Coverage for pygeodesy/ellipsoidalBase.py: 91%
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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 Transform, _WGS84, _EWGS84, _xinstanceof # _spherical_datum
20# from pygeodesy.ellipsoids import _EWGS84 # from .datums
21from pygeodesy.errors import _incompatible, _IsnotError, RangeError, _TypeError, \
22 _ValueError, _xattr, _xellipsoidal, _xError, _xkwds, \
23 _xkwds_not
24# from pygeodesy.fmath import favg # _MODS
25from pygeodesy.interns import NN, _COMMA_, _ellipsoidal_
26from pygeodesy.latlonBase import LatLonBase, _trilaterate5, fabs, _Wrap
27# from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS # from .named
28# from pygeodesy.lcc import toLcc # _MODS
29from pygeodesy.named import _name1__, _ALL_DOCS, _ALL_LAZY, _MODS
30# from pygeodesy.namedTuples import Vector3Tuple # _MODS
31from pygeodesy.props import deprecated_method, deprecated_property_RO, \
32 Property_RO, property_doc_, property_RO, _update_all
33# from pygeodesy.trf import _eT0Ds4 # _MODS
34from pygeodesy.units import Epoch, _isDegrees, Radius_, _1mm as _TOL_M
35# from pygeodesy.utily import _Wrap # from .latlonBase
37# from math import fabs # from .latlonBase
39__all__ = _ALL_LAZY.ellipsoidalBase
40__version__ = '24.05.21'
43class CartesianEllipsoidalBase(CartesianBase):
44 '''(INTERNAL) Base class for ellipsoidal C{Cartesian}s.
45 '''
46 _datum = _WGS84 # L{Datum}
47 _epoch = None # overriding .reframe.epoch (C{float})
48 _reframe = None # reference frame (L{RefFrame})
50 def __init__(self, x_xyz, y=None, z=None, reframe=None, epoch=None,
51 **datum_ll_name):
52 '''New ellispoidal C{Cartesian...}.
54 @kwarg reframe: Optional reference frame (L{RefFrame}).
55 @kwarg epoch: Optional epoch to observe for B{C{reframe}} (C{scalar}),
56 a non-zero, fractional calendar year; silently ignored
57 if C{B{reframe}=None}.
59 @raise TypeError: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}} coordinate
60 or B{C{x_xyz}} not a C{Cartesian} L{Ecef9Tuple},
61 L{Vector3Tuple} or L{Vector4Tuple} or B{C{datum}} is
62 not a L{Datum}, B{C{reframe}} is not a L{RefFrame} or
63 B{C{epoch}} is not C{scalar} non-zero.
65 @see: Class L{CartesianBase<CartesianBase.__init__>} for more details.
66 '''
67 CartesianBase.__init__(self, x_xyz, y=y, z=z, **datum_ll_name)
68 if reframe:
69 self.reframe = reframe
70 self.epoch = epoch
72# def __matmul__(self, other): # PYCHOK Python 3.5+
73# '''Return C{NotImplemented} for C{c_ = c @ datum}, C{c_ = c @ reframe} and C{c_ = c @ Transform}.
74# '''
75# RefFrame = _MODS.trf.RefFrame
76# return NotImplemented if isinstance(other, (Datum, RefFrame, Transform)) else \
77# _NotImplemented(self, other)
79 @deprecated_method
80 def convertRefFrame(self, reframe2, reframe, epoch=None):
81 '''DEPRECATED, use method L{toRefFrame}.'''
82 return self.toRefFrame(reframe2, reframe=reframe, epoch=epoch)
84 @property_RO
85 def ellipsoidalCartesian(self):
86 '''Get this C{Cartesian}'s ellipsoidal class.
87 '''
88 return type(self)
90 @property_doc_(''' this cartesian's observed or C{reframe} epoch (C{float}).''')
91 def epoch(self):
92 '''Get this cartesian's observed or C{reframe} epoch (C{Epoch}) or C{None}.
93 '''
94 return self._epoch or (self.reframe.epoch if self.reframe else None)
96 @epoch.setter # PYCHOK setter!
97 def epoch(self, epoch):
98 '''Set or clear this cartesian's observed epoch, a fractional
99 calendar year (L{Epoch}, C{scalar} or C{str}) or C{None}.
101 @raise TRFError: Invalid B{C{epoch}}.
102 '''
103 self._epoch = None if epoch is None else Epoch(epoch)
105 def intersections2(self, radius, center2, radius2, sphere=True,
106 Vector=None, **Vector_kwds):
107 '''Compute the intersection of two spheres or circles, each defined by a
108 cartesian center point and a radius.
110 @arg radius: Radius of this sphere or circle (same units as this point's
111 coordinates).
112 @arg center2: Center of the second sphere or circle (C{Cartesian}, L{Vector3d},
113 C{Vector3Tuple} or C{Vector4Tuple}).
114 @arg radius2: Radius of the second sphere or circle (same units as this and
115 the B{C{other}} point's coordinates).
116 @kwarg sphere: If C{True} compute the center and radius of the intersection
117 of two I{spheres}. If C{False}, ignore the C{z}-component and
118 compute the intersection of two I{circles} (C{bool}).
119 @kwarg Vector: Class to return intersections (C{Cartesian}, L{Vector3d} or
120 C{Vector3Tuple}) or C{None} for an instance of this (sub-)class.
121 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments,
122 ignored if C{B{Vector} is None}.
124 @return: If B{C{sphere}} is C{True}, a 2-tuple of the C{center} and C{radius}
125 of the intersection of the I{spheres}. The C{radius} is C{0.0} for
126 abutting spheres (and the C{center} is aka the I{radical center}).
128 If B{C{sphere}} is C{False}, a 2-tuple with the two intersection
129 points of the I{circles}. For abutting circles, both points are
130 the same instance, aka the I{radical center}.
132 @raise IntersectionError: Concentric, invalid or non-intersecting spheres or circles.
134 @raise TypeError: Invalid B{C{center2}}.
136 @raise UnitError: Invalid B{C{radius}} or B{C{radius2}}.
138 @see: U{Sphere-Sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>},
139 U{Circle-Circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>}
140 Intersection and function L{pygeodesy.radical2}.
141 '''
142 try:
143 return _MODS.vector3d._intersects2(self, Radius_(radius=radius),
144 center2, Radius_(radius2=radius2),
145 sphere=sphere, clas=self.classof,
146 Vector=Vector, **Vector_kwds)
147 except (TypeError, ValueError) as x:
148 raise _xError(x, center=self, radius=radius, center2=center2, radius2=radius2)
150 @property_doc_(''' this cartesian's reference frame (L{RefFrame}).''')
151 def reframe(self):
152 '''Get this cartesian's reference frame (L{RefFrame}) or C{None}.
153 '''
154 return self._reframe
156 @reframe.setter # PYCHOK setter!
157 def reframe(self, reframe):
158 '''Set or clear this cartesian's reference frame (L{RefFrame}) or C{None}.
160 @raise TypeError: The B{C{reframe}} is not a L{RefFrame}.
161 '''
162 _set_reframe(self, reframe)
164 def toLatLon(self, datum=None, height=None, **LatLon_and_kwds): # PYCHOK signature
165 '''Convert this cartesian to a I{geodetic} (lat-/longitude) point.
167 @see: Method L{toLatLon<cartesianBase.CartesianBase.toLatLon>}
168 for further details.
169 '''
170 kwds = LatLon_and_kwds
171 if kwds:
172 kwds = _xkwds(kwds, reframe=self.reframe, epoch=self.epoch)
173 return CartesianBase.toLatLon(self, datum=datum, height=height, **kwds)
175 def toRefFrame(self, reframe2, reframe=None, epoch=None, epoch2=None, **name):
176 '''Convert this point to an other reference frame and epoch.
178 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
179 @kwarg reframe: Optional reference frame to convert I{from} (L{RefFrame}),
180 overriding this point's reference frame.
181 @kwarg epoch: Optional epoch (L{Epoch}, C{scalar} or C{str}), overriding
182 this point's C{epoch or B{reframe}.epoch}.
183 @kwarg epoch2: Optional epoch to observe for the converted point (L{Epoch},
184 C{scalar} or C{str}), otherwise B{C{epoch}}.
185 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding C{B{reframe2}.name}.
187 @return: The converted point (ellipsoidal C{Cartesian}) or if conversion
188 C{isunity}, this point or a copy of this point if the B{C{name}}
189 is non-empty.
191 @raise TRFError: This point's C{reframe} is not defined, invalid B{C{epoch}}
192 or B{C{epoch2}} or conversion from this point's C{reframe}
193 to B{C{reframe2}} is not available.
195 @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a L{RefFrame}.
196 '''
197 return _MODS.trf._toRefFrame(self, reframe2, reframe=reframe, epoch=epoch,
198 epoch2=epoch2, **name)
200 @deprecated_method
201 def toTransforms_(self, *transforms, **datum): # PYCHOK no cover
202 '''DEPRECATED on 2024.02.14, use method C{toTransform}.'''
203 r = self
204 for t in transforms:
205 r = r.toTransform(t)
206 return r.dup(**datum) if datum else r
209class LatLonEllipsoidalBase(LatLonBase):
210 '''(INTERNAL) Base class for ellipsoidal C{LatLon}s.
211 '''
212 _datum = _WGS84 # L{Datum}
213 _elevation2to = None # _elevation2 timeout (C{secs})
214 _epoch = None # overriding .reframe.epoch (C{float})
215 _gamma = None # UTM/UPS meridian convergence (C{degrees})
216 _geoidHeight2to = None # _geoidHeight2 timeout (C{secs})
217 _reframe = None # reference frame (L{RefFrame})
218 _scale = None # UTM/UPS scale factor (C{float})
219 _toLLEB_args = () # Etm/Utm/Ups._toLLEB arguments
221 def __init__(self, latlonh, lon=None, height=0, datum=_WGS84, reframe=None,
222 epoch=None, wrap=False, **name):
223 '''Create an ellipsoidal C{LatLon} point from the given lat-, longitude
224 and height on the given datum, reference frame and epoch.
226 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or
227 a previous C{LatLon} instance provided C{B{lon}=None}.
228 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or
229 C(None), indicating B{C{latlonh}} is a C{LatLon}.
230 @kwarg height: Optional height above (or below) the earth surface
231 (C{meter}, same units as the datum's ellipsoid axes).
232 @kwarg datum: Optional, ellipsoidal datum to use (L{Datum}, L{Ellipsoid},
233 L{Ellipsoid2} or L{a_f2Tuple}).
234 @kwarg reframe: Optional reference frame (L{RefFrame}).
235 @kwarg epoch: Optional epoch to observe for B{C{reframe}} (C{scalar}),
236 a non-zero, fractional calendar year; silently ignored
237 if C{B{reframe}=None}.
238 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}}
239 (C{bool}).
240 @kwarg name: Optional C{B{name}=NN} (C{str}).
242 @raise RangeError: Value of C{lat} or B{C{lon}} outside the valid
243 range and L{rangerrors} set to C{True}.
245 @raise TypeError: If B{C{latlonh}} is not a C{LatLon}, B{C{datum}} is
246 not a L{Datum}, B{C{reframe}} is not a L{RefFrame}
247 or B{C{epoch}} is not C{scalar} non-zero.
249 @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}.
250 '''
251 LatLonBase.__init__(self, latlonh, lon=lon, height=height, wrap=wrap, **name)
252 if datum not in (None, self._datum, _EWGS84):
253 self.datum = _ellipsoidal_datum(datum, name=self.name)
254 if reframe:
255 self.reframe = reframe
256 self.epoch = epoch
258# def __matmul__(self, other): # PYCHOK Python 3.5+
259# '''Return C{NotImplemented} for C{ll_ = ll @ datum} and C{ll_ = ll @ reframe}.
260# '''
261# RefFrame = _MODS.trf.RefFrame
262# return NotImplemented if isinstance(other, (Datum, RefFrame)) else \
263# _NotImplemented(self, other)
265 def antipode(self, height=None):
266 '''Return the antipode, the point diametrically opposite
267 to this point.
269 @kwarg height: Optional height of the antipode, height
270 of this point otherwise (C{meter}).
272 @return: The antipodal point (C{LatLon}).
273 '''
274 lla = LatLonBase.antipode(self, height=height)
275 if lla.datum != self.datum:
276 lla.datum = self.datum
277 return lla
279 @deprecated_property_RO
280 def convergence(self):
281 '''DEPRECATED, use property C{gamma}.'''
282 return self.gamma
284 @deprecated_method
285 def convertDatum(self, datum2):
286 '''DEPRECATED, use method L{toDatum}.'''
287 return self.toDatum(datum2)
289 @deprecated_method
290 def convertRefFrame(self, reframe2):
291 '''DEPRECATED, use method L{toRefFrame}.'''
292 return self.toRefFrame(reframe2)
294 @Property_RO
295 def _css(self):
296 '''(INTERNAL) Get this C{LatLon} point as a Cassini-Soldner location (L{Css}).
297 '''
298 css = _MODS.css
299 return css.toCss(self, height=self.height, Css=css.Css, name=self.name)
301 @property_doc_(''' this points's datum (L{Datum}).''')
302 def datum(self):
303 '''Get this point's datum (L{Datum}).
304 '''
305 return self._datum
307 @datum.setter # PYCHOK setter!
308 def datum(self, datum):
309 '''Set this point's datum I{without conversion} (L{Datum}).
311 @raise TypeError: The B{C{datum}} is not a L{Datum}
312 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:
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 if e != E:
422 raise _ValueError(e.named2, txt=_incompatible(E.named2))
423 return E
425 @property_doc_(''' this point's observed or C{reframe} epoch (C{float}).''')
426 def epoch(self):
427 '''Get this point's observed or C{reframe} epoch (L{Epoch}) or C{None}.
428 '''
429 return self._epoch or (self.reframe.epoch if self.reframe else None)
431 @epoch.setter # PYCHOK setter!
432 def epoch(self, epoch):
433 '''Set or clear this point's observed epoch, a fractional
434 calendar year (L{Epoch}, C{scalar} or C{str}) or C{None}.
436 @raise TRFError: Invalid B{C{epoch}}.
437 '''
438 self._epoch = None if epoch is None else Epoch(epoch)
440 @Property_RO
441 def Equidistant(self):
442 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantKarney} or L{EquidistantExact}).
443 '''
444 try:
445 _ = self.datum.ellipsoid.geodesic
446 return _MODS.azimuthal.EquidistantKarney
447 except ImportError: # no geographiclib
448 return _MODS.azimuthal.EquidistantExact # XXX no longer L{azimuthal.Equidistant}
450 @Property_RO
451 def _etm(self):
452 '''(INTERNAL) Get this C{LatLon} point as an ETM coordinate (L{pygeodesy.toEtm8}).
453 '''
454 etm = _MODS.etm
455 return etm.toEtm8(self, datum=self.datum, Etm=etm.Etm)
457 @property_RO
458 def gamma(self):
459 '''Get this point's UTM or UPS meridian convergence (C{degrees}) or
460 C{None} if not available or not converted from L{Utm} or L{Ups}.
461 '''
462 return self._gamma
464 @Property_RO
465 def _geoidHeight2(self):
466 '''(INTERNAL) Get geoid height and model.
467 '''
468 return _MODS.elevations.geoidHeight2(self.lat, self.lon, model=0,
469 timeout=self._geoidHeight2to)
471 def geoidHeight2(self, adjust=False, datum=None, timeout=2):
472 '''Return geoid height of this point for its or the given datum, ellipsoid
473 or sphere.
475 @kwarg adjust: Adjust the geoid height for a B{C{datum}} other than
476 C{NAD83/NADV88} (C{bool}).
477 @kwarg datum: Optional datum overriding this point's datum (L{Datum},
478 L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar}
479 radius).
480 @kwarg timeout: Optional query timeout (C{seconds}).
482 @return: A L{GeoidHeight2Tuple}C{(height, model_name)} or
483 C{(None, error)} in case of errors.
485 @note: The adjustment applied is the difference in geocentric earth
486 radius between the B{C{datum}} and C{NAV83/NADV88} upon which
487 the L{elevations.geoidHeight2} is based.
489 @note: The geoid height is only available for locations within the U{Conterminous
490 US (CONUS)<https://WikiPedia.org/wiki/Contiguous_United_States>}.
492 @see: Function L{elevations.geoidHeight2} and method C{Ellipsoid.Rgeocentric}
493 for further details and possible C{error}s.
494 '''
495 if self._geoidHeight2to != timeout:
496 self._geoidHeight2to = timeout
497 LatLonEllipsoidalBase._geoidHeight2._update(self)
498 return self._Radjust2(adjust, datum, self._geoidHeight2)
500 def intermediateTo(self, other, fraction, height=None, wrap=False): # PYCHOK no cover
501 '''I{Must be overloaded}.'''
502 self._notOverloaded(other, fraction, height=height, wrap=wrap)
504 def intersection3(self, end1, other, end2, height=None, wrap=False, # was=True
505 equidistant=None, tol=_TOL_M):
506 '''I{Iteratively} compute the intersection point of two lines, each
507 defined by two points or a start point and bearing from North.
509 @arg end1: End point of this line (C{LatLon}) or the initial
510 bearing at this point (compass C{degrees360}).
511 @arg other: Start point of the other line (C{LatLon}).
512 @arg end2: End point of the other line (C{LatLon}) or the initial
513 bearing at the other point (compass C{degrees360}).
514 @kwarg height: Optional height at the intersection (C{meter},
515 conventionally) or C{None} for the mean height.
516 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
517 B{C{other}} and B{C{end*}} points (C{bool}).
518 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
519 function L{pygeodesy.equidistant}), or C{None}
520 for this point's preferred C{.Equidistant}.
521 @kwarg tol: Tolerance for convergence and skew line distance and
522 length (C{meter}, conventionally).
524 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)}
525 with C{point} a C{LatLon} instance.
527 @raise ImportError: Package U{geographiclib
528 <https://PyPI.org/project/geographiclib>}
529 not installed or not found, but only if
530 C{B{equidistant}=}L{EquidistantKarney}.
532 @raise IntersectionError: Skew, colinear, parallel or otherwise
533 non-intersecting lines or no convergence
534 for the given B{C{tol}}.
536 @raise TypeError: If B{C{end1}}, B{C{other}} or B{C{end2}} point
537 is not C{LatLon}.
539 @note: For each line specified with an initial bearing, a pseudo-end
540 point is computed as the C{destination} along that bearing at
541 about 1.5 times the distance from the start point to an initial
542 gu-/estimate of the intersection point (and between 1/8 and 3/8
543 of the authalic earth perimeter).
545 @see: I{Karney's} U{intersect.cpp<https://SourceForge.net/p/geographiclib/
546 discussion/1026621/thread/21aaff9f/>}, U{The B{ellipsoidal} case<https://
547 GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>}
548 and U{Karney's paper<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section
549 B{14. MARITIME BOUNDARIES} for more details about the iteration algorithm.
550 '''
551 try:
552 s2 = self.others(other)
553 return _MODS.ellipsoidalBaseDI._intersect3(self, end1,
554 s2, end2,
555 height=height, wrap=wrap,
556 equidistant=equidistant, tol=tol,
557 LatLon=self.classof, datum=self.datum)
558 except (TypeError, ValueError) as x:
559 raise _xError(x, start1=self, end1=end1, other=other, end2=end2,
560 height=height, wrap=wrap, tol=tol)
562 def intersections2(self, radius1, other, radius2, height=None, wrap=False, # was=True
563 equidistant=None, tol=_TOL_M):
564 '''I{Iteratively} compute the intersection points of two circles,
565 each defined by a center point and a radius.
567 @arg radius1: Radius of this circle (C{meter}, conventionally).
568 @arg other: Center of the other circle (C{LatLon}).
569 @arg radius2: Radius of the other circle (C{meter}, same units as
570 B{C{radius1}}).
571 @kwarg height: Optional height for the intersection points (C{meter},
572 conventionally) or C{None} for the I{"radical height"}
573 at the I{radical line} between both centers.
574 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}
575 center (C{bool}).
576 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
577 function L{pygeodesy.equidistant}) or C{None}
578 for this point's preferred C{.Equidistant}.
579 @kwarg tol: Convergence tolerance (C{meter}, same units as
580 B{C{radius1}} and B{C{radius2}}).
582 @return: 2-Tuple of the intersection points, each a C{LatLon}
583 instance. For abutting circles, both intersection
584 points are the same instance, aka the I{radical center}.
586 @raise ImportError: Package U{geographiclib
587 <https://PyPI.org/project/geographiclib>}
588 not installed or not found, but only if
589 C{B{equidistant}=}L{EquidistantKarney}.
591 @raise IntersectionError: Concentric, antipodal, invalid or
592 non-intersecting circles or no
593 convergence for the given B{C{tol}}.
595 @raise TypeError: Invalid B{C{other}} or B{C{equidistant}}.
597 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
599 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
600 calculating-intersection-of-two-circles>}, U{Karney's paper
601 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
602 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
603 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
604 intersections.
605 '''
606 try:
607 c2 = self.others(other)
608 return _MODS.ellipsoidalBaseDI._intersections2(self, radius1,
609 c2, radius2,
610 height=height, wrap=wrap,
611 equidistant=equidistant, tol=tol,
612 LatLon=self.classof, datum=self.datum)
613 except (AssertionError, TypeError, ValueError) as x:
614 raise _xError(x, center=self, radius1=radius1, other=other, radius2=radius2,
615 height=height, wrap=wrap, tol=tol)
617 def isenclosedBy(self, points, wrap=False):
618 '''Check whether a polygon or composite encloses this point.
620 @arg points: The polygon points or clips (C{LatLon}[],
621 L{BooleanFHP} or L{BooleanGH}).
622 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
623 B{C{points}} (C{bool}).
625 @return: C{True} if this point is inside the polygon or composite,
626 C{False} otherwise.
628 @raise PointsError: Insufficient number of B{C{points}}.
630 @raise TypeError: Some B{C{points}} are not C{LatLon}.
632 @raise ValueError: Invalid B{C{point}}, lat- or longitude.
634 @see: Functions L{pygeodesy.isconvex}, L{pygeodesy.isenclosedBy}
635 and L{pygeodesy.ispolar} especially if the B{C{points}} may
636 enclose a pole or wrap around the earth I{longitudinally}.
637 '''
638 return _MODS.points.isenclosedBy(self, points, wrap=wrap)
640 @property_RO
641 def iteration(self):
642 '''Get the most recent C{intersections2} or C{nearestOn} iteration
643 number (C{int}) or C{None} if not available/applicable.
644 '''
645 return self._iteration
647 @Property_RO
648 def _lcc(self):
649 '''(INTERNAL) Get this C{LatLon} point as a Lambert location (L{Lcc}).
650 '''
651 lcc = _MODS.lcc
652 return lcc.toLcc(self, height=self.height, Lcc=lcc.Lcc, name=self.name)
654 def midpointTo(self, other, height=None, fraction=_0_5, wrap=False):
655 '''Find the midpoint on a geodesic between this and an other point.
657 @arg other: The other point (C{LatLon}).
658 @kwarg height: Optional height for midpoint, overriding the
659 mean height (C{meter}).
660 @kwarg fraction: Midpoint location from this point (C{scalar}),
661 may be negative or greater than 1.0.
662 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
663 B{C{other}} point (C{bool}).
665 @return: Midpoint (C{LatLon}).
667 @raise TypeError: The B{C{other}} point is not C{LatLon}.
669 @raise ValueError: Invalid B{C{height}}.
671 @see: Methods C{intermediateTo} and C{rhumbMidpointTo}.
672 '''
673 return self.intermediateTo(other, fraction, height=height, wrap=wrap)
675 def nearestOn(self, point1, point2, within=True, height=None, wrap=False, # was=True
676 equidistant=None, tol=_TOL_M):
677 '''I{Iteratively} locate the closest point on the geodesic between
678 two other (ellipsoidal) points.
680 @arg point1: Start point (C{LatLon}).
681 @arg point2: End point (C{LatLon}).
682 @kwarg within: If C{True} return the closest point I{between}
683 B{C{point1}} and B{C{point2}}, otherwise the
684 closest point elsewhere on the geodesic (C{bool}).
685 @kwarg height: Optional height for the closest point (C{meter},
686 conventionally) or C{None} or C{False} for the
687 interpolated height. If C{False}, the closest
688 takes the heights of the points into account.
689 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both
690 B{C{point1}} and B{C{point2}} (C{bool}).
691 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
692 function L{pygeodesy.equidistant}) or C{None}
693 for this point's preferred C{.Equidistant}.
694 @kwarg tol: Convergence tolerance (C{meter}, conventionally).
696 @return: Closest point (C{LatLon}).
698 @raise ImportError: Package U{geographiclib
699 <https://PyPI.org/project/geographiclib>}
700 not installed or not found, but only if
701 C{B{equidistant}=}L{EquidistantKarney}.
703 @raise TypeError: Invalid B{C{point1}}, B{C{point2}} or
704 B{C{equidistant}}.
706 @raise ValueError: Datum or ellipsoid of B{C{point1}} or B{C{point2}} is
707 incompatible or no convergence for the given B{C{tol}}.
709 @see: I{Karney}'s U{intercept.cpp<https://SourceForge.net/p/geographiclib/
710 discussion/1026621/thread/21aaff9f/>}, U{The B{ellipsoidal} case<https://
711 GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>}
712 and U{Karney's paper<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section
713 B{14. MARITIME BOUNDARIES} for details about the iteration algorithm.
714 '''
715 try:
716 t = _MODS.ellipsoidalBaseDI._nearestOn2(self, point1, point2, within=within,
717 height=height, wrap=wrap,
718 equidistant=equidistant,
719 tol=tol, LatLon=self.classof)
720 except (TypeError, ValueError) as x:
721 raise _xError(x, point=self, point1=point1, point2=point2, within=within,
722 height=height, wrap=wrap, tol=tol)
723 return t.closest
725 @Property_RO
726 def _osgr(self):
727 '''(INTERNAL) Get this C{LatLon} point as an OSGR coordinate (L{Osgr}),
728 based on the OS recommendation.
729 '''
730 return _MODS.osgr.toOsgr(self, kTM=False, name=self.name) # datum=self.datum
732 @Property_RO
733 def _osgrTM(self):
734 '''(INTERNAL) Get this C{LatLon} point as an OSGR coordinate (L{Osgr})
735 based on I{Karney}'s Krüger implementation.
736 '''
737 return _MODS.osgr.toOsgr(self, kTM=True, name=self.name) # datum=self.datum
739 def parse(self, strllh, height=0, datum=None, epoch=None, reframe=None,
740 sep=_COMMA_, wrap=False, **name):
741 '''Parse a string consisting of C{"lat, lon[, height]"},
742 representing a similar, ellipsoidal C{LatLon} point.
744 @arg strllh: Lat, lon and optional height (C{str}),
745 see function L{pygeodesy.parse3llh}.
746 @kwarg height: Optional, default height (C{meter} or
747 C{None}).
748 @kwarg datum: Optional datum (L{Datum}), overriding this
749 datum I{without conversion}.
750 @kwarg epoch: Optional datum (L{Epoch}), overriding this
751 epoch I{without conversion}.
752 @kwarg reframe: Optional datum (L{RefFrame}), overriding
753 this reframe I{without conversion}.
754 @kwarg sep: Optional separator (C{str}).
755 @kwarg wrap: If C{True}, wrap or I{normalize} the lat-
756 and longitude (C{bool}).
757 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding
758 this name.
760 @return: The similar point (ellipsoidal C{LatLon}).
762 @raise ParseError: Invalid B{C{strllh}}.
763 '''
764 a, b, h = _MODS.dms.parse3llh(strllh, height=height, sep=sep, wrap=wrap)
765 r = self.classof(a, b, height=h, datum=self.datum)
766 if datum not in (None, self.datum):
767 r.datum = datum
768 if epoch not in (None, self.epoch):
769 r.epoch = epoch
770 if reframe not in (None, self.reframe):
771 r.reframe = reframe
772 return self._xnamed(r, force=True, **name) if name else r
774 def _Radjust2(self, adjust, datum, meter_text2):
775 '''(INTERNAL) Adjust an C{elevation} or C{geoidHeight} with
776 difference in Gaussian radii of curvature of the given
777 datum and NAD83 ellipsoids at this point's latitude.
779 @note: This is an arbitrary, possibly incorrect adjustment.
780 '''
781 if adjust: # Elevation2Tuple or GeoidHeight2Tuple
782 m, t = meter_text2
783 if isinstance(m, float) and fabs(m) > EPS:
784 n = Datums.NAD83.ellipsoid.rocGauss(self.lat)
785 if n > EPS0:
786 # use ratio, datum and NAD83 units may differ
787 E = self.ellipsoid() if datum in (None, self.datum) else \
788 _earth_ellipsoid(datum)
789 r = E.rocGauss(self.lat)
790 if r > EPS0 and fabs(r - n) > EPS: # EPS1
791 m *= r / n
792 meter_text2 = meter_text2.classof(m, t)
793 return self._xnamed(meter_text2)
795 @property_doc_(''' this point's reference frame (L{RefFrame}).''')
796 def reframe(self):
797 '''Get this point's reference frame (L{RefFrame}) or C{None}.
798 '''
799 return self._reframe
801 @reframe.setter # PYCHOK setter!
802 def reframe(self, reframe):
803 '''Set or clear this point's reference frame (L{RefFrame}) or C{None}.
805 @raise TypeError: The B{C{reframe}} is not a L{RefFrame}.
806 '''
807 _set_reframe(self, reframe)
809 @Property_RO
810 def scale(self):
811 '''Get this point's UTM grid or UPS point scale factor (C{float})
812 or C{None} if not converted from L{Utm} or L{Ups}.
813 '''
814 return self._scale
816 def toCartesian(self, height=None, **Cartesian_and_kwds): # PYCHOK signature
817 '''Convert this point to cartesian, I{geocentric} coordinates,
818 also known as I{Earth-Centered, Earth-Fixed} (ECEF).
820 @see: Method L{toCartesian<latlonBase.LatLonBase.toCartesian>}
821 for further details.
822 '''
823 kwds = Cartesian_and_kwds
824 if kwds:
825 kwds = _xkwds(kwds, reframe=self.reframe, epoch=self.epoch)
826 return LatLonBase.toCartesian(self, height=height, **kwds)
828 def toCss(self, **toCss_kwds):
829 '''Convert this C{LatLon} point to a Cassini-Soldner location.
831 @kwarg toCss_kwds: Optional L{pygeodesy.toCss} keyword arguments.
833 @return: The Cassini-Soldner location (L{Css}).
835 @see: Function L{pygeodesy.toCss}.
836 '''
837 return self._css if not toCss_kwds else _MODS.css.toCss(
838 self, **_name1__(toCss_kwds, _or_nameof=self))
840 def toDatum(self, datum2, height=None, **name):
841 '''Convert this point to an other datum.
843 @arg datum2: Datum to convert I{to} (L{Datum}).
844 @kwarg height: Optional height, overriding the
845 converted height (C{meter}).
846 @kwarg name: Optional C{B{name}=NN} (C{str}).
848 @return: The converted point (ellipsoidal C{LatLon})
849 or a copy of this point if B{C{datum2}}
850 matches this point's C{datum}.
852 @raise TypeError: Invalid B{C{datum2}}.
853 '''
854 n = self._name__(name)
855 d2 = _ellipsoidal_datum(datum2, name=n)
856 if self.datum == d2:
857 r = self.copy(name=n)
858 else:
859 kwds = _xkwds_not(None, LatLon=self.classof, name=n,
860 epoch=self.epoch, reframe=self.reframe)
861 c = self.toCartesian().toDatum(d2)
862 r = c.toLatLon(datum=d2, height=height, **kwds)
863 return r
865 def toEtm(self, **toEtm8_kwds):
866 '''Convert this C{LatLon} point to an ETM coordinate.
868 @kwarg toEtm8_kwds: Optional L{pygeodesy.toEtm8} keyword arguments.
870 @return: The ETM coordinate (L{Etm}).
872 @see: Function L{pygeodesy.toEtm8}.
873 '''
874 return self._etm if not toEtm8_kwds else _MODS.etm.toEtm8(
875 self, **_name1__(toEtm8_kwds, _or_nameof=self))
877 def toLcc(self, **toLcc_kwds):
878 '''Convert this C{LatLon} point to a Lambert location.
880 @kwarg toLcc_kwds: Optional L{pygeodesy.toLcc} keyword arguments.
882 @return: The Lambert location (L{Lcc}).
884 @see: Function L{pygeodesy.toLcc}.
885 '''
886 return self._lcc if not toLcc_kwds else _MODS.lcc.toLcc(
887 self, **_name1__(toLcc_kwds, _or_nameof=self))
889 def toMgrs(self, center=False, pole=NN):
890 '''Convert this C{LatLon} point to an MGRS coordinate.
892 @kwarg center: If C{True}, try to I{un}-center MGRS
893 to its C{lowerleft} (C{bool}) or by
894 C{B{center} meter} (C{scalar}).
895 @kwarg pole: Optional top/center for the MGRS UPS
896 projection (C{str}, 'N[orth]' or 'S[outh]').
898 @return: The MGRS coordinate (L{Mgrs}).
900 @see: Method L{toUtmUps} and L{Mgrs.toLatLon}.
901 '''
902 return self.toUtmUps(center=center, pole=pole).toMgrs(center=False)
904 def toOsgr(self, kTM=False, **toOsgr_kwds):
905 '''Convert this C{LatLon} point to an OSGR coordinate.
907 @kwarg kTM: If C{True} use I{Karney}'s Krüger method from module
908 L{ktm}, otherwise I{Ordinance Survery}'s recommended
909 formulation (C{bool}).
910 @kwarg toOsgr_kwds: Optional L{pygeodesy.toOsgr} keyword arguments.
912 @return: The OSGR coordinate (L{Osgr}).
914 @see: Function L{pygeodesy.toOsgr}.
915 '''
916 if toOsgr_kwds:
917 r = _MODS.osgr.toOsgr(self, kTM=kTM, **_xkwds(toOsgr_kwds, name=self.name))
918 else:
919 r = self._osgrTM if kTM else self._osgr
920 return r
922 def toRefFrame(self, reframe2, reframe=None, epoch=None, epoch2=None, height=None, **name):
923 '''Convert this point to an other reference frame and epoch.
925 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
926 @kwarg reframe: Optional reference frame to convert I{from} (L{RefFrame}),
927 overriding this point's reference frame.
928 @kwarg epoch: Optional epoch (L{Epoch}, C{scalar} or C{str}), overriding
929 this point's C{epoch or B{reframe}.epoch}.
930 @kwarg epoch2: Optional epoch to observe for the converted point (L{Epoch},
931 C{scalar} or C{str}), otherwise B{C{epoch}}.
932 @kwarg height: Optional height, overriding the converted height (C{meter}).
933 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding C{B{reframe2}.name}.
935 @return: The converted point (ellipsoidal C{LatLon}) or if conversion
936 C{isunity}, this point or a copy of this point if the B{C{name}}
937 is non-empty.
939 @raise TRFError: This point's C{reframe} is not defined, invalid B{C{epoch}}
940 or B{C{epoch2}} or conversion from this point's C{reframe}
941 to B{C{reframe2}} is not available.
943 @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a L{RefFrame}.
944 '''
945 return _MODS.trf._toRefFrame(self, reframe2, reframe=reframe, epoch=epoch,
946 epoch2=epoch2, height=height, **name)
948 def toTransform(self, transform, inverse=False, datum=None, **LatLon_kwds):
949 '''Apply a Helmert transform to this geodetic point.
951 @arg transform: Transform to apply (L{Transform} or L{TransformXform}).
952 @kwarg inverse: Apply the inverse of the Helmert transform (C{bool}).
953 @kwarg datum: Datum for the transformed point (L{Datum}), overriding
954 this point's datum but I{not} taken it into account.
955 @kwarg LatLon_kwds: Optional keyword arguments for the transformed
956 point, like C{B{height}=...}.
958 @return: A transformed point (C{LatLon}) or a copy of this point if
959 C{B{transform}.isunity}.
961 @raise TypeError: Invalid B{C{transform}}.
962 '''
963 _xinstanceof(Transform, transform=transform)
964 d = datum or self.datum
965 if transform.isunity:
966 r = self.dup(datum=d, **LatLon_kwds)
967 else:
968 c = self.toCartesian()
969 c = c.toTransform(transform, inverse=inverse, datum=d)
970 r = c.toLatLon(LatLon=self.classof, **_xkwds(LatLon_kwds, height=self.height))
971 return r
973 def toUps(self, pole=NN, falsed=True, center=False):
974 '''Convert this C{LatLon} point to a UPS coordinate.
976 @kwarg pole: Optional top/center of (stereographic)
977 projection (C{str}, 'N[orth]' or 'S[outh]').
978 @kwarg falsed: False easting and northing (C{bool}).
979 @kwarg center: If C{True}, I{un}-center the UPS
980 to its C{lowerleft} (C{bool}) or
981 by C{B{center} meter} (C{scalar}).
983 @return: The UPS coordinate (L{Ups}).
985 @see: Function L{pygeodesy.toUps8}.
986 '''
987 if self._upsOK(pole, falsed):
988 u = self._ups
989 else:
990 ups = _MODS.ups
991 u = ups.toUps8(self, datum=self.datum, Ups=ups.Ups,
992 pole=pole, falsed=falsed)
993 return _lowerleft(u, center)
995 def toUtm(self, center=False):
996 '''Convert this C{LatLon} point to a UTM coordinate.
998 @kwarg center: If C{True}, I{un}-center the UTM
999 to its C{lowerleft} (C{bool}) or
1000 by C{B{center} meter} (C{scalar}).
1002 @return: The UTM coordinate (L{Utm}).
1004 @see: Method L{Mgrs.toUtm} and function L{pygeodesy.toUtm8}.
1005 '''
1006 return _lowerleft(self._utm, center)
1008 def toUtmUps(self, pole=NN, center=False):
1009 '''Convert this C{LatLon} point to a UTM or UPS coordinate.
1011 @kwarg pole: Optional top/center of UPS (stereographic)
1012 projection (C{str}, 'N[orth]' or 'S[outh]').
1013 @kwarg center: If C{True}, I{un}-center the UTM or UPS to
1014 its C{lowerleft} (C{bool}) or by C{B{center}
1015 meter} (C{scalar}).
1017 @return: The UTM or UPS coordinate (L{Utm} or L{Ups}).
1019 @see: Function L{pygeodesy.toUtmUps8}.
1020 '''
1021 if self._utmOK():
1022 u = self._utm
1023 elif self._upsOK(pole):
1024 u = self._ups
1025 else: # no cover
1026 utmups = _MODS.utmups
1027 u = utmups.toUtmUps8(self, datum=self.datum, pole=pole, name=self.name,
1028 Utm=utmups.Utm, Ups=utmups.Ups)
1029 if isinstance(u, utmups.Utm):
1030 self._update(False, _utm=u) # PYCHOK kwds
1031 elif isinstance(u, utmups.Ups):
1032 self._update(False, _ups=u) # PYCHOK kwds
1033 else:
1034 _xinstanceof(utmups.Utm, utmups.Ups, toUtmUps8=u)
1035 return _lowerleft(u, center)
1037 @deprecated_method
1038 def to3xyz(self): # PYCHOK no cover
1039 '''DEPRECATED, use method C{toEcef}.
1041 @return: A L{Vector3Tuple}C{(x, y, z)}.
1043 @note: Overloads C{LatLonBase.to3xyz}
1044 '''
1045 r = self.toEcef()
1046 return _MODS.namedTuples.Vector3Tuple(r.x, r.y, r.z, name=self.name)
1048 def triangulate(self, bearing1, other, bearing2, **height_wrap_tol):
1049 '''I{Iteratively} locate a point given this, an other point and the (initial)
1050 bearing at this and at the other point.
1052 @arg bearing1: Bearing at this point (compass C{degrees360}).
1053 @arg other: Start point of the other line (C{LatLon}).
1054 @arg bearing2: Bearing at the other point (compass C{degrees360}).
1055 @kwarg height_wrap_tol: Optional keyword arguments C{B{height}=None},
1056 C{B{wrap}=False} and C{B{tol}}, see method L{intersection3}.
1058 @return: Triangulated point (C{LatLon}).
1060 @see: Method L{intersection3} for further details.
1061 '''
1062 if _isDegrees(bearing1) and _isDegrees(bearing2):
1063 r = self.intersection3(bearing1, other, bearing2, **height_wrap_tol)
1064 return r.point
1065 raise _TypeError(bearing1=bearing1, bearing2=bearing2 **height_wrap_tol)
1067 def trilaterate5(self, distance1, point2, distance2, point3, distance3,
1068 area=True, eps=EPS1, wrap=False):
1069 '''Trilaterate three points by I{area overlap} or I{perimeter
1070 intersection} of three intersecting circles.
1072 @arg distance1: Distance to this point (C{meter}), same units
1073 as B{C{eps}}).
1074 @arg point2: Second center point (C{LatLon}).
1075 @arg distance2: Distance to point2 (C{meter}, same units as
1076 B{C{eps}}).
1077 @arg point3: Third center point (C{LatLon}).
1078 @arg distance3: Distance to point3 (C{meter}, same units as
1079 B{C{eps}}).
1080 @kwarg area: If C{True} compute the area overlap, otherwise the
1081 perimeter intersection of the circles (C{bool}).
1082 @kwarg eps: The required I{minimal overlap} for C{B{area}=True}
1083 or the I{intersection margin} for C{B{area}=False}
1084 (C{meter}, conventionally).
1085 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
1086 B{C{point2}} and B{C{point3}} (C{bool}).
1088 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)}
1089 with C{min} and C{max} in C{meter}, same units as B{C{eps}},
1090 the corresponding trilaterated points C{minPoint} and
1091 C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number
1092 of trilatered points found for the given B{C{eps}}.
1094 If only a single trilaterated point is found, C{min I{is}
1095 max}, C{minPoint I{is} maxPoint} and C{n = 1}.
1097 For C{B{area}=True}, C{min} and C{max} are the smallest
1098 respectively largest I{radial} overlap found.
1100 For C{B{area}=False}, C{min} and C{max} represent the
1101 nearest respectively farthest intersection margin.
1103 If C{B{area}=True} and all 3 circles are concentric, C{n=0}
1104 and C{minPoint} and C{maxPoint} are the B{C{point#}} with
1105 the smallest B{C{distance#}} C{min} respectively C{max} the
1106 largest B{C{distance#}}.
1108 @raise IntersectionError: Trilateration failed for the given B{C{eps}},
1109 insufficient overlap for C{B{area}=True}, no
1110 circle intersections for C{B{area}=False} or
1111 all circles are (near-)concentric.
1113 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
1115 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}},
1116 B{C{distance2}} or B{C{distance3}}.
1118 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2}
1119 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib
1120 <https://PyPI.org/project/geographiclib>} if installed, otherwise
1121 the accurate (but slower) C{ellipsoidalExact.LatLon} methods.
1122 '''
1123 return _trilaterate5(self, distance1,
1124 self.others(point2=point2), distance2,
1125 self.others(point3=point3), distance3,
1126 area=area, eps=eps, wrap=wrap)
1128 @Property_RO
1129 def _ups(self): # __dict__ value overwritten by method C{toUtmUps}
1130 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}),
1131 see L{pygeodesy.toUps8}.
1132 '''
1133 ups = _MODS.ups
1134 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups,
1135 pole=NN, falsed=True, name=self.name)
1137 def _upsOK(self, pole=NN, falsed=True):
1138 '''(INTERNAL) Check matching C{Ups}.
1139 '''
1140 try:
1141 u = self._ups
1142 except RangeError:
1143 return False
1144 return falsed and (u.pole == pole[:1].upper() or not pole)
1146 @Property_RO
1147 def _utm(self): # __dict__ value overwritten by method C{toUtmUps}
1148 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}),
1149 see L{pygeodesy.toUtm8}.
1150 '''
1151 utm = _MODS.utm
1152 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name)
1154 def _utmOK(self):
1155 '''(INTERNAL) Check C{Utm}.
1156 '''
1157 try:
1158 _ = self._utm
1159 except RangeError:
1160 return False
1161 return True
1164def _lowerleft(utmups, center):
1165 '''(INTERNAL) Optionally I{un}-center C{utmups}.
1166 '''
1167 if center in (False, 0, _0_0):
1168 u = utmups
1169 elif center in (True,):
1170 u = utmups._lowerleft
1171 else:
1172 u = _MODS.utmupsBase._lowerleft(utmups, center)
1173 return u
1176def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True
1177 equidistant=None, tol=_TOL_M, **LatLon_and_kwds):
1178 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact,
1179 -GeodSolve, -Karney and -Vincenty to embellish exceptions.
1180 '''
1181 try:
1182 p = _xellipsoidal(point=point)
1183 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within,
1184 height=height, wrap=wrap,
1185 equidistant=equidistant,
1186 tol=tol, **LatLon_and_kwds)
1187 except (TypeError, ValueError) as x:
1188 raise _xError(x, point=point, point1=point1, point2=point2)
1189 return t.closest
1192def _set_reframe(inst, reframe):
1193 '''(INTERNAL) Set or clear an instance's reference frame.
1194 '''
1195 if reframe is not None:
1196 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe)
1197 inst._reframe = reframe
1198 elif inst.reframe is not None:
1199 inst._reframe = None
1202__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase)
1204# **) MIT License
1205#
1206# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1207#
1208# Permission is hereby granted, free of charge, to any person obtaining a
1209# copy of this software and associated documentation files (the "Software"),
1210# to deal in the Software without restriction, including without limitation
1211# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1212# and/or sell copies of the Software, and to permit persons to whom the
1213# Software is furnished to do so, subject to the following conditions:
1214#
1215# The above copyright notice and this permission notice shall be included
1216# in all copies or substantial portions of the Software.
1217#
1218# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1219# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1220# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1221# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1222# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1223# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1224# OTHER DEALINGS IN THE SOFTWARE.