bool}) or by C{B{center}
939 meter} (C{scalar}).
941 @return: The UPS coordinate (L{Ups}).
943 @see: Function L{pygeodesy.toUps8}.
944 '''
945 if self._upsOK(pole, falsed):
946 u = self._ups
947 else:
948 ups = _MODS.ups
949 u = ups.toUps8(self, datum=self.datum, Ups=ups.Ups,
950 pole=pole, falsed=falsed)
951 return _lowerleft(u, center)
953 def toUtm(self, center=False):
954 '''Convert this C{LatLon} point to a UTM coordinate.
956 @kwarg center: If C{True}, I{un}-center the UTM to its
957 C{lowerleft} (C{bool}) or by C{B{center}
958 meter} (C{scalar}).
960 @return: The UTM coordinate (L{Utm}).
962 @see: Method L{Mgrs.toUtm} and function L{pygeodesy.toUtm8}.
963 '''
964 return _lowerleft(self._utm, center)
966 def toUtmUps(self, pole=NN, center=False):
967 '''Convert this C{LatLon} point to a UTM or UPS coordinate.
969 @kwarg pole: Optional top/center of UPS (stereographic)
970 projection (C{str}, 'N[orth]' or 'S[outh]').
971 @kwarg center: If C{True}, I{un}-center the UTM or UPS to
972 its C{lowerleft} (C{bool}) or by C{B{center}
973 meter} (C{scalar}).
975 @return: The UTM or UPS coordinate (L{Utm} or L{Ups}).
977 @see: Function L{pygeodesy.toUtmUps8}.
978 '''
979 if self._utmOK():
980 u = self._utm
981 elif self._upsOK(pole):
982 u = self._ups
983 else: # no cover
984 utmups = _MODS.utmups
985 u = utmups.toUtmUps8(self, datum=self.datum, pole=pole, name=self.name,
986 Utm=utmups.Utm, Ups=utmups.Ups)
987 if isinstance(u, utmups.Utm):
988 self._update(False, _utm=u) # PYCHOK kwds
989 elif isinstance(u, utmups.Ups):
990 self._update(False, _ups=u) # PYCHOK kwds
991 else:
992 _xinstanceof(utmups.Utm, utmups.Ups, toUtmUps8=u)
993 return _lowerleft(u, center)
995 @deprecated_method
996 def to3xyz(self): # PYCHOK no cover
997 '''DEPRECATED, use method C{toEcef}.
999 @return: A L{Vector3Tuple}C{(x, y, z)}.
1001 @note: Overloads C{LatLonBase.to3xyz}
1002 '''
1003 r = self.toEcef()
1004 return _MODS.namedTuples.Vector3Tuple(r.x, r.y, r.z, name=self.name)
1006 def triangulate(self, bearing1, other, bearing2, **height_wrap_tol):
1007 '''I{Iteratively} locate a point given this, an other point and a bearing
1008 from North at each point.
1010 @arg bearing1: Bearing at this point (compass C{degrees360}).
1011 @arg other: The other point (C{LatLon}).
1012 @arg bearing2: Bearing at the B{C{other}} point (compass C{degrees360}).
1013 @kwarg height_wrap_tol: Optional keyword arguments C{B{height}=None},
1014 C{B{wrap}=False} and C{B{tol}}, see method L{intersection3
1015 <pygeodesy.ellipsoidalBase.LatLonEllipsoidalBase>}.
1017 @return: Triangulated point (C{LatLon}).
1019 @see: Method L{intersection3<pygeodesy.ellipsoidalBase.LatLonEllipsoidalBase>}
1020 for further details.
1021 '''
1022 if _isDegrees(bearing1) and _isDegrees(bearing2):
1023 r = self.intersection3(bearing1, other, bearing2, **height_wrap_tol)
1024 return r.point
1025 raise _TypeError(bearing1=bearing1, bearing2=bearing2 **height_wrap_tol)
1027 def trilaterate5(self, distance1, point2, distance2, point3, distance3,
1028 area=True, eps=EPS1, wrap=False):
1029 '''Trilaterate three points by I{area overlap} or I{perimeter intersection}
1030 of three intersecting circles.
1032 @arg distance1: Distance to this point (C{meter}), same units as B{C{eps}}).
1033 @arg point2: Second center point (C{LatLon}).
1034 @arg distance2: Distance to point2 (C{meter}, same units as B{C{eps}}).
1035 @arg point3: Third center point (C{LatLon}).
1036 @arg distance3: Distance to point3 (C{meter}, same units as B{C{eps}}).
1037 @kwarg area: If C{True}, compute the area overlap, otherwise the perimeter
1038 intersection of the circles (C{bool}).
1039 @kwarg eps: The required I{minimal overlap} for C{B{area}=True} or the
1040 I{intersection margin} for C{B{area}=False} (C{meter},
1041 conventionally).
1042 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{point2}}
1043 and B{C{point3}} (C{bool}).
1045 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} with
1046 C{min} and C{max} in C{meter}, same units as B{C{eps}}, the
1047 corresponding trilaterated points C{minPoint} and C{maxPoint}
1048 as I{ellipsoidal} C{LatLon} and C{n}, the number of trilatered
1049 points found for the given B{C{eps}}.
1051 If only a single trilaterated point is found, C{min I{is} max},
1052 C{minPoint I{is} maxPoint} and C{n=1}.
1054 If C{B{area}=False}, C{min} and C{max} represent the nearest
1055 respectively farthest intersection margin.
1057 If C{B{area}=True}, C{min} and C{max} are the smallest respectively
1058 largest I{radial} overlap found.
1060 If C{B{area}=True} and all 3 circles are concentric, C{n=0} and
1061 C{minPoint} and C{maxPoint} are the B{C{point#}} with the smallest
1062 B{C{distance#}} C{min} respectively largest B{C{distance#}} C{max}.
1064 @raise IntersectionError: Trilateration failed for the given B{C{eps}},
1065 insufficient overlap for C{B{area}=True}, no
1066 circle intersections for C{B{area}=False} or
1067 all circles are (near-)concentric.
1069 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
1071 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}},
1072 B{C{distance2}} or B{C{distance3}}.
1074 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2}
1075 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib
1076 <https://PyPI.org/project/geographiclib>} if installed, otherwise
1077 the accurate (but slower) C{ellipsoidalExact.LatLon} methods.
1078 '''
1079 return _trilaterate5(self, distance1,
1080 self.others(point2=point2), distance2,
1081 self.others(point3=point3), distance3,
1082 area=area, eps=eps, wrap=wrap)
1084 @Property_RO
1085 def _ups(self): # __dict__ value overwritten by method C{toUtmUps}
1086 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}),
1087 see L{pygeodesy.toUps8}.
1088 '''
1089 ups = _MODS.ups
1090 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups,
1091 pole=NN, falsed=True, name=self.name)
1093 def _upsOK(self, pole=NN, falsed=True):
1094 '''(INTERNAL) Check matching C{Ups}.
1095 '''
1096 try:
1097 u = self._ups
1098 except RangeError:
1099 return False
1100 return falsed and (u.pole == pole[:1].upper() or not pole)
1102 @Property_RO
1103 def _utm(self): # __dict__ value overwritten by method C{toUtmUps}
1104 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}),
1105 see L{pygeodesy.toUtm8}.
1106 '''
1107 utm = _MODS.utm
1108 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name)
1110 def _utmOK(self):
1111 '''(INTERNAL) Check C{Utm}.
1112 '''
1113 try:
1114 _ = self._utm
1115 except RangeError:
1116 return False
1117 return True
1120def _lowerleft(utmups, center):
1121 '''(INTERNAL) Optionally I{un}-center C{utmups}.
1122 '''
1123 if _isin(center, False, 0, _0_0):
1124 u = utmups
1125 elif _isin(center, True):
1126 u = utmups._lowerleft
1127 else:
1128 u = _MODS.utmupsBase._lowerleft(utmups, center)
1129 return u
1132def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True
1133 equidistant=None, tol=_TOL_M, **LatLon_and_kwds):
1134 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact,
1135 -GeodSolve, -Karney and -Vincenty to embellish exceptions.
1136 '''
1137 try:
1138 p = _xellipsoidal(point=point)
1139 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within,
1140 height=height, wrap=wrap,
1141 equidistant=equidistant,
1142 tol=tol, **LatLon_and_kwds)
1143 except (TypeError, ValueError) as x:
1144 raise _xError(x, point=point, point1=point1, point2=point2)
1145 return t.closest
1148def _set_reframe(inst, reframe):
1149 '''(INTERNAL) Set or clear an instance's reference frame.
1150 '''
1151 if reframe is not None:
1152 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe)
1153 inst._reframe = reframe
1154 elif inst.reframe is not None:
1155 inst._reframe = None
1158__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase)
1160# **) MIT License
1161#
1162# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
1163#
1164# Permission is hereby granted, free of charge, to any person obtaining a
1165# copy of this software and associated documentation files (the "Software"),
1166# to deal in the Software without restriction, including without limitation
1167# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1168# and/or sell copies of the Software, and to permit persons to whom the
1169# Software is furnished to do so, subject to the following conditions:
1170#
1171# The above copyright notice and this permission notice shall be included
1172# in all copies or substantial portions of the Software.
1173#
1174# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1175# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1176# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1177# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1178# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1179# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1180# OTHER DEALINGS IN THE SOFTWARE.